Uploaded Held-Karp to GitHub

.classpath

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+<?xml version="1.0" encoding="UTF-8"?>
+<classpath>
+	<classpathentry kind="src" path="src"/>
+	<classpathentry kind="con" path="org.eclipse.jdt.launching.JRE_CONTAINER/org.eclipse.jdt.internal.debug.ui.launcher.StandardVMType/JavaSE-1.8"/>
+	<classpathentry kind="output" path="bin"/>
+</classpath>

LICENSE

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+MIT License
+
+Copyright (c) [2021] [Samuel C. Donovan]
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.

README.md

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+# Held-Karp implementation for solving the TSP
+
+This is my implementation of the Held-Karp dynamic programming algorithm. It is an exact algorithm, and as such, returns the optimal path and cost for a given data set.
+
+## Why Held-Karp?
+The problem for which this project was designed for required an exact solution for all n <= 20 in less than one minute.
+This algorithm has a proposed time complexity of O(n^2 * 2n). For n = 20:   20^2 * (2*20) ≈ 16000, which is drastically lower than one minute. Though my implementation runs quite a bit slower than this, (for n = 20, it runs in approx. 20 seconds) it will still run in less than one minute for n <= 20, and will find the shortest path and its cost. 
+For n > 20,  the running time starts to get exponentially larger. It becomes infeasible to run this implementation on n > 30, where the running time is several hours long. This is not necessarily due to an issue with my implementation, but is more of an issue with the algorithm and the TSP in general, as the TSP is an NP-Hard problem and as such, finding exact solutions becomes increasingly more expensive the larger n is.

data/test1-2020.txt

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+1	110	40
+2	2	63
+3	172	25
+4	182	68
+5	192	39
+6	144	81
+7	76	31
+8	192	73
+9	16	63
+10	80	78
+11	70	79
+12	36	8

data/test1-21.txt

@@ -0,0 +1,12 @@
+1	85	93
+2	80	35
+3	38	19
+4	65	9
+5	38	5
+6	52	80
+7	76	84
+8	94	41
+9	99	63
+10	30	47
+11	53	98
+12	80	43

data/test2-2020.txt

@@ -0,0 +1,14 @@
+1	-34	85
+2	49	184
+3	85	18
+4	72	164
+5	-22	-8
+6	-8	0
+7	-53	172
+8	-84	58
+9	19	73
+10	69	26
+11	29	4
+12	-6	151
+13	67	90
+14	0	77

data/test2-21.txt

@@ -0,0 +1,14 @@
+1	-63	35
+2	99	91
+3	73	0
+4	27	20
+5	-6	-52
+6	48	-146
+7	-19	-127
+8	4	-22
+9	-36	-28
+10	91	-191
+11	-24	-38
+12	82	-169
+13	82	31
+14	-37	-16

data/test3-2020.txt

@@ -0,0 +1,18 @@
+1	10834	18658
+2	30756	3345
+3	19970	24600
+4	14669	25177
+5	29650	8784
+6	24669	18572
+7	3349	10191
+8	6553	8852
+9	4889	2771
+10	13418	28914
+11	30610	25659
+12	13919	18570
+13	-16	23422
+14	20855	21944
+15	15444	29757
+16	24671	11060
+17	4399	19731
+18	0	0

data/test3-21.txt

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+1	26378	4886
+2	30564	320
+3	12319	16264
+4	3251	28593
+5	4817	21078
+6	25713	3087
+7	8323	628
+8	26627	4370
+9	10504	19168
+10	5242	2316
+11	31388	65
+12	23941	27464
+13	30708	1016
+14	15295	22466
+15	9403	24404
+16	15454	27513
+17	16349	13418

data/test4-2020.txt

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+1	27985	147343
+2	20160	3508
+3	27960	214746
+4	14294	25899
+5	26573	3634
+6	773	11455
+7	14381	36932
+8	5279	72300
+9	14349	11721
+10	21645	69622
+11	25098	31683
+12	3595	273115
+13	1533	129427
+14	22560	111589
+15	5798	129816
+16	9629	58991
+17	25167	3126
+18	27305	248606
+19	7109	121380
+20	25743	36309
+21	6773	102159
+22	14012	35326
+23	6030	2565
+24	5849	78210
+25	22839	133162
+26	22688	60633
+27	8192	91821
+28	25685	71043
+29	21098	125138
+30	27342	13142
+31	22831	219085
+32	19628	22899

data/test4-21.txt

@@ -0,0 +1,27 @@
+1	72998	904383
+2	17182	401303
+3	42526	103033
+4	33855	446405
+5	38508	281016
+6	88516	456574
+7	79887	508613
+8	44426	328114
+9	14075	59229
+10	3342	981173
+11	18366	400905
+12	92080	564993
+13	43136	259655
+14	15968	820490
+15	27865	942274
+16	9564	263346
+17	65022	596732
+18	45058	619031
+19	32666	238232
+20	51384	672851
+21	88632	343223
+22	66179	840350
+23	76844	529953
+24	19202	711999
+25	12022	731249
+26	94124	453766
+27	60316	3439

data/train1.txt

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+1 1 1
+2 5 5
+3 10 3
+4 2 7

data/train2.txt

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+1 38 20
+2 39 26
+3 40 25
+4 36 23
+5 38 13
+6 37 20
+7 41 9
+8 36 -5

data/train3.txt

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+1 16 96
+2 46 94
+3 20 32
+4 22 43
+5 25 57
+6 22 16
+7 20 87
+8 17 16
+9 66 97