From 5b11ae58d6337f7bb948de45d5b5ff61c831be0f Mon Sep 17 00:00:00 2001
From: Maria Hartmann <lm.hartmann@gmx.de>
Date: Fri, 12 Feb 2021 14:13:34 +0100
Subject: [PATCH] added heap implementations, experimental scripts, results and
plots
---
data/sorting-loc-new-comps.csv | 32 +
data/sorting-loc-new-links.csv | 32 +
data/sorting-random-new-comps.csv | 16 +
data/sorting-random-new-links.csv | 16 +
data/sorting-sep-new-comps.csv | 19 +
data/sorting-sep-new-links.csv | 19 +
data/sorting-subseq-new-comps.csv | 21 +
data/sorting-subseq-new-links.csv | 21 +
data/sorting-uniform-new-comps.csv | 19 +
data/sorting-uniform-new-links.csv | 19 +
node.py | 16 +
pairing_heap.py | 98 ++
pairing_heap_interface.py | 23 +
pairing_heap_l.py | 181 +++
pairing_heap_standard.py | 171 +++
paper-dijkstra-test-new.py | 210 +++
paper-dijkstra-test2-new.py | 214 +++
paper-permutations.py | 91 ++
paper-sorting-loc-new.py | 176 +++
paper-sorting-sep-new.py | 183 +++
paper-sorting-subseq-new.py | 191 +++
plots/paper-dijkstra-new.svg | 1570 +++++++++++++++++++++
plots/paper-dijkstra2-new.svg | 1539 +++++++++++++++++++++
plots/paper-permutation-localized.pdf | Bin 0 -> 94000 bytes
plots/paper-permutation-localized.svg | 1427 +++++++++++++++++++
plots/paper-permutation-separable.pdf | Bin 0 -> 93549 bytes
plots/paper-permutation-separable.svg | 1427 +++++++++++++++++++
plots/paper-permutation-subseq.pdf | Bin 0 -> 96466 bytes
plots/paper-permutation-subseq.svg | 1427 +++++++++++++++++++
plots/paper-permutation-uniform.pdf | Bin 0 -> 94236 bytes
plots/paper-permutation-uniform.svg | 1427 +++++++++++++++++++
plots/paper-sorting-loc-new.pdf | Bin 0 -> 59636 bytes
plots/paper-sorting-loc-new.svg | 1804 +++++++++++++++++++++++++
plots/paper-sorting-sep-new.pdf | Bin 0 -> 52812 bytes
plots/paper-sorting-sep-new.svg | 1533 +++++++++++++++++++++
plots/paper-sorting-subseq-new.pdf | Bin 0 -> 50752 bytes
plots/paper-sorting-subseq-new.svg | 1532 +++++++++++++++++++++
plots/paper-sorting-uniform-new.pdf | Bin 0 -> 51201 bytes
plots/paper-sorting-uniform-new.svg | 1471 ++++++++++++++++++++
smooth_heap.py | 313 +++++
smooth_heap_l.py | 226 ++++
41 files changed, 17464 insertions(+)
create mode 100644 data/sorting-loc-new-comps.csv
create mode 100644 data/sorting-loc-new-links.csv
create mode 100644 data/sorting-random-new-comps.csv
create mode 100644 data/sorting-random-new-links.csv
create mode 100644 data/sorting-sep-new-comps.csv
create mode 100644 data/sorting-sep-new-links.csv
create mode 100644 data/sorting-subseq-new-comps.csv
create mode 100644 data/sorting-subseq-new-links.csv
create mode 100644 data/sorting-uniform-new-comps.csv
create mode 100644 data/sorting-uniform-new-links.csv
create mode 100755 node.py
create mode 100644 pairing_heap.py
create mode 100755 pairing_heap_interface.py
create mode 100644 pairing_heap_l.py
create mode 100644 pairing_heap_standard.py
create mode 100755 paper-dijkstra-test-new.py
create mode 100755 paper-dijkstra-test2-new.py
create mode 100755 paper-permutations.py
create mode 100644 paper-sorting-loc-new.py
create mode 100644 paper-sorting-sep-new.py
create mode 100644 paper-sorting-subseq-new.py
create mode 100644 plots/paper-dijkstra-new.svg
create mode 100644 plots/paper-dijkstra2-new.svg
create mode 100644 plots/paper-permutation-localized.pdf
create mode 100644 plots/paper-permutation-localized.svg
create mode 100644 plots/paper-permutation-separable.pdf
create mode 100644 plots/paper-permutation-separable.svg
create mode 100644 plots/paper-permutation-subseq.pdf
create mode 100644 plots/paper-permutation-subseq.svg
create mode 100644 plots/paper-permutation-uniform.pdf
create mode 100644 plots/paper-permutation-uniform.svg
create mode 100644 plots/paper-sorting-loc-new.pdf
create mode 100644 plots/paper-sorting-loc-new.svg
create mode 100644 plots/paper-sorting-sep-new.pdf
create mode 100644 plots/paper-sorting-sep-new.svg
create mode 100644 plots/paper-sorting-subseq-new.pdf
create mode 100644 plots/paper-sorting-subseq-new.svg
create mode 100644 plots/paper-sorting-uniform-new.pdf
create mode 100644 plots/paper-sorting-uniform-new.svg
create mode 100644 smooth_heap.py
create mode 100644 smooth_heap_l.py
diff --git a/data/sorting-loc-new-comps.csv b/data/sorting-loc-new-comps.csv
new file mode 100644
index 0000000..e5f6e07
--- /dev/null
+++ b/data/sorting-loc-new-comps.csv
@@ -0,0 +1,32 @@
+randomness parameter value;Pairing;Smooth
+randomness parameter value;0;12
+1e-05;3.3110000000000004;0.9997999999999998
+0.01001;9.695700000000002;10.025450000000001
+0.02001;10.85029;11.63291
+0.03001;11.54132;12.58502
+0.040010000000000004;12.00077;13.229379999999999
+0.050010000000000006;12.386989999999999;13.76429
+0.06001;12.68024;14.18097
+0.07001;12.901870000000002;14.504279999999998
+0.08001;13.10722;14.776249999999997
+0.09000999999999999;13.286290000000001;15.04036
+0.10001;13.454849999999999;15.25796
+0.11001;13.583470000000002;15.44508
+0.12000999999999999;13.70061;15.617080000000001
+0.13001000000000001;13.79743;15.745219999999998
+0.14001000000000002;13.926459999999999;15.91376
+0.15001;14.00538;16.05316
+0.16001;14.084409999999998;16.14607
+0.17001000000000002;14.157020000000001;16.25582
+0.18001;14.223750000000003;16.3467
+0.19001;14.300799999999999;16.46123
+0.20001000000000002;14.33816;16.52597
+0.21001;14.4027;16.58205
+0.22001;14.437909999999999;16.66046
+0.23001000000000002;14.500430000000001;16.726419999999997
+0.24001;14.531600000000001;16.78245
+0.25001;14.58332;16.8614
+0.26001;14.613059999999997;16.90503
+0.27001000000000003;14.6482;16.94697
+0.28001000000000004;14.68594;17.00532
+0.29001;14.715880000000002;17.047040000000003
diff --git a/data/sorting-loc-new-links.csv b/data/sorting-loc-new-links.csv
new file mode 100644
index 0000000..ce73ae8
--- /dev/null
+++ b/data/sorting-loc-new-links.csv
@@ -0,0 +1,32 @@
+randomness parameter value;Pairing;Smooth
+randomness parameter value;0;12
+1e-05;3.3110000000000004;0.9997999999999998
+0.01001;9.695700000000002;6.3199499999999995
+0.02001;10.85029;7.162200000000001
+0.03001;11.54132;7.654059999999999
+0.040010000000000004;12.00077;7.984989999999999
+0.050010000000000006;12.386989999999999;8.26281
+0.06001;12.68024;8.46781
+0.07001;12.901870000000002;8.63679
+0.08001;13.10722;8.77514
+0.09000999999999999;13.286290000000001;8.90821
+0.10001;13.454849999999999;9.01913
+0.11001;13.583470000000002;9.11216
+0.12000999999999999;13.70061;9.2018
+0.13001000000000001;13.79743;9.27063
+0.14001000000000002;13.926459999999999;9.354729999999998
+0.15001;14.00538;9.421119999999998
+0.16001;14.084409999999998;9.46995
+0.17001000000000002;14.157020000000001;9.527839999999998
+0.18001;14.223750000000003;9.57139
+0.19001;14.300799999999999;9.629190000000001
+0.20001000000000002;14.33816;9.65897
+0.21001;14.4027;9.688220000000001
+0.22001;14.437909999999999;9.73125
+0.23001000000000002;14.500430000000001;9.761690000000002
+0.24001;14.531600000000001;9.79034
+0.25001;14.58332;9.8314
+0.26001;14.613059999999997;9.85144
+0.27001000000000003;14.6482;9.87486
+0.28001000000000004;14.68594;9.90154
+0.29001;14.715880000000002;9.924119999999998
diff --git a/data/sorting-random-new-comps.csv b/data/sorting-random-new-comps.csv
new file mode 100644
index 0000000..3bffdd2
--- /dev/null
+++ b/data/sorting-random-new-comps.csv
@@ -0,0 +1,16 @@
+randomness parameter value;Pairing;Smooth;Smooth18
+randomness parameter value;0;12;14
+2;0.5;1.0;0.5
+4;1.35;1.6;1.15
+8;2.025;2.6999999999999997;2.1500000000000004
+16;3.5125;4.050000000000001;3.3875
+32;5.05;5.3125;4.5625
+64;6.4624999999999995;6.878125000000001;6.05625
+128;7.93125;8.309375;7.4609375
+256;9.46328125;9.95703125;9.011718750000002
+512;10.770703125;11.534765625;10.562890625
+1024;12.1029296875;13.253320312500001;12.276562499999999
+2048;13.376953125;14.994335937499999;13.99287109375
+4096;14.676660156250001;16.67939453125;15.68359375
+8192;15.946264648437499;18.4197021484375;17.4177490234375
+16384;17.20384521484375;20.120104980468753;19.1246826171875
diff --git a/data/sorting-random-new-links.csv b/data/sorting-random-new-links.csv
new file mode 100644
index 0000000..5091ba8
--- /dev/null
+++ b/data/sorting-random-new-links.csv
@@ -0,0 +1,16 @@
+randomness parameter value;Pairing;Smooth;Smooth18
+randomness parameter value;0;12;14
+2;0.5;0.0;0.5
+4;1.35;0.6;1.0499999999999998
+8;2.025;1.3;1.65
+16;3.5125;2.2125000000000004;2.45
+32;5.05;3.0250000000000004;3.18125
+64;6.4624999999999995;4.034375;4.121875
+128;7.93125;4.8203125;4.8984375
+256;9.46328125;5.690625000000001;5.715624999999999
+512;10.770703125;6.578125;6.59453125
+1024;12.1029296875;7.459765625;7.472460937500001
+2048;13.376953125;8.35986328125;8.36083984375
+4096;14.676660156250001;9.222314453125;9.225439453125
+8192;15.946264648437499;10.109228515625;10.107202148437498
+16384;17.20384521484375;10.96829833984375;10.96964111328125
diff --git a/data/sorting-sep-new-comps.csv b/data/sorting-sep-new-comps.csv
new file mode 100644
index 0000000..11bd244
--- /dev/null
+++ b/data/sorting-sep-new-comps.csv
@@ -0,0 +1,19 @@
+randomness parameter value;Pairing;Smooth
+randomness parameter value;0;12
+2;0.0;0.0
+4;0.65;0.6375
+8;1.23125;1.2812499999999998
+16;1.6718750000000004;1.7125000000000001
+32;2.2546875;2.109375
+64;2.5328125;2.51640625
+128;2.7156249999999997;2.7628906250000003
+256;3.0244140624999996;2.932421875
+512;3.17080078125;3.091015625
+1024;3.230126953125;3.182617187499999
+2048;3.3331298828125;3.2513427734374996
+4096;3.3716308593749997;3.2977294921875004
+8192;3.4386779785156256;3.3528076171875
+16384;3.4799468994140628;3.3715332031249994
+32768;3.4966629028320315;3.3828002929687506
+65536;3.5240753173828128;3.3962371826171878
+131072;3.5682422637939446;3.4042907714843755
diff --git a/data/sorting-sep-new-links.csv b/data/sorting-sep-new-links.csv
new file mode 100644
index 0000000..157b162
--- /dev/null
+++ b/data/sorting-sep-new-links.csv
@@ -0,0 +1,19 @@
+randomness parameter value;Pairing;Smooth
+randomness parameter value;0;12
+2;0.0;0.0
+4;0.65;0.5625000000000002
+8;1.23125;1.0187499999999998
+16;1.6718750000000004;1.3375
+32;2.2546875;1.55
+64;2.5328125;1.80078125
+128;2.7156249999999997;1.9242187499999999
+256;3.0244140624999996;1.9865234375000003
+512;3.17080078125;2.07734375
+1024;3.230126953125;2.1288574218750007
+2048;3.3331298828125;2.155859375
+4096;3.3716308593749997;2.1764892578125
+8192;3.4386779785156256;2.2006591796875
+16384;3.4799468994140628;2.2073852539062497
+32768;3.4966629028320315;2.211355590820313
+65536;3.5240753173828128;2.215667724609375
+131072;3.5682422637939446;2.218004608154297
diff --git a/data/sorting-subseq-new-comps.csv b/data/sorting-subseq-new-comps.csv
new file mode 100644
index 0000000..c9f3891
--- /dev/null
+++ b/data/sorting-subseq-new-comps.csv
@@ -0,0 +1,21 @@
+randomness parameter value;Pairing;Smooth
+randomness parameter value;0;12
+1900;7.140770000000002;6.0651
+1800;7.261944999999999;6.198515
+1700;7.313929999999999;6.256444999999999
+1600;7.462670000000001;6.48028
+1500;7.5541849999999995;6.535635000000001
+1400;7.711180000000001;6.737559999999998
+1300;7.786554999999999;6.852745
+1200;7.948655000000001;7.065579999999999
+1100;8.04499;7.18305
+1000;8.25514;7.484164999999999
+900;8.48538;7.764014999999999
+800;8.644215;7.9804650000000015
+700;8.897675;8.31422
+600;9.121414999999999;8.6109
+500;9.441964999999998;9.036955
+400;9.87564;9.61485
+300;10.334719999999999;10.22929
+200;10.993725;11.170739999999999
+100;12.144270000000002;12.770485
diff --git a/data/sorting-subseq-new-links.csv b/data/sorting-subseq-new-links.csv
new file mode 100644
index 0000000..a9d195f
--- /dev/null
+++ b/data/sorting-subseq-new-links.csv
@@ -0,0 +1,21 @@
+randomness parameter value;Pairing;Smooth
+randomness parameter value;0;12
+1900;7.140770000000002;4.111149999999999
+1800;7.261944999999999;4.206099999999998
+1700;7.313929999999999;4.23051
+1600;7.462670000000001;4.356905000000001
+1500;7.5541849999999995;4.397234999999999
+1400;7.711180000000001;4.501015000000001
+1300;7.786554999999999;4.575859999999999
+1200;7.948655000000001;4.6985
+1100;8.04499;4.7659400000000005
+1000;8.25514;4.933224999999999
+900;8.48538;5.093285
+800;8.644215;5.216295
+700;8.897675;5.39767
+600;9.121414999999999;5.562875000000001
+500;9.441964999999998;5.790405
+400;9.87564;6.099679999999998
+300;10.334719999999999;6.429255
+200;10.993725;6.9218
+100;12.144270000000002;7.751835000000001
diff --git a/data/sorting-uniform-new-comps.csv b/data/sorting-uniform-new-comps.csv
new file mode 100644
index 0000000..351c717
--- /dev/null
+++ b/data/sorting-uniform-new-comps.csv
@@ -0,0 +1,19 @@
+randomness parameter value;Pairing;Smooth
+randomness parameter value;0;12
+2;0.0;0.0
+4;0.7000000000000001;0.6000000000000001
+8;1.6749999999999998;1.6500000000000001
+16;2.9875;3.025
+32;4.05625;4.14375
+64;5.71875;5.665625
+128;7.171875;7.395312499999999
+256;8.4984375;8.960156249999999
+512;9.845703125;10.61015625
+1024;11.176171875;12.24921875
+2048;12.404296875000002;13.93369140625
+4096;13.6794921875;15.63544921875
+8192;14.9508056640625;17.39541015625
+16384;16.2085693359375;19.12520751953125
+32768;17.44716796875;20.857037353515626
+65536;18.6917236328125;22.592379760742183
+131072;19.929542541503906;24.330378723144527
diff --git a/data/sorting-uniform-new-links.csv b/data/sorting-uniform-new-links.csv
new file mode 100644
index 0000000..72aaf46
--- /dev/null
+++ b/data/sorting-uniform-new-links.csv
@@ -0,0 +1,19 @@
+randomness parameter value;Pairing;Smooth
+randomness parameter value;0;12
+2;0.0;0.0
+4;0.7000000000000001;0.55
+8;1.6749999999999998;1.25
+16;2.9875;2.1624999999999996
+32;4.05625;2.8999999999999995
+64;5.71875;3.8562499999999997
+128;7.171875;4.846875
+256;8.4984375;5.70703125
+512;9.845703125;6.605078125
+1024;11.176171875;7.468554687500001
+2048;12.404296875000002;8.33544921875
+4096;13.6794921875;9.20283203125
+8192;14.9508056640625;10.0988037109375
+16384;16.2085693359375;10.96561279296875
+32768;17.44716796875;11.841461181640625
+65536;18.6917236328125;12.714126586914062
+131072;19.929542541503906;13.582135009765626
diff --git a/node.py b/node.py
new file mode 100755
index 0000000..14dce07
--- /dev/null
+++ b/node.py
@@ -0,0 +1,16 @@
+#!/usr/bin/python3
+class Node:
+ def __init__(self, key):
+ #for now contains all pointers that might be needed in any implementation
+ #idea is to use only necessary ones in each implementation
+ self.key = key
+ self.parent = None
+ self.leftChild = None
+ self.rightChild=None
+ self.nextSibling=None
+ self.prevSibling=None
+ self.leftOnly=False
+ self.rightOnly=False
+
+ self.vertex=None #for testing with Dijkstra's algorithm
+
diff --git a/pairing_heap.py b/pairing_heap.py
new file mode 100644
index 0000000..93b4aeb
--- /dev/null
+++ b/pairing_heap.py
@@ -0,0 +1,98 @@
+#!/usr/bin/python3
+from node import Node
+from pairing_heap_interface import PairingHeapInterface
+from pairing_heap_standard import PairingHeapStandard
+from smooth_heap import SmoothHeap
+from pairing_heap_l import PairingHeapL
+from smooth_heap_l import SmoothHeapL
+
+COUNT_TYPE_LINKS=-1
+COUNT_TYPE_COMPS=-2
+COUNT_TYPE_BOTH=0
+
+class PairingHeap(PairingHeapInterface):
+ MODES={21:"Pairing_L", 22:"Smooth_L"}
+ mode=0
+ countType=COUNT_TYPE_COMPS
+ heap=None
+ def __init__(self, mode=0, countType=COUNT_TYPE_COMPS):
+ self.mode=mode
+ self.countType=countType
+
+ def make_heap(self):
+ if self.mode==0:
+ self.heap=PairingHeapStandard()
+ elif self.mode==12:
+ self.heap=SmoothHeap()
+ elif self.mode==21:#root list version, everything lazy, to be used for Dijkstra test in paper
+ self.heap=PairingHeapL()
+ elif self.mode==22:#root list version, everything lazy, to be used for Dijkstra test in paper
+ self.heap=SmoothHeapL()
+ else:
+ raise Exception("Invalid heap ID! No heap of type ID {} is implemented.")
+
+ def find_min(self):
+ #Careful! Implementation is inconsistent across pairing heap types.
+ return self.heap.find_min()
+
+ def insert(self, node):
+ #inserts node; returns number of linking operations performed
+ result=self.heap.insert(node)
+ if isinstance(result, tuple):
+ if self.countType==COUNT_TYPE_BOTH:
+ return (result[0], result[1])#(comps, links)
+ else:
+ return result[2+self.countType]
+ else:#result should be single number iff link count and comp count are the same
+ if self.countType==COUNT_TYPE_BOTH:
+ return (result, result)
+ else:
+ return result
+
+ def delete_min(self):
+ #deletes min; returns number of linking operations/comparisons performed
+ result=self.heap.delete_min()
+ if len(result)==3:
+ if self.countType==COUNT_TYPE_BOTH:
+ return (result[0], result[1], result[2])#min, comps, links
+ else:
+ return (result[0],result[3+self.countType])
+ else:#result should be 2-tuple iff link count and comp count are the same
+ if self.countType==COUNT_TYPE_BOTH:
+ return (result[0], result[1], result[1])
+ else:
+ return result
+
+ def merge(self, heap2):
+ #merges this heap and heap 2; returns number of linking operations performed
+ result = self.heap.merge(heap2)
+ if isinstance(result, tuple):
+ if self.countType==COUNT_TYPE_BOTH:
+ return (result[0], result[1])#(comps, links)
+ else:
+ return result[2+self.countType]
+ else:#result should be single number iff link count and comp count are the same
+ if self.countType==COUNT_TYPE_BOTH:
+ return (result, result)
+ else:
+ return result
+
+ def delete(self, node):
+ self.heap.delete(node)
+
+ def decrease_key(self, node, diff):
+ result = self.heap.decrease_key(node, diff)
+ if isinstance(result, tuple):
+ if self.countType==COUNT_TYPE_BOTH:
+ if result[0]==None or result[1]==None:
+ print("heap {} returns None".format(self.MODES[self.mode]))
+ return (result[0], result[1])#(comps, links)
+ else:
+ return result[2+self.countType]
+ else:#result should be single number iff link count and comp count are the same
+ if self.countType==COUNT_TYPE_BOTH:
+ if result==None:
+ print("heap {} returns None".format(self.MODES[self.mode]))
+ return (result, result)
+ else:
+ return result
diff --git a/pairing_heap_interface.py b/pairing_heap_interface.py
new file mode 100755
index 0000000..bd14710
--- /dev/null
+++ b/pairing_heap_interface.py
@@ -0,0 +1,23 @@
+#!/usr/bin/python3
+from node import Node
+class PairingHeapInterface:
+ def __init__(self):
+ self.count = 0
+
+ def make_heap(self):
+ pass
+
+ def find_min(self):
+ pass
+
+ def insert(self, node):
+ pass
+
+ def delete_min(self):
+ pass
+
+ def merge(self, heap2):
+ pass
+
+ def delete(self, node):
+ pass
diff --git a/pairing_heap_l.py b/pairing_heap_l.py
new file mode 100644
index 0000000..38c02c8
--- /dev/null
+++ b/pairing_heap_l.py
@@ -0,0 +1,181 @@
+#!/usr/bin/python3
+from node import Node
+from pairing_heap_interface import PairingHeapInterface
+
+class PairingHeapL(PairingHeapInterface):
+ # lazy variant of standard pairing heap (maintaining root-list and consolidating only upon extract-min)
+ forest=[] #list storing roots of all top-level trees
+ def __init__(self, root=None):
+ self.forest=[]
+ if root!=None:
+ root.parent=None
+ self.forest+=[root]
+
+ def listInorder(self):
+ forestList=[]
+ for root in self.forest:
+ forestList+=[self.listInorderTree(root)]
+ return forestList
+
+ def listInorderTree(self, root):
+ if root==None:
+ return []
+ else:
+ return self.listInorderTree(root.leftChild)+[root.key]+self.listInorderTree(root.nextSibling)
+
+ def insert(self, node):
+ #concatenates node to list of trees; returns number of linking ops (always 0) for sake of consistency
+ #print("trying to insert {}...".format(node.key))
+ if node==None:
+ return 0
+ node.parent=None
+ self.forest+=[node]
+ return 0
+
+ def pairing(self):
+ fs = len(self.forest)
+ #performs pairing pass and returns number of linking operations
+ linkCount=0
+ if fs<2:
+ return 0
+ else:
+ pairedForest=[]
+ index=-1
+ for i in range(0, fs, 2): # pairing pass
+ if i==fs-1: #last tree if length of forest is odd-numbered
+ pairedForest+=[self.forest[i]]#concatenate to new forest (no linking required)
+ else:#pair trees
+ if self.forest[i].key<=self.forest[i+1].key:
+ if self.forest[i].leftChild==None:
+ self.forest[i+1].parent=self.forest[i]
+ else:
+ self.forest[i+1].nextSibling=self.forest[i].leftChild
+ self.forest[i].leftChild=self.forest[i+1]
+ pairedForest+=[self.forest[i]]
+ else:
+ if self.forest[i+1].leftChild==None:
+ self.forest[i].parent=self.forest[i+1]
+ else:
+ self.forest[i].nextSibling=self.forest[i+1].leftChild
+ self.forest[i+1].leftChild=self.forest[i]
+ pairedForest+=[self.forest[i+1]]
+ self.forest=pairedForest
+ ##print("Result of 1st round {}.".format(self.listInorder()))
+ index = len(self.forest)-1
+ for i in range(len(self.forest)-2, -1, -1): # combining pass
+ if self.forest[index].key<=self.forest[i].key:
+ if self.forest[index].leftChild==None:
+ self.forest[i].parent=self.forest[index]
+ else:
+ self.forest[i].nextSibling=self.forest[index].leftChild
+ self.forest[index].leftChild=self.forest[i]
+ else:
+ if self.forest[i].leftChild==None:
+ self.forest[index].parent=self.forest[i]
+ else:
+ self.forest[index].nextSibling=self.forest[i].leftChild
+ self.forest[i].leftChild=self.forest[index]
+ index=i
+
+ self.forest=[self.forest[index]]
+ ##print("Result of 2nd round {}.".format(self.listInorder()))
+ return (fs-1)
+
+ def delete_min(self):
+ #finds and deletes min; restructures forest; returns number of linking operations
+ linkCount=0
+ compCount=0
+ cn = self.pairing()
+ assert len(self.forest)==1
+ #if (len(self.forest)==0):
+ # print("Cannot delete min of empty heap")
+ # return (None,0,0)
+ currentSibling=self.forest[0].leftChild
+ while currentSibling!=None:
+ nextSibling=currentSibling.nextSibling
+ self.forest+=[currentSibling]
+ currentSibling.nextSibling=None
+ currentSibling=nextSibling
+ self.forest[-1].parent=None #only for the last concatenated sibling as only this one carried parent pointer
+ minNode = self.forest[0]
+ self.forest=self.forest[1:]
+ ##print("Result of delete-min {}.".format(self.listInorder()))
+ ###print('**')
+ ###print(minNode.key)
+ return (minNode, cn, cn)
+
+ def decrease_key(self, node, diff):
+ linkCount=0
+ if node==None or diff<=0:
+ return 0
+ elif node.parent==None and node.nextSibling==None: #node is root
+ node.key=node.key-diff
+ else:
+ self.unlink_node(node)
+ node.key=node.key-diff
+ self.forest+=[node]
+ return 0
+
+ def merge(self, heap2):
+ #concatenates forests of this heap and heap2; returns number of link operations (always 0) for consistency
+ #print("Trying to merge {} and {}.".format(self.listInorder(), heap2.listInorder()))
+ self.forest+=heap2.forest
+ #print("Result of merge is {}.".format(self.listInorder()))
+ return 0
+
+ def delete(self, node):
+ if node==None:
+ print("Cannot delete None")
+ return
+ elif node.parent==None and node.nextSibling==None: #node is root
+ print("Trying to delete {}...".format(node.key))
+ index=self.forest.index(node)#slight cheating; would be nicer to use a linked list as forest instead
+ #remove node from forest list
+ self.forest=self.forest[:index]+self.forest[index+1:]
+ else: #node is a child somewhere
+ print("Trying to delete {}...".format(node.key))
+ self.unlink_node(node)
+ #concatenate potential children to forest list
+ sibling=node.leftChild
+ while sibling!=None:
+ self.forest+=[sibling]
+ sibling=sibling.nextSibling
+ if sibling!=None:
+ self.forest[-1].nextSibling=None
+ else:
+ self.forest[-1].parent=None
+ print("Result of deletion of {} is {}.".format(node.key, self.listInorder()))
+
+
+ def unlink_node(self, node):
+ #for non-root nodes only (does nothing about forest list, only tree-internal links)
+ if node==None:
+ return
+ else:
+ if node.nextSibling!=None:
+ temp=node.nextSibling
+ while temp.nextSibling!=None:#find rightmost child
+ temp=temp.nextSibling
+ if temp.parent.leftChild==node:#node is leftmost child
+ #link parent to next sibling
+ temp.parent.leftChild=node.nextSibling
+ node.nextSibling=None
+ else:
+ #node is neither first nor last child of parent
+ prevSibling=temp.parent.leftChild
+ while prevSibling.nextSibling!=node:#find left (previous) sibling
+ prevSibling=prevSibling.nextSibling
+ prevSibling.nextSibling=node.nextSibling #cut out node, link left and right sibling
+ node.nextSibling=None
+ else:
+ #node is rightmost child of parent
+ if node.parent.leftChild==node:
+ #node is only child: just remove
+ node.parent.leftChild=None
+ else:
+ prevSibling=node.parent.leftChild
+ while prevSibling.nextSibling!=node:#find left (previous) sibling
+ prevSibling=prevSibling.nextSibling
+ prevSibling.parent=node.parent
+ prevSibling.nextSibling=None
+ node.parent=None
diff --git a/pairing_heap_standard.py b/pairing_heap_standard.py
new file mode 100644
index 0000000..f1abe25
--- /dev/null
+++ b/pairing_heap_standard.py
@@ -0,0 +1,171 @@
+#!/usr/bin/python3
+from node import Node
+from pairing_heap_interface import PairingHeapInterface
+
+class PairingHeapStandard(PairingHeapInterface):
+ #performs a left-to-right forward pass, then a backward combining pass
+ #TODO: left/right child (page 115)
+ def __init__(self, root=None):
+ self.root=root
+
+ def make_heap(self):
+ #this is equivalent to init
+ pass
+
+ def listInorder(self, root):
+ if(root==None):
+ return []
+ return self.listInorder(root.leftChild)+[root.key]+self.listInorder(root.nextSibling)
+
+ def find_min(self):
+ if self.root==None:
+ return None
+ else:
+ return self.root
+
+ def insert(self, node):
+ #inserts node as child of root, returns number of link operations
+ linkCount=0
+ #print("trying to insert {}...".format(node.key))
+ if self.root==None:
+ #heap was empty before
+ self.root=node
+ else:
+ newheap=PairingHeapStandard(node)
+ linkCount=self.merge(newheap)
+ #print(self.listInorder(self.root))
+ return linkCount
+
+ def delete_min(self):
+ #print("trying to delete min...")
+ linkCount=0 #counts number of linking operations
+ minKey=None
+ minNode=None
+ if self.root==None:
+ print("Heap was already empty.")
+ return (minNode,linkCount)
+ elif self.root.leftChild==None:
+ #heap contained only one element
+ minNode=self.root
+ self.root=None
+ return (minNode, linkCount)
+ elif self.root.leftChild.nextSibling==None:
+ #first child has no siblings->first child becomes root
+ minNode=self.root
+ self.root=self.root.leftChild
+ self.root.parent=None
+ return (minNode, linkCount)
+ else:
+ minNode=self.root
+ self.root=self.root.leftChild
+ current=self.root
+ nextSibling=None
+ heaps=[]
+ paired=[]
+ #left-to-right pairing pass v2
+ while current!=None:#create heaps of all orphaned children
+ nextSibling=current.nextSibling
+ heaps+=[PairingHeapStandard(current)]
+ current.nextSibling=None
+ current=nextSibling
+ for j in range(0,len(heaps),2):
+ if(j==len(heaps)-1):#last one
+ paired+=[heaps[j]]
+ else:
+ heap=heaps[j]
+ linkCount+=heap.merge(heaps[j+1])#merge returns its number of link operations
+ paired+=[heap]
+ #combining backwards pass v2
+ combined=paired[-1]#start with last tree
+ for i in range(len(paired)-2, -1, -1):
+ linkCount+=combined.merge(paired[i])#merge returns its number of link operations
+ self.root=combined.root
+ self.root.parent=None
+ #print("result is {}".format(self.listInorder(self.root)))
+ return (minNode, linkCount)
+
+ def merge(self, heap2):
+ linkCount=0 #counts number of linking operations
+ #print("Trying to merge {} and {}...".format(self.listInorder(self.root), self.listInorder(heap2.root)))
+ if self.root==None:#heap is empty
+ self.root=heap2.root
+ elif heap2.root==None:#heap 2 is empty
+ pass #this heap is the result
+ else:
+ if self.root.key<=heap2.root.key:
+ heap2.root.nextSibling=self.root.leftChild
+ if heap2.root.nextSibling==None:
+ heap2.root.parent=self.root
+ self.root.leftChild=heap2.root
+ linkCount=1
+ else:
+ self.root.nextSibling=heap2.root.leftChild
+ if self.root.nextSibling==None:
+ self.root.parent=heap2.root
+ heap2.root.leftChild=self.root
+ self.root=heap2.root
+ linkCount=1
+ #TODO check for only children?
+ #print("Result is {}".format(self.listInorder(self.root)))
+ return linkCount
+
+ def decrease_key(self, node, diff):#TODO more testing
+ linkCount=0
+ if self.root==node:
+ self.root.key=self.root.key-diff
+ else:
+ #first step: cut node from heap
+ self.unlink_node(node)#helper function
+ #second step: decrease key
+ subheap=PairingHeapStandard(node)
+ subheap.root.key=subheap.root.key-diff
+ #third step: merge back in
+ linkCount = self.merge(subheap)
+ return linkCount
+
+ def delete(self, node): #TODO more testing?
+ print("trying to delete {} from {}".format(node.key, self.listInorder(self.root)))
+ if self.root.key==node.key:
+ self.delete_min()
+ else:
+ self.unlink_node(node)#helper function
+
+ subheap=PairingHeapStandard(node)
+ subheap.delete_min()
+ self.merge(subheap)
+ print("result is {}".format(self.listInorder(self.root)))
+ pass
+
+ def unlink_node(self, node):
+ #removes node from heap updating pointers
+ if self.root==node:#remove the whole heap
+ self.root=None
+ else:
+ if node.nextSibling!=None:
+ temp=node.nextSibling
+ while temp.nextSibling!=None:
+ temp=temp.nextSibling
+ if temp.parent.leftChild==node:#node is leftmost child
+ #link parent to next sibling
+ temp.parent.leftChild=node.nextSibling
+ node.nextSibling=None
+ else:
+ #node is neither first nor last child of parent
+ prevSibling=temp.parent.leftChild
+ while prevSibling.nextSibling!=node:#find left (previous) sibling
+ prevSibling=prevSibling.nextSibling
+ prevSibling.nextSibling=node.nextSibling #cut out node, link left and right sibling
+ else:
+ #node is rightmost child of parent
+ if node.parent.leftChild==node:
+ #node is only child: just remove
+ node.parent.leftChild=None
+ else:
+ prevSibling=node.parent.leftChild
+ while prevSibling.nextSibling!=node:#find left (previous) sibling
+ prevSibling=prevSibling.nextSibling
+ prevSibling.parent=node.parent
+ prevSibling.nextSibling=None
+ node.parent=None
+
+
diff --git a/paper-dijkstra-test-new.py b/paper-dijkstra-test-new.py
new file mode 100755
index 0000000..4125519
--- /dev/null
+++ b/paper-dijkstra-test-new.py
@@ -0,0 +1,210 @@
+#!/usr/bin/python3
+from node import Node
+from pairing_heap_interface import PairingHeapInterface
+from pairing_heap import PairingHeap
+import networkx as nx
+import sys
+import random
+import math
+import numpy as np
+import matplotlib.pyplot as plt
+import os
+import psutil
+import csv
+
+COUNT_TYPE_BOTH = 0
+COUNT_TYPE_LINKS = -1
+COUNT_TYPE_COMPS = -2
+
+TYPES = {21: "Pairing", 22: "Smooth"}
+MAX_TYPE_KEY = max(TYPES.keys())
+#COLOURS = ['xkcd:fire engine red', 'xkcd:dusty orange', 'xkcd:clear blue', 'xkcd:cool green',
+# 'xkcd:macaroni and cheese', 'xkcd:fire engine red', 'xkcd:dusty orange', 'xkcd:clear blue',
+# 'xkcd:cool green', 'xkcd:macaroni and cheese', 'xkcd:bright sky blue', 'xkcd:bright sky blue', 'xkcd:green',
+# 'xkcd:ochre', 'xkcd:sea blue', 'xkcd:sea green', 'xkcd:sea blue', 'xkcd:warm grey',
+# 'xkcd:bright sky blue', 'xkcd:bright sky blue']
+LINETYPES = 5 * ['-'] + 5 * ['--'] + ['--', '-'] + ['--', '--', '--', '--', '--', '--', '-', '-']
+FIG_LABELS = ["comparisons", "links"]
+MAX_TYPE_KEY = max(TYPES.keys())
+
+COLOURS = {21:'xkcd:fire engine red', 22:'xkcd:sea green'}
+SHADE_COLOURS = {21:'#fe4d4e', 22:'#58ab8e'}
+
+NUMBER_TESTS = 10 # number of tests to run
+TEST_SIZE = 500 # ,6000,7000,8000,9000,10000,20000,30000,40000,50000,60000,70000,80000,90000,100000
+EDGE_PROBABILITY = 0.05
+WEIGHT_RANGE = 10000
+
+
+def plot_avg_counts_old(avgCounts):
+ # colours from https://xkcd.com/color/rgb/
+ linetypes = 5 * ["-"] + 5 * ["--"] + ["--", "-"] + ["-, -"]
+ plt.figure('Dijkstra with variable connectivity')
+ for k in TYPES.keys():
+ avgComps = [acounts[k] for acounts in avgCounts[0]]
+ plt.plot([factor * EDGE_PROBABILITY for factor in range(1, 101, 1)], avgComps, color=COLOURS[k], linestyle='-',
+ label=TYPES[k] + " comparisons")
+ avgLinks = [acounts[k] for acounts in avgCounts[1]]
+ plt.plot([factor * EDGE_PROBABILITY for factor in range(1, 101, 1)], avgLinks, color=COLOURS[k], linestyle='--',
+ label=TYPES[k] + " links")
+ plt.grid(True)
+ plt.legend(loc='best')
+ plt.show()
+
+def plot_avg_counts(avgCounts):
+ # colours from https://xkcd.com/color/rgb/
+ MARKERS_COMP = {21:"o", 12:"d", 22:"^"}#https://matplotlib.org/3.1.1/api/markers_api.html
+ MARKERS_LINK = {21:"o", 12:"D", 22:"D"}
+ plt.figure('avg number of operations in Dijkstra\'s algorithm')
+ deviations = [factor * EDGE_PROBABILITY for factor in range(1, 21, 1)]
+ for k in TYPES.keys():
+ #print(k)
+ avgComps = [acounts[k] for acounts in avgCounts[0]]
+ maxComps = [acounts[k] for acounts in avgCounts[2]]
+ minComps = [acounts[k] for acounts in avgCounts[4]]
+ plt.plot(deviations, avgComps, color=COLOURS[k], linestyle="-", marker=MARKERS_COMP[k], markerfacecolor=COLOURS[k], markersize=9, markeredgewidth=1, markeredgecolor='black', label=TYPES[k] + " comparisons")
+ plt.fill_between(deviations, minComps, maxComps, color=SHADE_COLOURS[k], alpha=.3)
+ avgLinks = [acounts[k] for acounts in avgCounts[1]]
+ maxLinks = [acounts[k] for acounts in avgCounts[3]]
+ minLinks = [acounts[k] for acounts in avgCounts[5]]
+ plt.plot(deviations, avgLinks, color=COLOURS[k], linestyle="--", marker=MARKERS_LINK[k], markerfacecolor=COLOURS[k], markersize=9, markeredgewidth=1, markeredgecolor='black', label=TYPES[k] + " links")
+ plt.fill_between(deviations, minLinks, maxLinks, color=SHADE_COLOURS[k], alpha=.3)
+
+
+ plt.xlabel('Edge probability', fontsize=26)
+ plt.ylabel('Avg. number of operations / size', fontsize=26)
+ plt.xticks(fontsize=20)
+ plt.yticks(fontsize=20)
+ plt.rc('legend',fontsize=26) # using a size in points
+ plt.legend()
+ plt.grid(True)
+ #plt.gca().invert_xaxis()
+ figure = plt.gcf() # get current figure
+ figure.set_size_inches(16, 18) # set figure's size manually to full screen
+ plt.savefig('plots/paper-dijkstra-new.svg', bbox_inches='tight') # bbox_inches removes extra white spaces
+ plt.legend(loc='best')
+ plt.show()
+
+
+def export_results(xs, results, countType, heapTypes, filename="dijkstra"):
+ # parse data as randomness parameter; counts per heap type
+ if countType == COUNT_TYPE_BOTH:
+ with open("data/" + filename + '-comps.csv', 'w', newline='') as csvfile:
+ csvwriter = csv.writer(csvfile, delimiter=';', quotechar='|', quoting=csv.QUOTE_MINIMAL)
+ csvwriter.writerow(["randomness parameter value"] + [name for name in TYPES.values()])
+ csvwriter.writerow(["randomness parameter value"] + [name for name in TYPES.keys()])
+ for i in range(len(results[0])):
+ row = [xs[i]] + [results[0][i][k] for k in TYPES.keys()]
+ csvwriter.writerow(row)
+ with open("data/" + filename + '-links.csv', 'w', newline='') as csvfile:
+ csvwriter = csv.writer(csvfile, delimiter=';', quotechar='|', quoting=csv.QUOTE_MINIMAL)
+ csvwriter.writerow(["randomness parameter value"] + [name for name in TYPES.values()])
+ csvwriter.writerow(["randomness parameter value"] + [name for name in TYPES.keys()])
+ for i in range(len(results[1])):
+ row = [xs[i]] + [results[1][i][k] for k in TYPES.keys()]
+ csvwriter.writerow(row)
+ else:
+ fn = "data/" + filename + '-links.csv' if countType == COUNT_TYPE_LINKS else "data/" + filename + '-comps.csv'
+ with open(fn, 'w', newline='') as csvfile:
+ csvwriter = csv.writer(csvfile, delimiter=';', quotechar='|', quoting=csv.QUOTE_MINIMAL)
+ csvwriter.writerow(["randomness parameter value"] + [name for name in TYPES.values()])
+ csvwriter.writerow(["randomness parameter value"] + [name for name in TYPES.keys()])
+ for i in range(len(results)):
+ row = [xs[i]]+[results[i][k] for k in TYPES.keys()]
+ csvwriter.writerow(row)
+
+
+if __name__ == "__main__":
+
+ testOutputCount = []
+ avgLinksPerSize = []
+ avgCompsPerSize = []
+ maxLinksPerSize = []
+ maxCompsPerSize = []
+ minLinksPerSize = []
+ minCompsPerSize = []
+
+ xs = [factor * EDGE_PROBABILITY for factor in range(1, 21, 1)]
+ for x in xs:
+ avgCountsLinks = [0 for _ in range(MAX_TYPE_KEY + 1)]
+ avgCountsComps = [0 for _ in range(MAX_TYPE_KEY + 1)]
+ maxCountsLinks = [0 for _ in range(MAX_TYPE_KEY + 1)]
+ maxCountsComps = [0 for _ in range(MAX_TYPE_KEY + 1)]
+ minCountsLinks = [1000000000000 for _ in range(MAX_TYPE_KEY + 1)]
+ minCountsComps = [1000000000000 for _ in range(MAX_TYPE_KEY + 1)]
+
+
+ for _ in range(NUMBER_TESTS):
+ # some nice graph generators here: https://networkx.github.io/documentation/stable/reference/generators.html
+ graph = nx.fast_gnp_random_graph(TEST_SIZE, x)
+ # graph = nx.random_regular_graph(10, 1000)
+ for (u, v) in graph.edges():
+ graph.edges[u, v]['w'] = random.randint(1, WEIGHT_RANGE)
+ for heapType in TYPES.keys():
+ for v in graph.nodes():
+ graph.nodes[v]['v'] = False # "visited" marker
+ linkCount = 0
+ compCount = 0
+ vertex2qnode = {}
+ dist = [888888888 for _ in range(len(graph.nodes()))]
+ prev = [None for _ in range(len(graph.nodes()))]
+
+ heap = PairingHeap(heapType, COUNT_TYPE_BOTH)
+ heap.make_heap()
+
+ source = graph.nodes()[0]
+ dist[0] = 0
+ for idx, v in enumerate(graph.nodes()):
+ #qnode = Node(dist[idx])
+ qnode = Node(dist[v])
+ qnode.vertex = v
+ vertex2qnode[v] = qnode
+ (cc, lc) = heap.insert(qnode)
+ linkCount += lc
+ compCount += cc
+
+ for s in range(len(graph.nodes())):
+ (minNode, cc, lc) = heap.delete_min()
+ linkCount += lc
+ compCount += cc
+ if minNode is None:
+ raise Exception(
+ "delete-min on heap of type {} returned None with {} nodes removed".format(TYPES[heapType],
+ s))
+ u = minNode.vertex
+ uk = minNode.key
+ #print(uk)
+ #print('extracted {}'.format(minNode.key))
+ graph.nodes[u]['v'] = True # minNode has been visited
+ for idx, v in enumerate(graph.neighbors(u)):
+ alt = uk + graph.edges[u, v]['w']
+ if alt < dist[v] and not graph.nodes[v]['v']:
+ (cc, lc) = heap.decrease_key(vertex2qnode[v], dist[v] - alt)
+ #print('decreased from {} to {}'.format(dist[v],alt))
+ linkCount += lc
+ compCount += cc
+ dist[v] = alt
+ prev[v] = u
+ avgCountsLinks[heapType] += (linkCount / NUMBER_TESTS)/TEST_SIZE
+ avgCountsComps[heapType] += (compCount / NUMBER_TESTS)/TEST_SIZE
+ maxCountsLinks[heapType] = max(maxCountsLinks[heapType],linkCount/TEST_SIZE)
+ maxCountsComps[heapType] = max(maxCountsComps[heapType],compCount/TEST_SIZE)
+ minCountsLinks[heapType] = min(minCountsLinks[heapType],linkCount/TEST_SIZE)
+ minCountsComps[heapType] = min(minCountsComps[heapType],compCount/TEST_SIZE)
+
+ for heapType in TYPES.keys():
+ pid = os.getpid()
+ py = psutil.Process(pid)
+ memoryUse = py.memory_info()[0] / 2. ** 30 # memory use in GB
+ print(
+ "[{}] \t avgComp: {} \t avgLink: {} \t RAM: {} \t |V|={} \t |E|={}".format(
+ TYPES[heapType], avgCountsComps[heapType], avgCountsLinks[heapType], memoryUse, len(graph.nodes()), len(graph.edges())))
+ avgLinksPerSize += [avgCountsLinks]
+ avgCompsPerSize += [avgCountsComps]
+ maxLinksPerSize += [maxCountsLinks]
+ maxCompsPerSize += [maxCountsComps]
+ minLinksPerSize += [minCountsLinks]
+ minCompsPerSize += [minCountsComps]
+ # plot_avg_counts([avgCompsPerSize, avgLinksPerSize])
+ plot_avg_counts([avgCompsPerSize, avgLinksPerSize, maxCompsPerSize, maxLinksPerSize, minCompsPerSize, minLinksPerSize])
+ export_results(xs, [avgCompsPerSize, avgLinksPerSize], COUNT_TYPE_BOTH, TYPES, "dijkstra")
diff --git a/paper-dijkstra-test2-new.py b/paper-dijkstra-test2-new.py
new file mode 100755
index 0000000..9f71a2c
--- /dev/null
+++ b/paper-dijkstra-test2-new.py
@@ -0,0 +1,214 @@
+#!/usr/bin/python3
+from node import Node
+from pairing_heap_interface import PairingHeapInterface
+from pairing_heap import PairingHeap
+import networkx as nx
+import sys
+import random
+import math
+import numpy as np
+import matplotlib.pyplot as plt
+import os
+import psutil
+import csv
+
+COUNT_TYPE_BOTH = 0
+COUNT_TYPE_LINKS = -1
+COUNT_TYPE_COMPS = -2
+
+TYPES = {21: "Pairing", 22: "Smooth"}
+MAX_TYPE_KEY = max(TYPES.keys())
+#COLOURS = ['xkcd:fire engine red', 'xkcd:dusty orange', 'xkcd:clear blue', 'xkcd:cool green',
+# 'xkcd:macaroni and cheese', 'xkcd:fire engine red', 'xkcd:dusty orange', 'xkcd:clear blue',
+# 'xkcd:cool green', 'xkcd:macaroni and cheese', 'xkcd:bright sky blue', 'xkcd:bright sky blue', 'xkcd:green',
+# 'xkcd:ochre', 'xkcd:sea blue', 'xkcd:sea green', 'xkcd:sea blue', 'xkcd:warm grey',
+# 'xkcd:bright sky blue', 'xkcd:bright sky blue']
+LINETYPES = 5 * ['-'] + 5 * ['--'] + ['--', '-'] + ['--', '--', '--', '--', '--', '--', '-', '-']
+FIG_LABELS = ["comparisons", "links"]
+MAX_TYPE_KEY = max(TYPES.keys())
+
+COLOURS = {21:'xkcd:fire engine red', 22:'xkcd:sea green'}
+SHADE_COLOURS = {21:'#fe4d4e', 22:'#58ab8e'}
+
+NUMBER_TESTS = 10 # number of tests to run
+TEST_SIZE = 500 # ,6000,7000,8000,9000,10000,20000,30000,40000,50000,60000,70000,80000,90000,100000
+EDGE_PROBABILITY = 0.05
+WEIGHT_RANGE = 10000
+
+
+def plot_avg_counts_old(avgCounts):
+ # colours from https://xkcd.com/color/rgb/
+ linetypes = 5 * ["-"] + 5 * ["--"] + ["--", "-"] + ["-, -"]
+ plt.figure('Dijkstra with variable connectivity')
+ for k in TYPES.keys():
+ avgComps = [acounts[k] for acounts in avgCounts[0]]
+ plt.plot([factor * EDGE_PROBABILITY for factor in range(1, 101, 1)], avgComps, color=COLOURS[k], linestyle='-',
+ label=TYPES[k] + " comparisons")
+ avgLinks = [acounts[k] for acounts in avgCounts[1]]
+ plt.plot([factor * EDGE_PROBABILITY for factor in range(1, 101, 1)], avgLinks, color=COLOURS[k], linestyle='--',
+ label=TYPES[k] + " links")
+ plt.grid(True)
+ plt.legend(loc='best')
+ plt.show()
+
+def plot_avg_counts(avgCounts):
+ # colours from https://xkcd.com/color/rgb/
+ MARKERS_COMP = {21:"o", 12:"d", 22:"^"}#https://matplotlib.org/3.1.1/api/markers_api.html
+ MARKERS_LINK = {21:"o", 12:"D", 22:"D"}
+ plt.figure('avg number of operations in Dijkstra\'s algorithm')
+ deviations = [ 10+round(TEST_SIZE*20*factor * EDGE_PROBABILITY) for factor in range(1, 21, 1)]
+ for k in TYPES.keys():
+ #print(k)
+ avgComps = [acounts[k] for acounts in avgCounts[0]]
+ maxComps = [acounts[k] for acounts in avgCounts[2]]
+ minComps = [acounts[k] for acounts in avgCounts[4]]
+ plt.plot(deviations, avgComps, color=COLOURS[k], linestyle="-", marker=MARKERS_COMP[k], markerfacecolor=COLOURS[k], markersize=9, markeredgewidth=1, markeredgecolor='black', label=TYPES[k] + " comparisons")
+ plt.fill_between(deviations, minComps, maxComps, color=SHADE_COLOURS[k], alpha=.3)
+ avgLinks = [acounts[k] for acounts in avgCounts[1]]
+ maxLinks = [acounts[k] for acounts in avgCounts[3]]
+ minLinks = [acounts[k] for acounts in avgCounts[5]]
+ plt.plot(deviations, avgLinks, color=COLOURS[k], linestyle="--", marker=MARKERS_LINK[k], markerfacecolor=COLOURS[k], markersize=9, markeredgewidth=1, markeredgecolor='black', label=TYPES[k] + " links")
+ plt.fill_between(deviations, minLinks, maxLinks, color=SHADE_COLOURS[k], alpha=.3)
+
+
+ plt.xlabel('Graph size', fontsize=26)
+ plt.ylabel('Avg. number of operations / size', fontsize=26)
+ plt.xticks(fontsize=20)
+ plt.yticks(fontsize=20)
+ plt.rc('legend',fontsize=26) # using a size in points
+ plt.legend()
+ plt.grid(True)
+ #plt.gca().invert_xaxis()
+ figure = plt.gcf() # get current figure
+ figure.set_size_inches(16, 18) # set figure's size manually to full screen
+ plt.savefig('plots/paper-dijkstra2-new.svg', bbox_inches='tight') # bbox_inches removes extra white spaces
+ plt.legend(loc='best')
+ plt.show()
+
+
+def export_results(xs, results, countType, heapTypes, filename="dijkstra2"):
+ # parse data as randomness parameter; counts per heap type
+ if countType == COUNT_TYPE_BOTH:
+ with open("data/" + filename + '-comps.csv', 'w', newline='') as csvfile:
+ csvwriter = csv.writer(csvfile, delimiter=';', quotechar='|', quoting=csv.QUOTE_MINIMAL)
+ csvwriter.writerow(["randomness parameter value"] + [name for name in TYPES.values()])
+ csvwriter.writerow(["randomness parameter value"] + [name for name in TYPES.keys()])
+ for i in range(len(results[0])):
+ row = [xs[i]] + [results[0][i][k] for k in TYPES.keys()]
+ csvwriter.writerow(row)
+ with open("data/" + filename + '-links.csv', 'w', newline='') as csvfile:
+ csvwriter = csv.writer(csvfile, delimiter=';', quotechar='|', quoting=csv.QUOTE_MINIMAL)
+ csvwriter.writerow(["randomness parameter value"] + [name for name in TYPES.values()])
+ csvwriter.writerow(["randomness parameter value"] + [name for name in TYPES.keys()])
+ for i in range(len(results[1])):
+ row = [xs[i]] + [results[1][i][k] for k in TYPES.keys()]
+ csvwriter.writerow(row)
+ else:
+ fn = "data/" + filename + '-links.csv' if countType == COUNT_TYPE_LINKS else "data/" + filename + '-comps.csv'
+ with open(fn, 'w', newline='') as csvfile:
+ csvwriter = csv.writer(csvfile, delimiter=';', quotechar='|', quoting=csv.QUOTE_MINIMAL)
+ csvwriter.writerow(["randomness parameter value"] + [name for name in TYPES.values()])
+ csvwriter.writerow(["randomness parameter value"] + [name for name in TYPES.keys()])
+ for i in range(len(results)):
+ row = [xs[i]]+[results[i][k] for k in TYPES.keys()]
+ csvwriter.writerow(row)
+
+
+if __name__ == "__main__":
+
+ testOutputCount = []
+ avgLinksPerSize = []
+ avgCompsPerSize = []
+ maxLinksPerSize = []
+ maxCompsPerSize = []
+ minLinksPerSize = []
+ minCompsPerSize = []
+
+ xs = [factor * EDGE_PROBABILITY for factor in range(1, 21, 1)]
+ for x in xs:
+ avgCountsLinks = [0 for _ in range(MAX_TYPE_KEY + 1)]
+ avgCountsComps = [0 for _ in range(MAX_TYPE_KEY + 1)]
+ maxCountsLinks = [0 for _ in range(MAX_TYPE_KEY + 1)]
+ maxCountsComps = [0 for _ in range(MAX_TYPE_KEY + 1)]
+ minCountsLinks = [1000000000000 for _ in range(MAX_TYPE_KEY + 1)]
+ minCountsComps = [1000000000000 for _ in range(MAX_TYPE_KEY + 1)]
+
+
+ for _ in range(NUMBER_TESTS):
+ # some nice graph generators here: https://networkx.github.io/documentation/stable/reference/generators.html
+ ##graph = nx.fast_gnp_random_graph(100, 0.1)
+ graph = nx.random_regular_graph(10,10+round(TEST_SIZE*x*20))
+ ##graph = nx.random_regular_graph(10,100)
+ for (u, v) in graph.edges():
+ graph.edges[u, v]['w'] = random.randint(1, WEIGHT_RANGE)
+ for heapType in TYPES.keys():
+ #print('---')
+ for v in graph.nodes():
+ graph.nodes[v]['v'] = False # "visited" marker
+ linkCount = 0
+ compCount = 0
+ vertex2qnode = {}
+ dist = [888888888 for _ in range(len(graph.nodes()))]
+ prev = [None for _ in range(len(graph.nodes()))]
+
+ heap = PairingHeap(heapType, COUNT_TYPE_BOTH)
+ heap.make_heap()
+
+ source = graph.nodes()[0]
+ dist[0] = 0
+ for idx, v in enumerate(graph.nodes()):
+# qnode = Node(dist[idx])
+ qnode = Node(dist[v])
+ qnode.vertex = v
+ vertex2qnode[v] = qnode
+ (cc, lc) = heap.insert(qnode)
+ #print('inserted key {}',qnode.key)
+ linkCount += lc
+ compCount += cc
+
+ for s in range(len(graph.nodes())):
+ (minNode, cc, lc) = heap.delete_min()
+ linkCount += lc
+ compCount += cc
+ if minNode is None:
+ raise Exception(
+ "delete-min on heap of type {} returned None with {} nodes removed".format(TYPES[heapType],
+ s))
+ u = minNode.vertex
+ uk = minNode.key
+ #print(uk)
+ #print('extracted {}'.format(minNode.key))
+ graph.nodes[u]['v'] = True # minNode has been visited
+ for idx, v in enumerate(graph.neighbors(u)):
+ alt = uk + graph.edges[u, v]['w']
+ if alt < dist[v] and not graph.nodes[v]['v']:
+ (cc, lc) = heap.decrease_key(vertex2qnode[v], dist[v] - alt)
+ #print('decreased from {} to {}'.format(dist[v],alt))
+ linkCount += lc
+ compCount += cc
+ dist[v] = alt
+ prev[v] = u
+ TSIZE = 10+round(TEST_SIZE*x*20)
+ avgCountsLinks[heapType] += (linkCount / NUMBER_TESTS)/TSIZE
+ avgCountsComps[heapType] += (compCount / NUMBER_TESTS)/TSIZE
+ maxCountsLinks[heapType] = max(maxCountsLinks[heapType],linkCount/TSIZE)
+ maxCountsComps[heapType] = max(maxCountsComps[heapType],compCount/TSIZE)
+ minCountsLinks[heapType] = min(minCountsLinks[heapType],linkCount/TSIZE)
+ minCountsComps[heapType] = min(minCountsComps[heapType],compCount/TSIZE)
+
+ for heapType in TYPES.keys():
+ pid = os.getpid()
+ py = psutil.Process(pid)
+ memoryUse = py.memory_info()[0] / 2. ** 30 # memory use in GB
+ print(
+ "[{}] \t avgComp: {} \t avgLink: {} \t RAM: {} \t |V|={} \t |E|={}".format(
+ TYPES[heapType], avgCountsComps[heapType], avgCountsLinks[heapType], memoryUse, len(graph.nodes()), len(graph.edges())))
+ avgLinksPerSize += [avgCountsLinks]
+ avgCompsPerSize += [avgCountsComps]
+ maxLinksPerSize += [maxCountsLinks]
+ maxCompsPerSize += [maxCountsComps]
+ minLinksPerSize += [minCountsLinks]
+ minCompsPerSize += [minCountsComps]
+ # plot_avg_counts([avgCompsPerSize, avgLinksPerSize])
+ plot_avg_counts([avgCompsPerSize, avgLinksPerSize, maxCompsPerSize, maxLinksPerSize, minCompsPerSize, minLinksPerSize])
+ export_results(xs, [avgCompsPerSize, avgLinksPerSize], COUNT_TYPE_BOTH, TYPES, "dijkstra")
diff --git a/paper-permutations.py b/paper-permutations.py
new file mode 100755
index 0000000..e384830
--- /dev/null
+++ b/paper-permutations.py
@@ -0,0 +1,91 @@
+#!/usr/bin/python3
+import random
+import copy
+import matplotlib.pyplot as plt
+import math
+import numpy as np
+
+"""This file generates visualizations of the different random permutation classes"""
+
+def plot_permutation(permutation, title, filename):
+ # visualizing given permutation as element index in permutation over element index in sorted list
+ # colours from https://xkcd.com/color/rgb/
+ plt.figure(title)
+ sortedList = copy.copy(permutation)
+ sortedList.sort()
+ indices = [i for i in range(len(sortedList))]
+ pindices = [permutation.index(x) for x in sortedList]
+ plt.plot(indices, pindices, color='xkcd:charcoal', marker='o', linestyle="", label="(sorted index, permuted index)")
+ plt.xlabel('Index in sorted list', fontsize=26)
+ plt.ylabel('Index in permutation', fontsize=26)
+ plt.xticks(fontsize=20)
+ plt.yticks(fontsize=20)
+ plt.rc('legend',fontsize=26) # using a size in points
+ plt.legend()
+ plt.grid(True)
+ figure = plt.gcf() # get current figure
+ figure.set_size_inches(16, 18) # set figure's size manually to full screen
+ plt.savefig('plots/paper-permutation-{}.svg'.format(filename), bbox_inches='tight') # bbox_inches removes extra white spaces
+ plt.legend(loc='best')
+ plt.show()
+
+def localizedShuffleByIndex(llist, sdev):
+ tuples = []
+ for element in llist:
+ key = np.random.normal(llist.index(element) * 1.0 / len(llist),
+ sdev) # generate key using gaussian distribution over sorted index
+ tuples += [(key, element)] # store element with key
+ sortedTuples = sorted(tuples, key=lambda x: x[0]) # sort key-element tuples by keys
+ sortedList = [tup[1] for tup in sortedTuples] # discard keys
+ return sortedList
+
+
+def separablePermutation(n):
+ assert (n & (n - 1) == 0) and n != 0 and n > 1, "n must be a power of two > 1" # bit magic
+
+ def generateSepPermutation(l, r):
+ flip = random.random() >= 0.5
+ if r - l == 1:
+ if flip == 0:
+ return [r, l]
+ else:
+ return [l, r]
+ else:
+ m = math.floor((l + r) / 2)
+ if flip == 0:
+ return generateSepPermutation(m + 1, r) + generateSepPermutation(l, m)
+ else:
+ return generateSepPermutation(l, m) + generateSepPermutation(m + 1, r)
+
+ return generateSepPermutation(0, n - 1)
+
+
+def generateContSortedSubseq(llist, sublen):
+ listcopy = copy.copy(llist)
+ random.shuffle(listcopy)
+ res = []
+ l = 0
+ while l < len(llist):
+ clen = random.randint(1, sublen)
+# clen = sublen
+ sublist = copy.copy(listcopy[l:min(l + clen, len(listcopy))])
+ sublist.sort()
+ res += sublist
+ l += clen
+ return res
+
+sortedList = [x for x in range(512)]
+# generating uniformly random permutation
+randomPermutation = copy.copy(sortedList)
+random.shuffle(randomPermutation)
+plot_permutation(randomPermutation, "Uniformly Random Permutation", "uniform")
+# generating random separable permutation
+separablePermutation = separablePermutation(512)
+plot_permutation(separablePermutation, "Random Separable Permutation", "separable")
+# generating random localized permutation
+localizedPermutation = localizedShuffleByIndex(sortedList, 0.15)
+plot_permutation(localizedPermutation, "Random Localized Permutation", "localized")
+# generating random permutation with continuous sorted subsequences
+subseqPermutation = generateContSortedSubseq(sortedList, 30)
+plot_permutation(subseqPermutation, "Random Subsequence Permutation", "subseq")
+
diff --git a/paper-sorting-loc-new.py b/paper-sorting-loc-new.py
new file mode 100644
index 0000000..3a3d686
--- /dev/null
+++ b/paper-sorting-loc-new.py
@@ -0,0 +1,176 @@
+#!/usr/bin/python3
+from random import shuffle
+import random
+import numpy as np
+import matplotlib.pyplot as plt
+import sys
+import signal
+import copy
+import math
+import csv
+from node import Node
+from pairing_heap import PairingHeap
+
+COUNT_TYPE_BOTH = 0
+COUNT_TYPE_LINKS = -1
+COUNT_TYPE_COMPS = -2
+MAXSIZE = 17
+NUMBER_TESTS = 10 # number of tests to run
+TEST_SIZES = [j for j in range(MAXSIZE)]
+LIST_LEN = 10000 # number of elements in test list
+TEST_SIZE = 10000 # number of elements in test list
+STEP_SIZE = 100
+INCREMENT_LOC = 0.01
+INCREMENT_SUBSEQS = 100
+TYPES = {0: "Pairing", 12: "Smooth"}
+MAX_TYPE_KEY = max(TYPES.keys())
+COLOURS = {0:'xkcd:fire engine red', 12:'xkcd:green'}
+SHADE_COLOURS = {0:'#fe4d4e', 12:'#58ab8e'}
+
+
+def isSorted(list0):
+ return all(list0[i] < list0[i + 1] for i in range(len(list0) - 1))
+
+
+def localizedShuffleByIndex(llist, sdev):
+ tuples = []
+ for element in llist:
+ key = np.random.normal(llist.index(element) * 1.0 / len(llist),
+ sdev) # generate key using gaussian distribution over sorted index
+ tuples += [(key, element)] # store element with key
+ sortedTuples = sorted(tuples, key=lambda x: x[0]) # sort key-element tuples by keys
+ sortedList = [tup[1] for tup in sortedTuples] # discard keys
+ # print(sortedList)
+ return sortedList
+
+
+def plot_avg_counts(avgCounts):
+ # colours from https://xkcd.com/color/rgb/
+ MARKERS_COMP = {0:"o", 12:"^"}#https://matplotlib.org/3.1.1/api/markers_api.html
+ MARKERS_LINK = {0:"o", 12:"D"}
+
+ plt.figure('avg number of operations by heap type')
+ deviations = [fac * INCREMENT_LOC for fac in range(0, math.ceil(0.3 / INCREMENT_LOC), 1)]
+ for k in TYPES.keys():
+ #print(k)
+ avgComps = [acounts[k] for acounts in avgCounts[0]]
+ maxComps = [acounts[k] for acounts in avgCounts[2]]
+ minComps = [acounts[k] for acounts in avgCounts[4]]
+ plt.plot(deviations, avgComps, color=COLOURS[k], linestyle="-", marker=MARKERS_COMP[k], markerfacecolor=COLOURS[k], markersize=9, markeredgewidth=1, markeredgecolor='black', label=TYPES[k] + " comparisons")
+ plt.fill_between(deviations, minComps, maxComps, color=SHADE_COLOURS[k], alpha=.3)
+ avgLinks = [acounts[k] for acounts in avgCounts[1]]
+ maxLinks = [acounts[k] for acounts in avgCounts[3]]
+ minLinks = [acounts[k] for acounts in avgCounts[5]]
+ plt.plot(deviations, avgLinks, color=COLOURS[k], linestyle="--", marker=MARKERS_LINK[k], markerfacecolor=COLOURS[k], markersize=9, markeredgewidth=1, markeredgecolor='black', label=TYPES[k] + " links")
+ plt.fill_between(deviations, minLinks, maxLinks, color=SHADE_COLOURS[k], alpha=.3)
+
+ #plt.title('Sorting random separable permutations', fontsize=25)
+ plt.xlabel('Locality parameter', fontsize=26)
+ plt.ylabel('Avg. number of operations / size', fontsize=26)
+ plt.xticks(fontsize=20)
+ plt.yticks(fontsize=20)
+ plt.rc('legend',fontsize=26) # using a size in points
+ plt.legend()
+ plt.grid(True)
+ figure = plt.gcf() # get current figure
+ figure.set_size_inches(16, 18) # set figure's size manually to your full screen (32x18)
+ plt.savefig('plots/paper-sorting-loc-new.svg', bbox_inches='tight') # bbox_inches removes extra white spaces
+ plt.legend(loc='best')
+ plt.show()
+
+
+
+def export_results(params, results, countType, heapTypes, filename="dijkstra"):
+ # exports results of simulation as separate .csv files, one for links and one for comparisons, into /data directory
+ # each row contains randomness parameter value; plus one column containing the number of operations for each heap type
+ if countType == COUNT_TYPE_BOTH:
+ with open("data/" + filename + '-comps.csv', 'w', newline='') as csvfile:
+ csvwriter = csv.writer(csvfile, delimiter=';', quotechar='|', quoting=csv.QUOTE_MINIMAL)
+ csvwriter.writerow(["randomness parameter value"] + [name for name in TYPES.values()])
+ csvwriter.writerow(["randomness parameter value"] + [name for name in TYPES.keys()])
+ for i in range(len(results[0])):
+ row = [params[i]] + [results[0][i][k] for k in TYPES.keys()]
+ csvwriter.writerow(row)
+ with open("data/" + filename + '-links.csv', 'w', newline='') as csvfile:
+ csvwriter = csv.writer(csvfile, delimiter=';', quotechar='|', quoting=csv.QUOTE_MINIMAL)
+ csvwriter.writerow(["randomness parameter value"] + [name for name in TYPES.values()])
+ csvwriter.writerow(["randomness parameter value"] + [name for name in TYPES.keys()])
+ for i in range(len(results[1])):
+ row = [params[i]] + [results[1][i][k] for k in TYPES.keys()]
+ csvwriter.writerow(row)
+ else:
+ fn = "data/" + filename + '-links.csv' if countType == COUNT_TYPE_LINKS else "data/" + filename + '-comps.csv'
+ with open(fn, 'w', newline='') as csvfile:
+ csvwriter = csv.writer(csvfile, delimiter=';', quotechar='|', quoting=csv.QUOTE_MINIMAL)
+ csvwriter.writerow(["randomness parameter value"] + [name for name in TYPES.values()])
+ csvwriter.writerow(["randomness parameter value"] + [name for name in TYPES.keys()])
+ for i in range(len(results)):
+ row = [params[i]] + [results[i][k] for k in TYPES.keys()]
+ csvwriter.writerow(row)
+
+
+if __name__ == "__main__":
+ testOutputCount = []
+ avgLinksPerSize = []
+ avgCompsPerSize = []
+ maxLinksPerSize = []
+ maxCompsPerSize = []
+ minLinksPerSize = []
+ minCompsPerSize = []
+
+ sortedInput = []
+ #testInput = []
+
+ # ----------localised permutation inputs--------------
+ # randomness parameter: standard deviation
+ params = [fac * INCREMENT_LOC+0.00001 for fac in range(0, math.ceil(0.3 / INCREMENT_LOC), 1)]
+
+ for x in params:
+ sortedInput = [k for k in range(10000)]
+ avgCountsLinks = [0 for _ in range(MAX_TYPE_KEY + 1)]
+ avgCountsComps = [0 for _ in range(MAX_TYPE_KEY + 1)]
+ maxCountsLinks = [0 for _ in range(MAX_TYPE_KEY + 1)]
+ maxCountsComps = [0 for _ in range(MAX_TYPE_KEY + 1)]
+ minCountsLinks = [1000000000000 for _ in range(MAX_TYPE_KEY + 1)]
+ minCountsComps = [1000000000000 for _ in range(MAX_TYPE_KEY + 1)]
+
+ for zz in range(NUMBER_TESTS):
+ testInput = localizedShuffleByIndex(sortedInput, x)
+ print(len(testInput))
+ for heapType in TYPES.keys():
+ linkCount = 0
+ compCount = 0
+ testOutput = []
+ heap = PairingHeap(heapType, COUNT_TYPE_BOTH)
+ heap.make_heap()
+ for element in testInput:
+ node = Node(element)
+ (cc, lc) = heap.insert(node)
+ for i in range(len(testInput)):
+ (minNode, cc, lc) = heap.delete_min()
+ testOutput += [minNode.key]
+ compCount += cc
+ linkCount += lc
+ if isSorted(testOutput): # sanity check
+ #divide by size for visualization
+ avgCountsLinks[heapType] += (linkCount/10000) / NUMBER_TESTS
+ avgCountsComps[heapType] += (compCount/10000) / NUMBER_TESTS
+ maxCountsLinks[heapType] = max(maxCountsLinks[heapType],linkCount/10000)
+ maxCountsComps[heapType] = max(maxCountsComps[heapType],compCount/10000)
+ minCountsLinks[heapType] = min(minCountsLinks[heapType],linkCount/10000)
+ minCountsComps[heapType] = min(minCountsComps[heapType],compCount/10000)
+ else:
+ raise Exception("Invalid result for {}".format(TYPES[heapType]))
+ print("[{}: {}, {}/{}] \t Links: {} \t Comps: {}".format(
+ TYPES[heapType], x, zz+1, NUMBER_TESTS, linkCount, compCount))# diagnostics
+ for heapType in TYPES.keys():
+ print("[{}: {}, avg] \t Links: {} \t Comps: {}".format(TYPES[heapType], x, avgCountsLinks[heapType], avgCountsComps[heapType]))
+ avgLinksPerSize += [avgCountsLinks]
+ avgCompsPerSize += [avgCountsComps]
+ maxLinksPerSize += [maxCountsLinks]
+ maxCompsPerSize += [maxCountsComps]
+ minLinksPerSize += [minCountsLinks]
+ minCompsPerSize += [minCountsComps]
+ plot_avg_counts([avgCompsPerSize, avgLinksPerSize, maxCompsPerSize, maxLinksPerSize, minCompsPerSize, minLinksPerSize])
+ export_results(params, [avgCompsPerSize, avgLinksPerSize], COUNT_TYPE_BOTH, TYPES, "sorting-loc-new")
+
diff --git a/paper-sorting-sep-new.py b/paper-sorting-sep-new.py
new file mode 100644
index 0000000..00b11c9
--- /dev/null
+++ b/paper-sorting-sep-new.py
@@ -0,0 +1,183 @@
+#!/usr/bin/python3
+from random import shuffle
+import random
+import numpy as np
+import matplotlib.pyplot as plt
+import sys
+import signal
+import copy
+import math
+import csv
+from node import Node
+from pairing_heap import PairingHeap
+
+COUNT_TYPE_BOTH = 0
+COUNT_TYPE_LINKS = -1
+COUNT_TYPE_COMPS = -2
+MAXSIZE = 18
+NUMBER_TESTS = 20 # number of tests to run
+TEST_SIZES = [j for j in range(MAXSIZE)]
+LIST_LEN = 10000 # number of elements in test list
+TEST_SIZE = 10000 # number of elements in test list
+STEP_SIZE = 100
+INCREMENT_LOC = 0.005
+INCREMENT_SUBSEQS = 100
+TYPES = {0: "Pairing", 12: "Smooth"}
+MAX_TYPE_KEY = max(TYPES.keys())
+COLOURS = {0:'xkcd:fire engine red', 12:'xkcd:green'}
+SHADE_COLOURS = {0:'#fe4d4e', 12:'#58ab8e'}
+
+
+def isSorted(list0):
+ return all(list0[i] < list0[i + 1] for i in range(len(list0) - 1))
+
+
+def plot_avg_counts(avgCounts):
+ # colours from https://xkcd.com/color/rgb/
+ MARKERS_COMP = {0:"o", 12:"^"}#https://matplotlib.org/3.1.1/api/markers_api.html
+ MARKERS_LINK = {0:"o", 12:"D"}
+
+ plt.figure('avg number of operations by heap type')
+ for k in TYPES.keys():
+ print(k)
+ avgComps = [acounts[k] for acounts in avgCounts[0]]
+ maxComps = [acounts[k] for acounts in avgCounts[2]]
+ minComps = [acounts[k] for acounts in avgCounts[4]]
+ plt.plot([2**p for p in range(4, MAXSIZE)], avgComps[3:MAXSIZE-1], color=COLOURS[k], linestyle="-", marker=MARKERS_COMP[k], markerfacecolor=COLOURS[k], markersize=9, markeredgewidth=1, markeredgecolor='black', label=TYPES[k] + " comparisons")
+ plt.fill_between([2**p for p in range(4, MAXSIZE)], minComps[3:MAXSIZE-1], maxComps[3:MAXSIZE-1], color=SHADE_COLOURS[k], alpha=.3)
+ avgLinks = [acounts[k] for acounts in avgCounts[1]]
+ maxLinks = [acounts[k] for acounts in avgCounts[3]]
+ minLinks = [acounts[k] for acounts in avgCounts[5]]
+ plt.plot([2**p for p in range(4, MAXSIZE)], avgLinks[3:MAXSIZE-1], color=COLOURS[k], linestyle="--", marker=MARKERS_LINK[k], markerfacecolor=COLOURS[k], markersize=9, markeredgewidth=1, markeredgecolor='black', label=TYPES[k] + " links")
+ plt.fill_between([2**p for p in range(4, MAXSIZE)], minLinks[3:MAXSIZE-1], maxLinks[3:MAXSIZE-1], color=SHADE_COLOURS[k], alpha=.3)
+
+ #plt.title('Sorting random separable permutations', fontsize=25)
+ plt.xlabel('Input size', fontsize=26)
+ plt.ylabel('Avg. number of operations / size', fontsize=26)
+ plt.xticks(fontsize=20)
+ plt.yticks(fontsize=20)
+ plt.rc('legend',fontsize=26) # using a size in points
+ plt.legend()
+ plt.grid(True)
+ figure = plt.gcf() # get current figure
+ figure.set_size_inches(16, 18) # set figure's size manually to full screen
+ plt.savefig('plots/paper-sorting-sep-new.svg', bbox_inches='tight') # bbox_inches removes extra white spaces
+ plt.legend(loc='best')
+ plt.show()
+
+
+def export_results(params, results, countType, heapTypes, filename="dijkstra"):
+ # exports results of simulation as separate .csv files, one for links and one for comparisons, into /data directory
+ # each row contains randomness parameter value; plus one column containing the number of operations for each heap type
+ if countType == COUNT_TYPE_BOTH:
+ with open("data/" + filename + '-comps.csv', 'w', newline='') as csvfile:
+ csvwriter = csv.writer(csvfile, delimiter=';', quotechar='|', quoting=csv.QUOTE_MINIMAL)
+ csvwriter.writerow(["randomness parameter value"] + [name for name in TYPES.values()])
+ csvwriter.writerow(["randomness parameter value"] + [name for name in TYPES.keys()])
+ for i in range(len(results[0])):
+ row = [params[i]] + [results[0][i][k] for k in TYPES.keys()]
+ csvwriter.writerow(row)
+ with open("data/" + filename + '-links.csv', 'w', newline='') as csvfile:
+ csvwriter = csv.writer(csvfile, delimiter=';', quotechar='|', quoting=csv.QUOTE_MINIMAL)
+ csvwriter.writerow(["randomness parameter value"] + [name for name in TYPES.values()])
+ csvwriter.writerow(["randomness parameter value"] + [name for name in TYPES.keys()])
+ for i in range(len(results[1])):
+ row = [params[i]] + [results[1][i][k] for k in TYPES.keys()]
+ csvwriter.writerow(row)
+ else:
+ fn = "data/" + filename + '-links.csv' if countType == COUNT_TYPE_LINKS else "data/" + filename + '-comps.csv'
+ with open(fn, 'w', newline='') as csvfile:
+ csvwriter = csv.writer(csvfile, delimiter=';', quotechar='|', quoting=csv.QUOTE_MINIMAL)
+ csvwriter.writerow(["randomness parameter value"] + [name for name in TYPES.values()])
+ csvwriter.writerow(["randomness parameter value"] + [name for name in TYPES.keys()])
+ for i in range(len(results)):
+ row = [params[i]] + [results[i][k] for k in TYPES.keys()]
+ csvwriter.writerow(row)
+
+
+def separablePermutation(n):
+ assert (n & (n - 1) == 0) and n != 0 and n > 1, "n must be a power of two > 1" # bit magic
+
+ def generateSepPermutation(l, r):
+ flip = random.random() >= 0.5
+ if r - l == 1:
+ if flip == 0:
+ return [r, l]
+ else:
+ return [l, r]
+ else:
+ m = math.floor((l + r) / 2)
+ if flip == 0:
+ return generateSepPermutation(m + 1, r) + generateSepPermutation(l, m)
+ else:
+ return generateSepPermutation(l, m) + generateSepPermutation(m + 1, r)
+
+ return generateSepPermutation(0, n - 1)
+
+
+if __name__ == "__main__":
+ testOutputCount = []
+ avgLinksPerSize = []
+ avgCompsPerSize = []
+ maxLinksPerSize = []
+ maxCompsPerSize = []
+ minLinksPerSize = []
+ minCompsPerSize = []
+
+ sortedInput = []
+ # testInput = []
+
+ # ----------separable permutation---------------------
+ # parameter: length (must be power of two)
+ params = [2**p for p in range(1, MAXSIZE)]
+
+ for x in params:
+ sortedInput = [k for k in range(x)]
+ avgCountsLinks = [0 for _ in range(MAX_TYPE_KEY + 1)]
+ avgCountsComps = [0 for _ in range(MAX_TYPE_KEY + 1)]
+ maxCountsLinks = [0 for _ in range(MAX_TYPE_KEY + 1)]
+ maxCountsComps = [0 for _ in range(MAX_TYPE_KEY + 1)]
+ minCountsLinks = [1000000000000 for _ in range(MAX_TYPE_KEY + 1)]
+ minCountsComps = [1000000000000 for _ in range(MAX_TYPE_KEY + 1)]
+
+ for zz in range(NUMBER_TESTS):
+ testInput = copy.copy(sortedInput)
+ testInput = separablePermutation(x)
+ testInput[0] = -1
+ for heapType in TYPES.keys():
+ linkCount = 0
+ compCount = 0
+ testOutput = []
+ heap = PairingHeap(heapType, COUNT_TYPE_BOTH)
+ heap.make_heap()
+ for element in testInput:
+ node = Node(element)
+ (cc, lc) = heap.insert(node)
+ for i in range(len(testInput)):
+ (minNode, cc, lc) = heap.delete_min()
+ testOutput += [minNode.key]
+ compCount += cc
+ linkCount += lc
+ if isSorted(testOutput): # sanity check
+ #divide by size for visualization
+ avgCountsLinks[heapType] += (linkCount/x) / NUMBER_TESTS
+ avgCountsComps[heapType] += (compCount/x) / NUMBER_TESTS
+ maxCountsLinks[heapType] = max(maxCountsLinks[heapType],linkCount/x)
+ maxCountsComps[heapType] = max(maxCountsComps[heapType],compCount/x)
+ minCountsLinks[heapType] = min(minCountsLinks[heapType],linkCount/x)
+ minCountsComps[heapType] = min(minCountsComps[heapType],compCount/x)
+ else:
+ raise Exception("Invalid result for {}".format(TYPES[heapType]))
+ print("[{}: {}, {}/{}] \t Links: {} \t Comps: {}".format(
+ TYPES[heapType], x, zz+1, NUMBER_TESTS, linkCount, compCount))
+ for heapType in TYPES.keys():
+ print("[{}: {}, avg] \t Links: {} \t Comps: {}".format(TYPES[heapType], x, avgCountsLinks[heapType], avgCountsComps[heapType]))
+ avgLinksPerSize += [avgCountsLinks]
+ avgCompsPerSize += [avgCountsComps]
+ maxLinksPerSize += [maxCountsLinks]
+ maxCompsPerSize += [maxCountsComps]
+ minLinksPerSize += [minCountsLinks]
+ minCompsPerSize += [minCountsComps]
+ plot_avg_counts([avgCompsPerSize, avgLinksPerSize, maxCompsPerSize, maxLinksPerSize, minCompsPerSize, minLinksPerSize])
+ export_results(params, [avgCompsPerSize, avgLinksPerSize], COUNT_TYPE_BOTH, TYPES, "sorting-sep-new")
+
diff --git a/paper-sorting-subseq-new.py b/paper-sorting-subseq-new.py
new file mode 100644
index 0000000..f21db3d
--- /dev/null
+++ b/paper-sorting-subseq-new.py
@@ -0,0 +1,191 @@
+#!/usr/bin/python3
+from random import shuffle
+import random
+import numpy as np
+import matplotlib.pyplot as plt
+import sys
+import signal
+import copy
+import math
+import csv
+from node import Node
+from pairing_heap import PairingHeap
+from pairing_heap_interface import PairingHeapInterface
+from pairing_heap_standard import PairingHeapStandard
+from variants.pairing_heap_multipass import PairingHeapMultipass
+from variants.pairing_heap_ftb import PairingHeapFTB
+from variants.pairing_heap_btf import PairingHeapBTF
+from variants.pairing_heap_lazy import PairingHeapLazy
+from variants.pairing_heap_standard_stable import PairingHeapStandardStable
+from variants.pairing_heap_ftb_stable import PairingHeapFTBStable
+from variants.pairing_heap_btf_stable import PairingHeapBTFStable
+from variants.pairing_heap_multipass_stable import PairingHeapMultipassStable
+from variants.pairing_heap_lazy_stable import PairingHeapLazyStable
+from pairing_heap_smooth import PairingHeapSmooth
+from variants.pairing_heap_smooth_unstable import PairingHeapSmoothUnstable
+from smooth_heap_corey import SmoothHeapCorey
+
+COUNT_TYPE_BOTH = 0
+COUNT_TYPE_LINKS = -1
+COUNT_TYPE_COMPS = -2
+MAXSIZE = 17
+NUMBER_TESTS = 20 # number of tests to run
+TEST_SIZES = [j for j in range(MAXSIZE)]
+LIST_LEN = 10000 # number of elements in test list
+TEST_SIZE = 10000 # number of elements in test list
+STEP_SIZE = 100
+INCREMENT_SUBSEQS = 100
+TYPES = {0: "Pairing", 12: "Smooth"}
+MAX_TYPE_KEY = max(TYPES.keys())
+COLOURS = {0:'xkcd:fire engine red', 12:'xkcd:green'}
+SHADE_COLOURS = {0:'#fe4d4e', 12:'#58ab8e'}
+
+
+def isSorted(list0):
+ return all(list0[i] < list0[i + 1] for i in range(len(list0) - 1))
+
+
+def generateContSortedSubseq(llist, sublen):
+ listcopy = copy.copy(llist)
+ shuffle(listcopy)
+ res = []
+ l = 0
+ while l < len(llist):
+ clen = random.randint(1, sublen)
+ sublist = copy.copy(listcopy[l:min(l + clen, len(listcopy))])
+ sublist.sort()
+ res += sublist
+ l += clen
+ return res
+
+
+def plot_avg_counts(avgCounts):
+ # colours from https://xkcd.com/color/rgb/
+ MARKERS_COMP = {0:"o", 12:"^"}#https://matplotlib.org/3.1.1/api/markers_api.html
+ MARKERS_LINK = {0:"o", 12:"D"}
+ plt.figure('avg number of operations by heap type')
+ deviations = [fac*INCREMENT_SUBSEQS/200 for fac in range(1, math.ceil((TEST_SIZE/5)/INCREMENT_SUBSEQS), 1)]
+ deviations.reverse()
+ for k in TYPES.keys():
+ print(k)
+ avgComps = [acounts[k] for acounts in avgCounts[0]]
+ maxComps = [acounts[k] for acounts in avgCounts[2]]
+ minComps = [acounts[k] for acounts in avgCounts[4]]
+ plt.plot(deviations, avgComps, color=COLOURS[k], linestyle="-", marker=MARKERS_COMP[k], markerfacecolor=COLOURS[k], markersize=9, markeredgewidth=1, markeredgecolor='black', label=TYPES[k] + " comparisons")
+ plt.fill_between(deviations, minComps, maxComps, color=SHADE_COLOURS[k], alpha=.3)
+ avgLinks = [acounts[k] for acounts in avgCounts[1]]
+ maxLinks = [acounts[k] for acounts in avgCounts[3]]
+ minLinks = [acounts[k] for acounts in avgCounts[5]]
+ plt.plot(deviations, avgLinks, color=COLOURS[k], linestyle="--", marker=MARKERS_LINK[k], markerfacecolor=COLOURS[k], markersize=9, markeredgewidth=1, markeredgecolor='black', label=TYPES[k] + " links")
+ plt.fill_between(deviations, minLinks, maxLinks, color=SHADE_COLOURS[k], alpha=.3)
+
+
+ plt.xlabel('Avg. length of sorted blocks, % of size', fontsize=26)
+ plt.ylabel('Avg. number of operations / size', fontsize=26)
+ plt.xticks(fontsize=20)
+ plt.yticks(fontsize=20)
+ plt.rc('legend',fontsize=26) # using a size in points
+ plt.legend()
+ plt.grid(True)
+ plt.gca().invert_xaxis()
+ figure = plt.gcf() # get current figure
+ figure.set_size_inches(16, 18) # set figure's size manually to full screen
+ plt.savefig('plots/paper-sorting-subseq-new.svg', bbox_inches='tight') # bbox_inches removes extra white spaces
+ plt.legend(loc='best')
+ plt.show()
+
+
+def export_results(params, results, countType, heapTypes, filename="dijkstra"):
+ # exports results of simulation as separate .csv files, one for links and one for comparisons, into /data directory
+ # each row contains randomness parameter value; plus one column containing the number of operations for each heap type
+ if countType == COUNT_TYPE_BOTH:
+ with open("data/" + filename + '-comps.csv', 'w', newline='') as csvfile:
+ csvwriter = csv.writer(csvfile, delimiter=';', quotechar='|', quoting=csv.QUOTE_MINIMAL)
+ csvwriter.writerow(["randomness parameter value"] + [name for name in TYPES.values()])
+ csvwriter.writerow(["randomness parameter value"] + [name for name in TYPES.keys()])
+ for i in range(len(results[0])):
+ row = [params[i]] + [results[0][i][k] for k in TYPES.keys()]
+ csvwriter.writerow(row)
+ with open("data/" + filename + '-links.csv', 'w', newline='') as csvfile:
+ csvwriter = csv.writer(csvfile, delimiter=';', quotechar='|', quoting=csv.QUOTE_MINIMAL)
+ csvwriter.writerow(["randomness parameter value"] + [name for name in TYPES.values()])
+ csvwriter.writerow(["randomness parameter value"] + [name for name in TYPES.keys()])
+ for i in range(len(results[1])):
+ row = [params[i]] + [results[1][i][k] for k in TYPES.keys()]
+ csvwriter.writerow(row)
+ else:
+ fn = "data/" + filename + '-links.csv' if countType == COUNT_TYPE_LINKS else "data/" + filename + '-comps.csv'
+ with open(fn, 'w', newline='') as csvfile:
+ csvwriter = csv.writer(csvfile, delimiter=';', quotechar='|', quoting=csv.QUOTE_MINIMAL)
+ csvwriter.writerow(["randomness parameter value"] + [name for name in TYPES.values()])
+ csvwriter.writerow(["randomness parameter value"] + [name for name in TYPES.keys()])
+ for i in range(len(results)):
+ row = [params[i]] + [results[i][k] for k in TYPES.keys()]
+ csvwriter.writerow(row)
+
+
+if __name__ == "__main__":
+ testOutputCount = []
+ avgLinksPerSize = []
+ avgCompsPerSize = []
+ maxLinksPerSize = []
+ maxCompsPerSize = []
+ minLinksPerSize = []
+ minCompsPerSize = []
+
+ sortedInput = []
+ # testInput = []
+ # ----------continuous sorted subsequences inputs-----
+ # randomness parameter: subsequence lengths
+ params = [fac*INCREMENT_SUBSEQS for fac in range(1, math.ceil((TEST_SIZE/5)/INCREMENT_SUBSEQS), 1)]
+ params.reverse()
+
+ for x in params:
+ sortedInput = [k for k in range(LIST_LEN)]
+ avgCountsLinks = [0 for _ in range(MAX_TYPE_KEY + 1)]
+ avgCountsComps = [0 for _ in range(MAX_TYPE_KEY + 1)]
+ maxCountsLinks = [0 for _ in range(MAX_TYPE_KEY + 1)]
+ maxCountsComps = [0 for _ in range(MAX_TYPE_KEY + 1)]
+ minCountsLinks = [1000000000000 for _ in range(MAX_TYPE_KEY + 1)]
+ minCountsComps = [1000000000000 for _ in range(MAX_TYPE_KEY + 1)]
+
+ for zz in range(NUMBER_TESTS):
+ testInput = generateContSortedSubseq(sortedInput, x)
+ #print(len(testInput))
+ for heapType in TYPES.keys():
+ linkCount = 0
+ compCount = 0
+ testOutput = []
+ heap = PairingHeap(heapType, COUNT_TYPE_BOTH)
+ heap.make_heap()
+ for element in testInput:
+ node = Node(element)
+ (cc, lc) = heap.insert(node)
+ for i in range(len(testInput)):
+ (minNode, cc, lc) = heap.delete_min()
+ testOutput += [minNode.key]
+ compCount += cc
+ linkCount += lc
+ if isSorted(testOutput): # sanity check
+ #divide by size for visualization
+ avgCountsLinks[heapType] += (linkCount/LIST_LEN) / NUMBER_TESTS
+ avgCountsComps[heapType] += (compCount/LIST_LEN) / NUMBER_TESTS
+ maxCountsLinks[heapType] = max(maxCountsLinks[heapType],linkCount/LIST_LEN)
+ maxCountsComps[heapType] = max(maxCountsComps[heapType],compCount/LIST_LEN)
+ minCountsLinks[heapType] = min(minCountsLinks[heapType],linkCount/LIST_LEN)
+ minCountsComps[heapType] = min(minCountsComps[heapType],compCount/LIST_LEN)
+ else:
+ raise Exception("Invalid result for {}".format(TYPES[heapType]))
+ print("[{}: {}, {}/{}] \t Links: {} \t Comps: {}".format(
+ TYPES[heapType], x, zz+1, NUMBER_TESTS, linkCount, compCount))
+ for heapType in TYPES.keys():
+ print("[{}: {}, avg] \t Links: {} \t Comps: {}".format(TYPES[heapType], x, avgCountsLinks[heapType], avgCountsComps[heapType]))
+ avgLinksPerSize += [avgCountsLinks]
+ avgCompsPerSize += [avgCountsComps]
+ maxLinksPerSize += [maxCountsLinks]
+ maxCompsPerSize += [maxCountsComps]
+ minLinksPerSize += [minCountsLinks]
+ minCompsPerSize += [minCountsComps]
+ plot_avg_counts([avgCompsPerSize, avgLinksPerSize, maxCompsPerSize, maxLinksPerSize, minCompsPerSize, minLinksPerSize])
+ export_results(params, [avgCompsPerSize, avgLinksPerSize], COUNT_TYPE_BOTH, TYPES, "sorting-subseq-new")
+
diff --git a/plots/paper-dijkstra-new.svg b/plots/paper-dijkstra-new.svg
new file mode 100644
index 0000000..b581527
--- /dev/null
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diff --git a/plots/paper-permutation-separable.pdf b/plots/paper-permutation-separable.pdf
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diff --git a/smooth_heap.py b/smooth_heap.py
new file mode 100644
index 0000000..f1edb87
--- /dev/null
+++ b/smooth_heap.py
@@ -0,0 +1,313 @@
+#!/usr/bin/python3
+from node import Node
+import math
+from pairing_heap_interface import PairingHeapInterface
+
+class SmoothHeapCorey(PairingHeapInterface):
+ forest=[] #list storing roots of all top-level trees not in buffer
+ buffer=[] #decrease buffer
+ minNode=None
+ size=0
+
+ def __init__(self, root=None):
+ self.forest=[]
+ self.buffer=[]
+ if root!=None:
+ root.parent=None
+ root.nextSibling=root
+ self.minNode=root
+ self.forest+=[root]
+ #self.size=0
+
+ def make_heap(self):
+ #this is equivalent to init
+ pass
+
+ def find_min(self):
+ return self.minNode
+
+ def listPreOrderHelper(self, root):
+ res=[]
+ if root.rightChild==None:
+ return [root.key]
+ else:
+ current=root.rightChild
+ res+=[root.key, self.listPreOrderHelper(current)]
+ while current.nextSibling!=root.rightChild:
+ current=current.nextSibling
+ res+=[self.listPreOrderHelper(current)]
+ return [res]
+
+ def listPreOrder(self):
+ res=[]
+ buf=[]
+ for item in self.forest:
+ res+=self.listPreOrderHelper(item)
+ print(res)
+ for elem in self.buffer:
+ buf+=self.listPreOrderHelper(elem)
+ print("buffer: {}".format(buf))
+
+ def stable_link_left(self, left, right):
+ #left node becomes parent of right node
+ #print("left-linking nodes {} and {}".format(left.key, right.key))
+ if left.rightChild!=None:
+ right.nextSibling = left.rightChild.nextSibling
+ left.rightChild.nextSibling=right
+ else:
+ right.nextSibling = right
+ left.rightChild=right
+ right.parent=left
+
+ def stable_link_right(self, left, right):
+ #right node becomes parent of left node
+ if right.rightChild==None:
+ right.rightChild=left
+ left.nextSibling=left
+ else:
+ left.nextSibling=right.rightChild.nextSibling
+ right.rightChild.nextSibling=left
+ left.parent=right
+
+ def insert(self, node):
+ #concatenates node to list of trees in pool
+ if node==None:
+ return (0,0)#no comparisons, no links
+ node.nextSibling=node
+ node.parent=None
+ self.forest+=[node]
+ self.size+=1
+ if self.minNode==None or node.key<=self.minNode.key:
+ self.minNode=node
+ #print("Result of insert is {}.".format(self.listInorder()))
+ return (1, 0)#1 comparison, no links
+
+ def merge(self, heap2):
+ if heap2==None:
+ return(0,0)
+ compCount=0
+ linkCount=0
+ if len(self.forest)+len(self.buffer)>len(heap2.forest)+len(heap2.buffer):
+ #first heap larger than second
+ (cc,lc)=heap2.clean_buffer()
+ linkCount+=lc
+ compCount+=cc+1#accounting for minNode comparison (at the end) as well
+ self.forest+=heap2.forest
+ else:
+ (cc,lc)=self.clean_buffer()
+ linkCount+=lc
+ compCount+=cc+1#accounting for minNode comparison (at the end) as well
+ self.forest=heap2.forest+self.forest
+ self.buffer=heap2.buffer
+ self.size+=heap2.size
+ if(self.minNode.key>=heap2.minNode.key):
+ self.minNode=heap2.minNode
+ return (compCount, linkCount)
+
+ def delete_min(self):
+ (compCount, linkCount)=self.clean_buffer()
+ if self.minNode==None or len(self.forest)+len(self.buffer)==0:#this should be the same
+ return (None, 0, 0)
+ minKey = self.minNode.key
+ minKeyNode = self.minNode
+ minNodeChildren=[]
+
+ if self.minNode.rightChild!=None:
+ minNodeChildren+=[self.minNode.rightChild]
+ self.minNode.rightChild.parent=None
+ current=self.minNode.rightChild.nextSibling
+ self.minNode.rightChild.nextSibling=self.minNode.rightChild
+
+ while current!=self.minNode.rightChild:
+ minNodeChildren+=[current]
+ tempNode = current
+ current=current.nextSibling
+ tempNode.nextSibling = tempNode
+ tempNode.parent = None
+ idx = self.forest.index(self.minNode)#should we count this somehow?
+ self.forest = self.forest[:idx]+minNodeChildren+self.forest[idx+1:]#replace minNode with its children
+ self.size-=1
+ (cc, lc)=self.treapify()
+ return (minKeyNode, compCount+cc, linkCount+lc)
+
+ def treapify(self):
+ #links roots in pool (forest) into treap and returns number of links/comparisons
+ #this uses the pseudocode of delete-min from https://arxiv.org/abs/1802.05471
+ linkCount=0#counts only number of links
+ compCount=0#counts only number of comparisons
+ if len(self.forest)==0: #pool is empty
+ self.minNode=None
+ return (compCount, linkCount)
+
+ elif len(self.forest)==1:
+ self.minNode=self.forest[0]
+ return (compCount, linkCount)
+
+ else:
+ i=0
+ curr_forest=self.forest
+ while i<len(curr_forest)-1:
+ compCount+=1#first if-else comparison
+ if curr_forest[i].key<curr_forest[i+1].key:
+ i=i+1
+ else:
+ skip=False
+ while i>0:
+ compCount+=1
+ linkCount+=1
+ if curr_forest[i-1].key>curr_forest[i+1].key:
+ #stable-link predecessor as parent of current node
+ self.stable_link_left(curr_forest[i-1], curr_forest[i])
+ #remove node at index i from top-list
+ curr_forest=curr_forest[:i]+curr_forest[i+1:]
+ i=i-1
+ else:
+ #stable-link successor as parent of current node
+ self.stable_link_right(curr_forest[i], curr_forest[i+1])
+ #remove node at index i from top-list
+ curr_forest=curr_forest[:i]+curr_forest[i+1:]
+ #i=i+1
+ skip=True
+ break
+ if not skip:#i==0
+ #stable-link current as leftmost child of successor
+ self.stable_link_right(curr_forest[i], curr_forest[i+1])
+ #remove node from top-list
+ curr_forest=curr_forest[i+1:]
+ linkCount+=1
+
+ while i>0:
+ #stable-link predecessor as parent of current node
+ self.stable_link_left(curr_forest[i-1], curr_forest[i])
+ curr_forest=curr_forest[:i]
+ linkCount+=1
+ i=i-1
+ self.forest=curr_forest
+ assert len(self.forest)==1
+ self.minNode=self.forest[0]
+ return (compCount, linkCount)
+
+
+ def mergesort(self, llist):
+ #standard mergesort, implemented to count comparisons properly
+ if len(llist)<2:
+ return 0, llist
+ split_idx = int(math.floor(len(llist)/2))
+ compsleft, lleft = self.mergesort(llist[:split_idx])
+ compsright, lright = self.mergesort(llist[split_idx:])
+ l=0
+ r=0
+ comps = compsleft+compsright
+ sorted = []
+ while l+r<len(llist):
+ if r==len(lright) or (l<len(lleft) and lleft[l].key<=lright[r].key):
+ sorted+=[lleft[l]]
+ l+=1
+ else:
+ sorted+=[lright[r]]
+ r+=1
+ comps+=1
+ return comps, sorted
+
+ def clean_buffer(self):
+ if len(self.buffer)==0:#buffer is empty
+ return (0,0)
+ comps,self.buffer = self.mergesort(self.buffer)
+ self.buffer.reverse()
+ n=len(self.buffer)
+
+ while len(self.buffer)>1:
+ self.stable_link_right(self.buffer[0], self.buffer[1])
+ self.buffer=self.buffer[1:]
+
+ treapified = self.buffer[0]
+ self.buffer=[]
+ (compCount,linkCount)=self.merge(SmoothHeapCorey(treapified))
+
+ return (compCount+comps, linkCount+n-1) #(n-1)links while consolidating
+
+ def decrease_key(self, node, diff):
+ assert node!=None
+ linkCount=0
+ compCount=0
+ node.key = node.key-diff
+ #if self.minNode==None or node.key<self.minNode.key:
+ # self.minNode=node
+ #compCount+=1
+
+ if node.parent==None and node.rightChild==None: #node is root and has no children
+ #could just leave this in place
+ if node in self.forest:
+ idx = self.forest.index(node)
+ self.forest=self.forest[:idx]+self.forest[idx+1:]
+ self.buffer+=[node]
+ elif node in self.buffer:
+ pass
+ else:
+ self.listPreOrder()
+ raise Exception("node with key {} is not in heap".format(node.key))
+
+ elif node.parent==None: #node is a root and has children
+ leftChild=node.rightChild.nextSibling
+ if leftChild.nextSibling!=leftChild:
+ node.rightChild.nextSibling=leftChild.nextSibling#cut out leftmost child
+ else:
+ node.rightChild=None
+ leftChild.nextSibling=leftChild
+ leftChild.parent=None
+ if node in self.forest:
+ idx = self.forest.index(node)#remove node from pool and replace with leftChild
+ self.forest = self.forest[:idx] + [leftChild] + self.forest[idx+1:]
+ self.buffer+=[node]
+ elif node in self.buffer:
+ pass
+ else:
+ self.listPreOrder()
+ raise Exception("node with key {} is not in heap".format(node.key))
+ else:#node is not a root
+ leftChild=None
+ if node.rightChild!=None:
+ leftChild=node.rightChild.nextSibling
+ leftChild.parent=node.parent
+ current=node.parent.rightChild
+
+ if node.nextSibling==node and leftChild!=None:#node not a leaf and has no siblings
+ if leftChild.nextSibling!=leftChild:
+ node.rightChild.nextSibling=leftChild.nextSibling#cut out leftmost child
+ else:
+ node.rightChild=None
+ leftChild.nextSibling=leftChild
+ node.parent.rightChild = leftChild
+
+ elif leftChild!=None:#node is not a leaf and has siblings
+ if leftChild.nextSibling!=leftChild:
+ node.rightChild.nextSibling=leftChild.nextSibling#cut out leftmost child
+ else:
+ node.rightChild=None
+ while current.nextSibling!=node:#find predecessor of node
+ current=current.nextSibling
+ current.nextSibling=leftChild
+ leftChild.nextSibling=node.nextSibling
+ if node.parent.rightChild==node:
+ node.parent.rightChild=leftChild
+
+ elif node.nextSibling!=node:#node is leaf and has siblings
+ while current.nextSibling!=node:
+ current=current.nextSibling
+ current.nextSibling=node.nextSibling
+ if node.parent.rightChild==node:
+ node.parent.rightChild=current
+
+ else: #node is leaf and has no siblings
+ node.parent.rightChild=None
+
+ node.parent=None
+ node.nextSibling=node
+ self.buffer+=[node]
+
+ if len(self.buffer)>math.ceil(math.log(self.size,2)):
+ #(cc2, lc2)=self.clean_buffer()
+ (cc2, lc2)=self.clean_buffer()
+ compCount+=cc2
+ linkCount+=lc2
+ return (compCount, linkCount)
diff --git a/smooth_heap_l.py b/smooth_heap_l.py
new file mode 100644
index 0000000..0c62c78
--- /dev/null
+++ b/smooth_heap_l.py
@@ -0,0 +1,226 @@
+#!/usr/bin/python3
+from node import Node
+import math
+from pairing_heap_interface import PairingHeapInterface
+
+class SmoothHeapL(PairingHeapInterface):
+ forest=[] #list storing roots of all top-level trees not in buffer
+ minNode=None
+
+ def __init__(self, root=None):
+ self.forest=[]
+ if root!=None:
+ root.parent=None
+ root.nextSibling=root
+ self.minNode=root
+ self.forest+=[root]
+
+ def make_heap(self):
+ #this is equivalent to init
+ pass
+
+ def find_min(self):
+ return self.minNode
+
+ def listPreOrderHelper(self, root):
+ res=[]
+ if root.rightChild==None:
+ return [root.key]
+ else:
+ current=root.rightChild
+ res+=[root.key, self.listPreOrderHelper(current)]
+ while current.nextSibling!=root.rightChild:
+ current=current.nextSibling
+ res+=[self.listPreOrderHelper(current)]
+ return [res]
+
+ def listPreOrder(self):
+ res=[]
+ buf=[]
+ for item in self.forest:
+ res+=self.listPreOrderHelper(item)
+ print(res)
+
+ def stable_link_left(self, left, right):
+ #left node becomes parent of right node
+ #print("left-linking nodes {} and {}".format(left.key, right.key))
+ if left.rightChild!=None:
+ right.nextSibling = left.rightChild.nextSibling
+ left.rightChild.nextSibling=right
+ else:
+ right.nextSibling = right
+ left.rightChild=right
+ right.parent=left
+
+ def stable_link_right(self, left, right):
+ #right node becomes parent of left node
+ if right.rightChild==None:
+ right.rightChild=left
+ left.nextSibling=left
+ else:
+ left.nextSibling=right.rightChild.nextSibling
+ right.rightChild.nextSibling=left
+ left.parent=right
+
+ def insert(self, node):
+ #concatenates node to list of trees in pool
+ if node==None:
+ return (0,0)#no comparisons, no links
+ node.nextSibling=node
+ node.parent=None
+ self.forest+=[node]
+ #if self.minNode==None or node.key<self.minNode.key:
+ # self.minNode=node
+ #print("Result of insert is {}.".format(self.listInorder()))
+ return (0, 0)#1 comparison, no links
+
+ def merge(self, heap2):
+ if heap2==None:
+ return(0,0)
+ compCount=0
+ linkCount=0
+ if len(self.forest)>len(heap2.forest):
+ #first heap larger than second
+ self.forest+=heap2.forest
+ else:
+ self.forest=heap2.forest+self.forest
+ #if(self.minNode.key>heap2.minNode.key):
+ # self.minNode=heap2.minNode
+ return (compCount, linkCount)#TODO add 1 if comparing minnode
+
+ def delete_min(self):
+ if (len(self.forest)==0):
+ return(None,0,0)
+ (cc, lc)=self.treapify()
+ assert len(self.forest)==1
+ minKey = self.minNode.key
+ minKeyNode = self.minNode
+ minNodeChildren=[]
+
+ if self.minNode.rightChild!=None:
+ minNodeChildren+=[self.minNode.rightChild]
+ self.minNode.rightChild.parent=None
+ current=self.minNode.rightChild.nextSibling
+ self.minNode.rightChild.nextSibling=self.minNode.rightChild
+
+ while current!=self.minNode.rightChild:
+ minNodeChildren+=[current]
+ tempNode = current
+ current=current.nextSibling
+ tempNode.nextSibling = tempNode
+ tempNode.parent = None
+ self.forest = minNodeChildren
+ #print('###')
+ #print(minKeyNode.key)
+ return (minKeyNode, cc, lc)
+
+ def treapify(self):
+ #links roots in pool (forest) into treap and returns number of links/comparisons
+ #this uses the pseudocode of delete-min from https://arxiv.org/abs/1802.05471
+ linkCount=0#counts only number of links
+ compCount=0#counts only number of comparisons
+ fs = len(self.forest)
+ if len(self.forest)==0: #pool is empty
+ self.minNode=None
+ return (compCount, linkCount)
+
+ elif len(self.forest)==1:
+ self.minNode=self.forest[0]
+ return (compCount, linkCount)
+
+ else:
+ i=0
+ curr_forest=self.forest
+ while i<len(curr_forest)-1:
+ compCount+=1#first if-else comparison
+ if curr_forest[i].key<curr_forest[i+1].key:
+ i=i+1
+ else:
+ skip=False
+ while i>0:
+ compCount+=1
+ linkCount+=1
+ if curr_forest[i-1].key>curr_forest[i+1].key:
+ #stable-link predecessor as parent of current node
+ self.stable_link_left(curr_forest[i-1], curr_forest[i])
+ #remove node at index i from top-list
+ curr_forest=curr_forest[:i]+curr_forest[i+1:]
+ i=i-1
+ else:
+ #stable-link successor as parent of current node
+ self.stable_link_right(curr_forest[i], curr_forest[i+1])
+ #remove node at index i from top-list
+ curr_forest=curr_forest[:i]+curr_forest[i+1:]
+ #i=i+1
+ skip=True
+ break
+ if not skip:#i==0
+ #stable-link current as leftmost child of successor
+ self.stable_link_right(curr_forest[i], curr_forest[i+1])
+ #remove node from top-list
+ curr_forest=curr_forest[i+1:]
+ linkCount+=1
+
+ while i>0:
+ #stable-link predecessor as parent of current node
+ self.stable_link_left(curr_forest[i-1], curr_forest[i])
+ curr_forest=curr_forest[:i]
+ linkCount+=1
+ i=i-1
+ self.forest=curr_forest
+ assert len(self.forest)==1
+ self.minNode=self.forest[0]
+ assert(fs-1 == linkCount)
+ return (compCount, linkCount)
+
+
+ def mergesort(self, llist):
+ #standard mergesort, implemented to count comparisons properly
+ if len(llist)<2:
+ return 0, llist
+ split_idx = int(math.floor(len(llist)/2))
+ compsleft, lleft = self.mergesort(llist[:split_idx])
+ compsright, lright = self.mergesort(llist[split_idx:])
+ l=0
+ r=0
+ comps = compsleft+compsright
+ sorted = []
+ while l+r<len(llist):
+ if r==len(lright) or (l<len(lleft) and lleft[l].key<=lright[r].key):
+ sorted+=[lleft[l]]
+ l+=1
+ else:
+ sorted+=[lright[r]]
+ r+=1
+ comps+=1
+ return comps, sorted
+
+ def decrease_key(self, node, diff):
+ assert node!=None
+ node.key = node.key-diff
+
+ #concatenates node to list of trees in pool
+
+ if node.parent==None: #node is a root and has children
+ if node in self.forest:
+ pass #leave in-place
+ else:
+ self.listPreOrder()
+ raise Exception("node with key {} is not in heap".format(node.key))
+ else:#node is not a root
+
+ if node.nextSibling==node:#node has no siblings
+ node.parent.rightChild=None
+
+ else:#node has siblings
+ current=node.nextSibling
+ while current.nextSibling!=node:#find predecessor of node
+ current=current.nextSibling
+ current.nextSibling=node.nextSibling
+ if node.parent.rightChild==node:
+ node.parent.rightChild=current
+
+ node.parent=None
+ node.nextSibling=node
+ self.forest+=[node]
+ return (0, 0)
--
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