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"text/plain": [
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"text/plain": [
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"<matplotlib.figure.Figure at 0x114f26ac8>"
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"<matplotlib.figure.Figure at 0x111d20940>"
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]
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]
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},
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},
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"metadata": {},
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"metadata": {},
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"name": "stdout",
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"output_type": "stream",
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"output_type": "stream",
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"text": [
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"text": [
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"alltours: 9 cities ⇒ tour length 2450 (in 1.088 sec)\n"
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"alltours: 9 cities ⇒ tour length 2450 (in 1.040 sec)\n"
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]
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]
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},
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},
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{
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{
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"data": {
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"data": {
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truncated
|
||||||
"text/plain": [
|
"text/plain": [
|
||||||
"<matplotlib.figure.Figure at 0x11727a240>"
|
"<matplotlib.figure.Figure at 0x111f83a58>"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
@@ -372,14 +372,14 @@
|
|||||||
"name": "stdout",
|
"name": "stdout",
|
||||||
"output_type": "stream",
|
"output_type": "stream",
|
||||||
"text": [
|
"text": [
|
||||||
"alltours: 10 cities ⇒ tour length 2720 (in 1.521 sec)\n"
|
"alltours: 10 cities ⇒ tour length 2720 (in 1.470 sec)\n"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
"data": {
|
"data": {
|
||||||
"image/png": 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truncated
|
"image/png": 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truncated
|
||||||
"text/plain": [
|
"text/plain": [
|
||||||
"<matplotlib.figure.Figure at 0x114f28ba8>"
|
"<matplotlib.figure.Figure at 0x111d2e198>"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
@@ -472,14 +472,14 @@
|
|||||||
"name": "stdout",
|
"name": "stdout",
|
||||||
"output_type": "stream",
|
"output_type": "stream",
|
||||||
"text": [
|
"text": [
|
||||||
"nn: 200 cities ⇒ tour length 11477 (in 0.006 sec)\n"
|
"nn: 200 cities ⇒ tour length 11477 (in 0.005 sec)\n"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
"data": {
|
"data": {
|
||||||
"image/png": 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truncated
|
||||||
"text/plain": [
|
"text/plain": [
|
||||||
"<matplotlib.figure.Figure at 0x117298f28>"
|
"<matplotlib.figure.Figure at 0x111d2f0f0>"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
@@ -499,14 +499,14 @@
|
|||||||
"name": "stdout",
|
"name": "stdout",
|
||||||
"output_type": "stream",
|
"output_type": "stream",
|
||||||
"text": [
|
"text": [
|
||||||
"nn: 1998 cities ⇒ tour length 33688 (in 0.601 sec)\n"
|
"nn: 1998 cities ⇒ tour length 33688 (in 0.523 sec)\n"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
"data": {
|
"data": {
|
||||||
"image/png": 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truncated
|
||||||
"text/plain": [
|
"text/plain": [
|
||||||
"<matplotlib.figure.Figure at 0x114f1be80>"
|
"<matplotlib.figure.Figure at 0x111f8f048>"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
@@ -540,7 +540,7 @@
|
|||||||
"data": {
|
"data": {
|
||||||
"image/png": 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truncated
|
||||||
"text/plain": [
|
"text/plain": [
|
||||||
"<matplotlib.figure.Figure at 0x11929c198>"
|
"<matplotlib.figure.Figure at 0x1161261d0>"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
@@ -606,7 +606,7 @@
|
|||||||
"data": {
|
"data": {
|
||||||
"image/png": 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truncated
|
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truncated
|
||||||
"text/plain": [
|
"text/plain": [
|
||||||
"<matplotlib.figure.Figure at 0x1192829b0>"
|
"<matplotlib.figure.Figure at 0x112014470>"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
@@ -626,14 +626,14 @@
|
|||||||
"name": "stdout",
|
"name": "stdout",
|
||||||
"output_type": "stream",
|
"output_type": "stream",
|
||||||
"text": [
|
"text": [
|
||||||
"rep_nn: 200 cities ⇒ tour length 10461 (in 0.159 sec)\n"
|
"rep_nn: 200 cities ⇒ tour length 10461 (in 0.143 sec)\n"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
"data": {
|
"data": {
|
||||||
"image/png": 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truncated
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truncated
|
||||||
"text/plain": [
|
"text/plain": [
|
||||||
"<matplotlib.figure.Figure at 0x1141db0b8>"
|
"<matplotlib.figure.Figure at 0x110faa0f0>"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
@@ -678,7 +678,7 @@
|
|||||||
"data": {
|
"data": {
|
||||||
"image/png": "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\n",
|
"image/png": "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\n",
|
||||||
"text/plain": [
|
"text/plain": [
|
||||||
"<matplotlib.figure.Figure at 0x1178c7f98>"
|
"<matplotlib.figure.Figure at 0x11251fbe0>"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
@@ -717,7 +717,7 @@
|
|||||||
"data": {
|
"data": {
|
||||||
"image/png": "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\n",
|
"image/png": "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\n",
|
||||||
"text/plain": [
|
"text/plain": [
|
||||||
"<matplotlib.figure.Figure at 0x1178d00b8>"
|
"<matplotlib.figure.Figure at 0x1125f8908>"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
@@ -815,7 +815,7 @@
|
|||||||
"source": [
|
"source": [
|
||||||
"# Improved Nearest Neighbor Algorithms\n",
|
"# Improved Nearest Neighbor Algorithms\n",
|
||||||
"\n",
|
"\n",
|
||||||
"Here are three ways of improving nearest neighbor algorithms:"
|
"Here are two ways of improving nearest neighbor algorithms:"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
@@ -828,10 +828,6 @@
|
|||||||
" \"Improve the tour produced by nn_tsp.\"\n",
|
" \"Improve the tour produced by nn_tsp.\"\n",
|
||||||
" return improve_tour(nn_tsp(cities))\n",
|
" return improve_tour(nn_tsp(cities))\n",
|
||||||
"\n",
|
"\n",
|
||||||
"def improve_rep_nn_tsp(cities, k=15):\n",
|
|
||||||
" \"Improve the tour produced by rep_nn_tsp.\"\n",
|
|
||||||
" return improve_tour(rep_nn_tsp(cities, k))\n",
|
|
||||||
"\n",
|
|
||||||
"def rep_improve_nn_tsp(cities, k=5):\n",
|
"def rep_improve_nn_tsp(cities, k=5):\n",
|
||||||
" \"Run nn_tsp from k different starts, improve each tour; keep the best.\"\n",
|
" \"Run nn_tsp from k different starts, improve each tour; keep the best.\"\n",
|
||||||
" return shortest_tour(improve_tour(nn_tsp(cities, start)) \n",
|
" return shortest_tour(improve_tour(nn_tsp(cities, start)) \n",
|
||||||
@@ -854,14 +850,14 @@
|
|||||||
"name": "stdout",
|
"name": "stdout",
|
||||||
"output_type": "stream",
|
"output_type": "stream",
|
||||||
"text": [
|
"text": [
|
||||||
"nn: 200 cities ⇒ tour length 11477 (in 0.006 sec)\n"
|
"nn: 200 cities ⇒ tour length 11477 (in 0.005 sec)\n"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
"data": {
|
"data": {
|
||||||
"image/png": 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truncated
|
||||||
"text/plain": [
|
"text/plain": [
|
||||||
"<matplotlib.figure.Figure at 0x117a999b0>"
|
"<matplotlib.figure.Figure at 0x11260bdd8>"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
@@ -881,14 +877,14 @@
|
|||||||
"name": "stdout",
|
"name": "stdout",
|
||||||
"output_type": "stream",
|
"output_type": "stream",
|
||||||
"text": [
|
"text": [
|
||||||
"improve_nn: 200 cities ⇒ tour length 9523 (in 0.070 sec)\n"
|
"improve_nn: 200 cities ⇒ tour length 9523 (in 0.087 sec)\n"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
"data": {
|
"data": {
|
||||||
"image/png": 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truncated
|
||||||
"text/plain": [
|
"text/plain": [
|
||||||
"<matplotlib.figure.Figure at 0x1178c7d30>"
|
"<matplotlib.figure.Figure at 0x1125fd160>"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
@@ -908,14 +904,14 @@
|
|||||||
"name": "stdout",
|
"name": "stdout",
|
||||||
"output_type": "stream",
|
"output_type": "stream",
|
||||||
"text": [
|
"text": [
|
||||||
"rep_improve_nn: 200 cities ⇒ tour length 9450 (in 0.333 sec)\n"
|
"rep_improve_nn: 200 cities ⇒ tour length 9450 (in 0.472 sec)\n"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
"data": {
|
"data": {
|
||||||
"image/png": 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truncated
|
||||||
"text/plain": [
|
"text/plain": [
|
||||||
"<matplotlib.figure.Figure at 0x1186c89e8>"
|
"<matplotlib.figure.Figure at 0x1155e9eb8>"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
@@ -956,14 +952,14 @@
|
|||||||
"name": "stdout",
|
"name": "stdout",
|
||||||
"output_type": "stream",
|
"output_type": "stream",
|
||||||
"text": [
|
"text": [
|
||||||
"rep_improve_nn, 50: 200 cities ⇒ tour length 9264 (in 3.631 sec)\n"
|
"rep_improve_nn, 50: 200 cities ⇒ tour length 9264 (in 3.695 sec)\n"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
"data": {
|
"data": {
|
||||||
"image/png": 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truncated
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truncated
|
||||||
"text/plain": [
|
"text/plain": [
|
||||||
"<matplotlib.figure.Figure at 0x117b4c358>"
|
"<matplotlib.figure.Figure at 0x11563d780>"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
@@ -1037,7 +1033,7 @@
|
|||||||
"data": {
|
"data": {
|
||||||
"image/png": 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truncated
|
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truncated
|
||||||
"text/plain": [
|
"text/plain": [
|
||||||
"<matplotlib.figure.Figure at 0x117acf940>"
|
"<matplotlib.figure.Figure at 0x112692320>"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
@@ -1059,14 +1055,14 @@
|
|||||||
"name": "stdout",
|
"name": "stdout",
|
||||||
"output_type": "stream",
|
"output_type": "stream",
|
||||||
"text": [
|
"text": [
|
||||||
"rep_improve_nn, 80: 80 cities ⇒ tour length 13512 (in 0.887 sec)\n"
|
"rep_improve_nn, 80: 80 cities ⇒ tour length 13512 (in 0.890 sec)\n"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
"data": {
|
"data": {
|
||||||
"image/png": 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truncated
|
||||||
"text/plain": [
|
"text/plain": [
|
||||||
"<matplotlib.figure.Figure at 0x11796b198>"
|
"<matplotlib.figure.Figure at 0x112692da0>"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
@@ -1120,14 +1116,14 @@
|
|||||||
"name": "stdout",
|
"name": "stdout",
|
||||||
"output_type": "stream",
|
"output_type": "stream",
|
||||||
"text": [
|
"text": [
|
||||||
"nn: 1089 cities ⇒ tour length 52879 (in 0.166 sec)\n"
|
"nn: 1089 cities ⇒ tour length 52879 (in 0.164 sec)\n"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
"data": {
|
"data": {
|
||||||
"image/png": 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truncated
|
||||||
"text/plain": [
|
"text/plain": [
|
||||||
"<matplotlib.figure.Figure at 0x1179b4eb8>"
|
"<matplotlib.figure.Figure at 0x1125e5a58>"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
@@ -1156,14 +1152,14 @@
|
|||||||
"name": "stdout",
|
"name": "stdout",
|
||||||
"output_type": "stream",
|
"output_type": "stream",
|
||||||
"text": [
|
"text": [
|
||||||
"rep_improve_nn, 3: 1089 cities ⇒ tour length 44877 (in 10.171 sec)\n"
|
"rep_improve_nn, 3: 1089 cities ⇒ tour length 44877 (in 10.007 sec)\n"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
"data": {
|
"data": {
|
||||||
"image/png": 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truncated
|
"image/png": 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truncated
|
||||||
"text/plain": [
|
"text/plain": [
|
||||||
"<matplotlib.figure.Figure at 0x114b05860>"
|
"<matplotlib.figure.Figure at 0x11200c7f0>"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
@@ -1281,7 +1277,7 @@
|
|||||||
"data": {
|
"data": {
|
||||||
"image/png": 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truncated
|
||||||
"text/plain": [
|
"text/plain": [
|
||||||
"<matplotlib.figure.Figure at 0x11781d160>"
|
"<matplotlib.figure.Figure at 0x114c440f0>"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
@@ -1301,14 +1297,14 @@
|
|||||||
"name": "stdout",
|
"name": "stdout",
|
||||||
"output_type": "stream",
|
"output_type": "stream",
|
||||||
"text": [
|
"text": [
|
||||||
"greedy: 1089 cities ⇒ tour length 46982 (in 0.569 sec)\n"
|
"greedy: 1089 cities ⇒ tour length 46982 (in 0.612 sec)\n"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
"data": {
|
"data": {
|
||||||
"image/png": 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truncated
|
||||||
"text/plain": [
|
"text/plain": [
|
||||||
"<matplotlib.figure.Figure at 0x11926b588>"
|
"<matplotlib.figure.Figure at 0x111f91cf8>"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
@@ -1344,14 +1340,14 @@
|
|||||||
"name": "stdout",
|
"name": "stdout",
|
||||||
"output_type": "stream",
|
"output_type": "stream",
|
||||||
"text": [
|
"text": [
|
||||||
"improve_greedy: 80 cities ⇒ tour length 14220 (in 0.015 sec)\n"
|
"improve_greedy: 80 cities ⇒ tour length 14220 (in 0.016 sec)\n"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
"data": {
|
"data": {
|
||||||
"image/png": 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truncated
|
||||||
"text/plain": [
|
"text/plain": [
|
||||||
"<matplotlib.figure.Figure at 0x117accc18>"
|
"<matplotlib.figure.Figure at 0x114c676a0>"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
@@ -1371,14 +1367,14 @@
|
|||||||
"name": "stdout",
|
"name": "stdout",
|
||||||
"output_type": "stream",
|
"output_type": "stream",
|
||||||
"text": [
|
"text": [
|
||||||
"improve_greedy: 1089 cities ⇒ tour length 43733 (in 2.996 sec)\n"
|
"improve_greedy: 1089 cities ⇒ tour length 43733 (in 2.967 sec)\n"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
"data": {
|
"data": {
|
||||||
"image/png": 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truncated
|
||||||
"text/plain": [
|
"text/plain": [
|
||||||
"<matplotlib.figure.Figure at 0x10d9661d0>"
|
"<matplotlib.figure.Figure at 0x11a634208>"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
@@ -1441,7 +1437,7 @@
|
|||||||
"data": {
|
"data": {
|
||||||
"image/png": 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truncated
|
||||||
"text/plain": [
|
"text/plain": [
|
||||||
"<matplotlib.figure.Figure at 0x114f1bf28>"
|
"<matplotlib.figure.Figure at 0x112903128>"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
@@ -1451,7 +1447,7 @@
|
|||||||
"data": {
|
"data": {
|
||||||
"image/png": 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truncated
|
||||||
"text/plain": [
|
"text/plain": [
|
||||||
"<matplotlib.figure.Figure at 0x117ac36a0>"
|
"<matplotlib.figure.Figure at 0x111fe2470>"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
@@ -1461,7 +1457,7 @@
|
|||||||
"data": {
|
"data": {
|
||||||
"image/png": 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truncated
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truncated
|
||||||
"text/plain": [
|
"text/plain": [
|
||||||
"<matplotlib.figure.Figure at 0x11c8f0860>"
|
"<matplotlib.figure.Figure at 0x11aada978>"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
@@ -1471,7 +1467,7 @@
|
|||||||
"data": {
|
"data": {
|
||||||
"image/png": 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truncated
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truncated
|
||||||
"text/plain": [
|
"text/plain": [
|
||||||
"<matplotlib.figure.Figure at 0x118723a90>"
|
"<matplotlib.figure.Figure at 0x10b3b3b70>"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
@@ -1481,7 +1477,7 @@
|
|||||||
"data": {
|
"data": {
|
||||||
"image/png": 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truncated
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truncated
|
||||||
"text/plain": [
|
"text/plain": [
|
||||||
"<matplotlib.figure.Figure at 0x117993978>"
|
"<matplotlib.figure.Figure at 0x1125dc470>"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
@@ -1491,7 +1487,7 @@
|
|||||||
"data": {
|
"data": {
|
||||||
"image/png": 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truncated
|
||||||
"text/plain": [
|
"text/plain": [
|
||||||
"<matplotlib.figure.Figure at 0x11781d128>"
|
"<matplotlib.figure.Figure at 0x11a41db38>"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
@@ -1508,7 +1504,7 @@
|
|||||||
"data": {
|
"data": {
|
||||||
"image/png": 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truncated
|
||||||
"text/plain": [
|
"text/plain": [
|
||||||
"<matplotlib.figure.Figure at 0x117b4c208>"
|
"<matplotlib.figure.Figure at 0x11b8a1b70>"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
@@ -1544,7 +1540,7 @@
|
|||||||
"data": {
|
"data": {
|
||||||
"image/png": 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truncated
|
||||||
"text/plain": [
|
"text/plain": [
|
||||||
"<matplotlib.figure.Figure at 0x1179057b8>"
|
"<matplotlib.figure.Figure at 0x11b8aab38>"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
@@ -1576,7 +1572,7 @@
|
|||||||
"data": {
|
"data": {
|
||||||
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|
||||||
"text/plain": [
|
"text/plain": [
|
||||||
"<matplotlib.figure.Figure at 0x11c7ed0b8>"
|
"<matplotlib.figure.Figure at 0x11982e780>"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
@@ -1604,7 +1600,7 @@
|
|||||||
"data": {
|
"data": {
|
||||||
"image/png": 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truncated
|
||||||
"text/plain": [
|
"text/plain": [
|
||||||
"<matplotlib.figure.Figure at 0x11dc48a90>"
|
"<matplotlib.figure.Figure at 0x1192da2e8>"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
@@ -1735,7 +1731,7 @@
|
|||||||
"data": {
|
"data": {
|
||||||
"image/png": 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truncated
|
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truncated
|
||||||
"text/plain": [
|
"text/plain": [
|
||||||
"<matplotlib.figure.Figure at 0x11e442e48>"
|
"<matplotlib.figure.Figure at 0x1192da550>"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
@@ -1755,14 +1751,14 @@
|
|||||||
"name": "stdout",
|
"name": "stdout",
|
||||||
"output_type": "stream",
|
"output_type": "stream",
|
||||||
"text": [
|
"text": [
|
||||||
"improve_divide: 80 cities ⇒ tour length 14117 (in 0.138 sec)\n"
|
"improve_divide: 80 cities ⇒ tour length 14117 (in 0.109 sec)\n"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
"data": {
|
"data": {
|
||||||
"image/png": 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truncated
|
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"text/plain": [
|
"text/plain": [
|
||||||
"<matplotlib.figure.Figure at 0x11c3bfa20>"
|
"<matplotlib.figure.Figure at 0x11b245780>"
|
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]
|
]
|
||||||
},
|
},
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
@@ -1779,12 +1775,14 @@
|
|||||||
"source": [
|
"source": [
|
||||||
"Divide and conquer performs adequately, but not exceptionally. \n",
|
"Divide and conquer performs adequately, but not exceptionally. \n",
|
||||||
"\n",
|
"\n",
|
||||||
"# Shoulders of Giants: Minimum Spanning Tree Algorithm: `mst_tsp`\n",
|
"# Shoulders of Giants: Minimum Spanning Tree Algorithm\n",
|
||||||
"\n",
|
"\n",
|
||||||
"\n",
|
"\n",
|
||||||
"<a href=\"https://en.wikipedia.org/wiki/Joseph_Kruskal\">\n",
|
"| |\n",
|
||||||
"<img src=\"http://people.inf.elte.hu/hytruongson/Kruskal/J.Kruskal.jpg\">\n",
|
"|----|\n",
|
||||||
"<center>Joseph Kruskal (Wikipedia)</center></a>\n",
|
"|  |\n",
|
||||||
|
"| [Joseph Kruskal (Wikipedia)](https://en.wikipedia.org/wiki/Joseph_Kruskal) |\n",
|
||||||
|
"\n",
|
||||||
"\n",
|
"\n",
|
||||||
"\n",
|
"\n",
|
||||||
"I hope you now believe that you could have come up with some ideas for solving the TSP, using the set of **strategies**. But even if you can't come up with something all on your own, you can follow the **Stand on the Shoulders of Giants Strategy**, also known as the **[Just Google it Strategy](http://bit.ly/XNGt2y)**, in which case you'll no doubt find a giant of a mathematician, [Joseph Kruskal](http://en.wikipedia.org/wiki/Joseph_Kruskal), who, in 1956, published [a paper](http://www.cmat.edu.uy/~marclan/TAG/Sellanes/Kruskal.pdf) that led to an algorithm that\n",
|
"I hope you now believe that you could have come up with some ideas for solving the TSP, using the set of **strategies**. But even if you can't come up with something all on your own, you can follow the **Stand on the Shoulders of Giants Strategy**, also known as the **[Just Google it Strategy](http://bit.ly/XNGt2y)**, in which case you'll no doubt find a giant of a mathematician, [Joseph Kruskal](http://en.wikipedia.org/wiki/Joseph_Kruskal), who, in 1956, published [a paper](http://www.cmat.edu.uy/~marclan/TAG/Sellanes/Kruskal.pdf) that led to an algorithm that\n",
|
||||||
@@ -1869,7 +1867,7 @@
|
|||||||
"data": {
|
"data": {
|
||||||
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAYsAAADqCAYAAABTP2nAAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAIABJREFUeJzt3Xl8XHX1//HXSdqkW9oCAi0QNmldcEFALSCCiorirkFEEFcUXNCvXxRB/YGyKPrVr7iDqEDlixRFQRFFEWUrIIsLFChLS1q2At23NMn5/fGZaSeTmUyWmfu59877+Xjk0WSazBzo5J772c4xd0dERGQoLbEDEBGR9FOyEBGRmpQsRESkJiULERGpSclCRERqUrIQEZGalCxERKQmJQsREalJyUJERGpSshARkZqULEREpCYlCxERqWlc7ADGYj+zczthdvnj3XD/ze7HxohJRCSPMp0sOmH2pXBQ+eOHxwhGRCTHNA0lIiI1KVmIiEhNShYiIlKTkoWIiNSU6QXubrj/cGA8tO8Oe98HNxcfjxyaiEiuWC56cJu1AuuBDtw3xg5HRCRv8jEN5d4HPArsGDsUEZE8ykeyCBYDu8QOQkQkjzI/DTXHbEEnzGyHSX2wqRc2AXTDY/Pdnxc7PhGRPMj0AjdAJ8ycB9MKX44vPt4VKR4RkTzK0zSUiIg0iJKFiIjUlPlpKJFaiuta5Y9rXUvqKe9VsJUsJFUacWEvW9farJ7rWnm/UEhtea+Cnflk0Q2PdQG7wuSnYOMa6C0+HjcyGY26XNjNDJgETAGmTExgujXvFwqRzCeLzXebZguBN+N+b9yIpBG2hXbMzgA6KCSBCh/Fv5sEbADWAGt2gMlRghbJkcwnC6B4J7kT0B07FGmMFjBgHfAEhSQwxMfawql+AB40W0GF0Uo9tUF7I59fJLZ8JAvYBliP+9rYgUhjPAEbcD+jns85ASZjtiPuS8f0RGa77wovqU9UIumUl2TRSZ1HFdpBE8e4koOV9VJc1yq3BnqAOzA7HvdfjerJzWYDf34GHgFmjSFMybhuuP942GEiTO2Ge0sfjxlXvShZVH/Chu+gkTJmU3qh7QhY0wd9pX81lg0LQyZ3s5cBv8DsjcAJuK8ZQbzPB64BvnQnzDk8FLMcIC8XCqntZvdjMbsc+BXuc2PHU29KFinUxKOaU+bBL3E/KrFXdL8Vs5cA3wHuxOy9uN9a8+fMXgRcDXwO97k3w08bHKmkndk44GDguMiRNISSBRQXyHcA9gSeD+w5MeyqiaIRo5rUJ6AwnfMR4EWJv3YYTXwIs3cBV2J2DvC10kXyAcz2Bq4ijER+mVygknL7At24Px47kEbIdLKYY7a8EzraoaUPvNfsKwDdsHq++1aDfiAkhR0pJISyPzcA9wB3A3f0wBFETBiV7AZTMPsDsGqEH2tSPa0W/l2KF+hBUzmJcb8Ms/nAhcDrMTsa98UDvidMW10JfAz3yyNEKen1WsK0ZC5lOll0Qsc8aC18acXHu6ADs50YnBCKSeFuQmK4HbgIuBv3p0ufu8/srMb/F1TWuuW/aYAnQjfA7wJTyz52rvBY6ceUSemuA/YWQi+Sc2IHgvsSzA4BPtsFD48z815wCG8wg9alsPYGJQoZ7LXAmbGDaJRMJ4tqWsLF9h+EpHB34fMLgHvKk0I1pTto2qBlN5jyIKxu+Mlws9e1VzlEtg76cL9qFM/Zsh6eocFnDUbFbCLwbeCjuPfEDgcA937gGy1mZ/1fhcTdBRMiRCVpZtYB7A1cHzuURsllsugPF9UZY3mOQfP4Zt8AtsL9w2N53iGZvRs4ZyOspZ5TYO79blb7++I4EbgD99QN3/tjByBZchBwW57PeuUyWTTI6cB9mO2F+111f3az44BTgEMWwaVdVRaj6/2yO8JEzFqrLuY2ktmuwAmEOzKRLMv1egUoWQyf+0rMTgO+hdlrqFc/2rC4+yXgfcArcX9oPtR9d1Klg2ktwM7hPfCLwmLupnq/bg3fAr49aBE5JVS/Q0bgEOD9sYNopEwni25Y/V7o2AVaF5Yc4uqG1Q16yfOAjxMWZH875mczawH+F3gl8IpGbrmruj3WbAJwKfBrzLpw39CoGMpe9/XAi4EjE3m9kTLbbZcqGw1EYMt29PFgz4aO++AaN0vPdvQ6s3rdIEcT9ryfj3sytXnCRe57wJ5jWpA1Gw/8nFAA8S24r6xLfKOM5QR4qg0mPQJrS+fqG/LGN2sD/g18Fvff1fW568FsB+D698LMHmgr/+uqW7OlqXSZraiyHX3lPPfpMWJqpEyPLAqmAcldaN3/WCiH/nHCLp6RM5sMzCP03jgU9/X1C3AU3Dc9ZuaXhvfDgDd/g85hfBpYmNJEsQ3wJ+D8X7jndhukyEgpWYzOZ4G/Y3bhcLfibma2NfA7Qs2gD+Pe24D4Rqza+NJKzq/UhdmOwOeAOXV93nowm0oo4XEVEO2cTZG670ma5CVZrEr0Fd0XYPZL4FTgk8P+uXChvBr4I6GmUOp3Z06EqZjdCvy58HHTGNc1vgH8CPcH6hJgvYTzHlcAdwCfr9sGhjFQ9710a0n3Qde6y0uyiDHffyqwALMf4L6g5nebzSJMb/wIODsNF6PhWBf+336OsNvjTGBPzG5mS/K4a9hJzyws5IcaUOkR1o/mEbYmH5+VfxsZmbrWRzObUe3wbF4pWYyW+1OEkiDfBA4b8ntDVdPfA1/G/ScJRFdf7tcB1wFfxGw64W73EOAXwLaYXUsxebg/VPyxYu0uCHNZu0PrMui/G5bMh3QsEJu1EmpBAbwvynkTSUTd6qOZTQOuXgZPd1XeANHYKg+R5CVZPBnptb8HHIfZ63D/U8XvMDuIcNf6Mdx/nWRwI1GtQdCgN777CsK24bB1ONTgeg0heZyG2QYKiaOsdldRS1chgUQXzrj8AJgBvDHCORPJmrDV/DfAjX+ATzTTKDQvyWJhlFd278HsRMJBvb0GLVabvZVwNuMI3K+NEeJwjXp7rPsSQt2tCwoX3+cTEsdRLWk+pxBi/TqhHeprou9Ik2iGvfYQRqEXAU8Bn2qmRAH5SRbxziiEO+wTgA8T1iMCsw8Q5vjfgPvtcUJLWPjlKRZv/E6/WS/pTRhfAN4IHIR7ow5xjkk33F9czH4O7P8g3NYLm9R9b3SqZYQJofT/bcDFhOZbj8LAaVQIBUVbgAdg1c1NOF2Zh2QxlZjJwt0PNdtnXzj4AbPv9RG2mxq0dMOqm5olUaRY+cLmeGgbB+0PwUM3jHTrc4IGbI81uwv4JO53xIso255VpVrwurCb8mRCNYEvY3YHcPGu0HFJ5arDqepzk5Q8JIvYIws6YNLp4dMBb6yuJtstkVZDLGxuGyOeUXqU0LhLyWI0zHbbHsYdCas2lR0r6obHClWPr8HseMKI88hZ6R0VR5GXZJHsOQsZlm5YfTRM3wT9fSW/oA2s3ZVnSwnJQkbnW1+GU3E/fcjvCmtXvwJ+tTDd06iJy0uyiDqykMrmh11SlwPPTstJ9QxbSugTLyNl9jpCb/f3jOTHmm5RooY8nEBUskivjxNOaytRjJ1GFqMRilaeA3w6sYrKOZXtkYXZOGAisCZ2KFImFOR7BxVqG8nwFRfnO2Dc1tC+2Oyd0KBqwA0Usc7Vp4CHCPXYRuRRWPdu6OgvG2Q06zRqtpNF2Am1OnaNpW5Y3QUdE6F1I/T1lzweM67IPgBcifuy2IGUHjjcESauh75noCcLJ20rLM5Pg4ZVA26YpOpcle58Gw+2O3QsgjUPwD0jbSp2Yzg/9DTup9Y5zEzKerJIxRTU5t4GYXvj+xvSdjVLwuGl4xnhHHGjDLgDN/soMAf3D8SLSBqlys63jkptiocUTmq/B9i3XrFlXdbXLOKesRisFUh9JdkEHAo8DdwaO5AKbgNeGjuIpmJmz8re4vzbgTtxXxQ7kLTI5MiiONRshdY2mLjebAWkYh63BW2igLCw/f20lUOYY7ZgZ5j5XJh2n9mKkunC2O+bVGjIuoLZTOD8aSO9s4+gdAprAkzuhZ5esxV6fwSZTBYpnsdtodlHFmZ7EIbu74wdSrlOmHnplvfN5vdPCt43qVD3dQWzLkKxzR89GA6ovnIM4TVchevKOND7oyiTySLFNA0FxwE/U2G++ihdnB8PbQatPbA+1YvzZlsB3yVM970Z91u7zc49vEJDRtW5yg4li/pq7mkos0nAMWhRsG7KFucPAb6I+8HRAqolxPhTQtfBl+C+DsrqXDVQMblOgMmbYGNf6HOf2x4TScpkshhX777Q9dPsI4sjCW1XF8UOJG/mmC3YBXaYAB3rCmt0kKL1lnCj8DXCwvCHqvZ3abDN/y/M7izEoVpadZK9ZGE2def0Fuir+8gi4mGmkQn9IT5BaMEqddYJM38Zdv9B2tZbzF5K6DZ4F/Bi3J+JHBGETowran4XA37Hppxa8vgE4KQGBJZV2UoW4e7ld6tgVVeFbb8pGGrWfYE7qcNMdbA/MInQJS+Vyuf/W2DcRliXgvdNKpT2zwBog/bdYG+DtRV/IPQuP5mw++1TuF+SQJjDNR1YPpxvrPY71gV9XbBG748gO8ki1Hj5FbDoh3Bw7FPbVTTzNNQnCNtlU/vfXzb/vxPwT2D74dSuKu+JUZSaaaA6qDhSNTu4C/5yuFlv6ep0O7AT8DX4C2FtYmlCYdZm1kJoWjSmatQGN1ya5vWhhKU2WZRNv9jO8DwDuwl+c2PKLkjFjlrPgdYHYXGvhSWVbli9+XR3noW99IcSdkJlwhy4ZjZM64HlfWabpw6rXfyH6ImRb+7XjTfj4gqluo8NN0aHpu08DWG6bg1N2M2ukVKbLIaYfpkVI56hdELHvC2/TJt/qbpKWjLmTVkNnvYWaNkIi7rNMnGn3QkzLwz/VgO6nm2++JtNIbzXZgOzdgpTbE2pvFlQ0XLwFCYKCFNQw1qvkOFLbbKQdKtyp92W9Tvt3UI/5kcJF5wHgIXA/WvDFszxseIqW2+xZ0PHQlil+fSKlCwaQMmiDqrt4zVowexUwi6RfwKLRnonVlx03AVesBILine truncated
|
"image/png": "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 truncated
|
||||||
"text/plain": [
|
"text/plain": [
|
||||||
"<matplotlib.figure.Figure at 0x11ce3c6d8>"
|
"<matplotlib.figure.Figure at 0x1197bf828>"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
@@ -1951,7 +1949,7 @@
|
|||||||
"data": {
|
"data": {
|
||||||
"image/png": 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truncated
|
||||||
"text/plain": [
|
"text/plain": [
|
||||||
"<matplotlib.figure.Figure at 0x11dac5b00>"
|
"<matplotlib.figure.Figure at 0x11b87e898>"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
@@ -1971,14 +1969,14 @@
|
|||||||
"name": "stdout",
|
"name": "stdout",
|
||||||
"output_type": "stream",
|
"output_type": "stream",
|
||||||
"text": [
|
"text": [
|
||||||
"mst: 1089 cities ⇒ tour length 58059 (in 0.843 sec)\n"
|
"mst: 1089 cities ⇒ tour length 58059 (in 0.874 sec)\n"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
"data": {
|
"data": {
|
||||||
"image/png": 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truncated
|
||||||
"text/plain": [
|
"text/plain": [
|
||||||
"<matplotlib.figure.Figure at 0x10d9661d0>"
|
"<matplotlib.figure.Figure at 0x111909860>"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
@@ -1998,14 +1996,14 @@
|
|||||||
"name": "stdout",
|
"name": "stdout",
|
||||||
"output_type": "stream",
|
"output_type": "stream",
|
||||||
"text": [
|
"text": [
|
||||||
"improve_mst: 1089 cities ⇒ tour length 44779 (in 5.871 sec)\n"
|
"improve_mst: 1089 cities ⇒ tour length 44779 (in 5.559 sec)\n"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
"data": {
|
"data": {
|
||||||
"image/png": 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truncated
|
||||||
"text/plain": [
|
"text/plain": [
|
||||||
"<matplotlib.figure.Figure at 0x117872fd0>"
|
"<matplotlib.figure.Figure at 0x11a3e7048>"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
@@ -2043,12 +2041,16 @@
|
|||||||
"# Shoulders of Giants: Held-Karp Algorithm: `held_karp_tsp`\n",
|
"# Shoulders of Giants: Held-Karp Algorithm: `held_karp_tsp`\n",
|
||||||
"\n",
|
"\n",
|
||||||
"\n",
|
"\n",
|
||||||
"<a href=\"http://www.computerhistory.org/collections/catalog/102650390\"><img src=\"http://archive.computerhistory.org/resources/still-image/IBM/IBM_People/IBM.3_mathematicians_Held_Shareshian_Karp.ca1964.102650390.lg.jpg\">\n",
|
"| |\n",
|
||||||
"<center>Held, Shareshian, Karp (Computer History Museum)</center></a>\n",
|
"|----|\n",
|
||||||
|
"|  |\n",
|
||||||
|
"| [Held, Shareshian, Karp (Computer History Museum)](http://www.computerhistory.org/collections/catalog/102650390) |\n",
|
||||||
|
"\n",
|
||||||
|
"| |\n",
|
||||||
|
"|----|\n",
|
||||||
|
"|  |\n",
|
||||||
|
"| [xkcd 399](http://xkcd.com/399/) |\n",
|
||||||
"\n",
|
"\n",
|
||||||
"<a href=\"http://xkcd.com/399/\">\n",
|
|
||||||
"<img src=\"http://imgs.xkcd.com/comics/travelling_salesman_problem.png\">\n",
|
|
||||||
"<center>xkcd 399</center></a>\n",
|
|
||||||
"\n",
|
"\n",
|
||||||
"Another algorithm that shows up with a literature search is the [Held-Karp Dynamic Programming Algorithm](http://en.wikipedia.org/wiki/Held%E2%80%93Karp_algorithm), named after giants [Michael Held](http://www.computerhistory.org/collections/catalog/102650390) and [Richard Karp](http://en.wikipedia.org/wiki/Richard_M._Karp). It is an algorithm for finding optimal tours, not approximate ones, so it is not appropriate for large *n*. But even in its simplest form, without any programming tricks, it can go quite a bit further than `alltours_tsp`. That is because `alltours_tsp` is O(*n*!), while the Held-Karp algorithm is only O(*n*<sup>2</sup> 2<sup>*n*</sup>). How did Held and Karp achieve this speedup? They noticed that `alltours_tsp` wastes a lot of time with permutations that can't possibly be optimal tours. Here's the key idea:\n",
|
"Another algorithm that shows up with a literature search is the [Held-Karp Dynamic Programming Algorithm](http://en.wikipedia.org/wiki/Held%E2%80%93Karp_algorithm), named after giants [Michael Held](http://www.computerhistory.org/collections/catalog/102650390) and [Richard Karp](http://en.wikipedia.org/wiki/Richard_M._Karp). It is an algorithm for finding optimal tours, not approximate ones, so it is not appropriate for large *n*. But even in its simplest form, without any programming tricks, it can go quite a bit further than `alltours_tsp`. That is because `alltours_tsp` is O(*n*!), while the Held-Karp algorithm is only O(*n*<sup>2</sup> 2<sup>*n*</sup>). How did Held and Karp achieve this speedup? They noticed that `alltours_tsp` wastes a lot of time with permutations that can't possibly be optimal tours. Here's the key idea:\n",
|
||||||
"\n",
|
"\n",
|
||||||
@@ -2130,14 +2132,14 @@
|
|||||||
"name": "stdout",
|
"name": "stdout",
|
||||||
"output_type": "stream",
|
"output_type": "stream",
|
||||||
"text": [
|
"text": [
|
||||||
"alltours: 10 cities ⇒ tour length 2720 (in 1.690 sec)\n"
|
"alltours: 10 cities ⇒ tour length 2720 (in 1.624 sec)\n"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
"data": {
|
"data": {
|
||||||
"image/png": 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truncated
|
"image/png": 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truncated
|
||||||
"text/plain": [
|
"text/plain": [
|
||||||
"<matplotlib.figure.Figure at 0x1141db0b8>"
|
"<matplotlib.figure.Figure at 0x1192daf98>"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
@@ -2157,14 +2159,14 @@
|
|||||||
"name": "stdout",
|
"name": "stdout",
|
||||||
"output_type": "stream",
|
"output_type": "stream",
|
||||||
"text": [
|
"text": [
|
||||||
"held_karp: 10 cities ⇒ tour length 2720 (in 0.033 sec)\n"
|
"held_karp: 10 cities ⇒ tour length 2720 (in 0.034 sec)\n"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
"data": {
|
"data": {
|
||||||
"image/png": 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truncated
|
"image/png": 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truncated
|
||||||
"text/plain": [
|
"text/plain": [
|
||||||
"<matplotlib.figure.Figure at 0x11ecce630>"
|
"<matplotlib.figure.Figure at 0x11a41e860>"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
@@ -2191,14 +2193,14 @@
|
|||||||
"name": "stdout",
|
"name": "stdout",
|
||||||
"output_type": "stream",
|
"output_type": "stream",
|
||||||
"text": [
|
"text": [
|
||||||
"held_karp: 18 cities ⇒ tour length 2771 (in 43.741 sec)\n"
|
"held_karp: 18 cities ⇒ tour length 2771 (in 45.137 sec)\n"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
"data": {
|
"data": {
|
||||||
"image/png": 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truncated
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"image/png": 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truncated
|
||||||
"text/plain": [
|
"text/plain": [
|
||||||
"<matplotlib.figure.Figure at 0x11dc59358>"
|
"<matplotlib.figure.Figure at 0x11260fc88>"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
@@ -2257,14 +2259,14 @@
|
|||||||
"name": "stdout",
|
"name": "stdout",
|
||||||
"output_type": "stream",
|
"output_type": "stream",
|
||||||
"text": [
|
"text": [
|
||||||
"ensemble: 80 cities ⇒ tour length 13534 (in 0.191 sec)\n"
|
"ensemble: 80 cities ⇒ tour length 13534 (in 0.197 sec)\n"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
"data": {
|
"data": {
|
||||||
"image/png": 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truncated
|
||||||
"text/plain": [
|
"text/plain": [
|
||||||
"<matplotlib.figure.Figure at 0x11ecef7f0>"
|
"<matplotlib.figure.Figure at 0x11a3e77b8>"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
@@ -2288,7 +2290,7 @@
|
|||||||
"- **Divide and Conquer Strategy**: `divide_tsp`\n",
|
"- **Divide and Conquer Strategy**: `divide_tsp`\n",
|
||||||
"- **Ensemble Strategy**: `rep_nn_tsp`, `ensemble_tsp`\n",
|
"- **Ensemble Strategy**: `rep_nn_tsp`, `ensemble_tsp`\n",
|
||||||
"- **Giant Shoulders Strategy**: `mst_tsp`, `held_karp_tsp`\n",
|
"- **Giant Shoulders Strategy**: `mst_tsp`, `held_karp_tsp`\n",
|
||||||
"- **Improvement Strategy**: `improve_nn_tsp`, `improve_greedy_tsp`, `improve_divide_tsp`, `improve_rep_nn_tsp`, `rep_improve_nn_tsp`, `improve_mst_tsp`\n",
|
"- **Improvement Strategy**: `improve_nn_tsp`, `improve_greedy_tsp`, `improve_divide_tsp`, `rep_improve_nn_tsp`, `improve_mst_tsp`\n",
|
||||||
"\n",
|
"\n",
|
||||||
"\n",
|
"\n",
|
||||||
"# Comparison of Algorithms: Benchmark Experiments\n",
|
"# Comparison of Algorithms: Benchmark Experiments\n",
|
||||||
@@ -2405,9 +2407,9 @@
|
|||||||
"outputs": [
|
"outputs": [
|
||||||
{
|
{
|
||||||
"data": {
|
"data": {
|
||||||
"image/png": 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truncated
|
||||||
"text/plain": [
|
"text/plain": [
|
||||||
"<matplotlib.figure.Figure at 0x114f1b198>"
|
"<matplotlib.figure.Figure at 0x1160fb320>"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
@@ -2464,9 +2466,9 @@
|
|||||||
"outputs": [
|
"outputs": [
|
||||||
{
|
{
|
||||||
"data": {
|
"data": {
|
||||||
"image/png": 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truncated
|
||||||
"text/plain": [
|
"text/plain": [
|
||||||
"<matplotlib.figure.Figure at 0x117acc4a8>"
|
"<matplotlib.figure.Figure at 0x11a41ee10>"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
@@ -2513,9 +2515,9 @@
|
|||||||
"outputs": [
|
"outputs": [
|
||||||
{
|
{
|
||||||
"data": {
|
"data": {
|
||||||
"image/png": 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truncated
|
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truncated
|
||||||
"text/plain": [
|
"text/plain": [
|
||||||
"<matplotlib.figure.Figure at 0x11ce53080>"
|
"<matplotlib.figure.Figure at 0x112903c50>"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
@@ -2525,20 +2527,18 @@
|
|||||||
"name": "stdout",
|
"name": "stdout",
|
||||||
"output_type": "stream",
|
"output_type": "stream",
|
||||||
"text": [
|
"text": [
|
||||||
" #1 #2 #3 #4 #5 #6 | Algorithm\n",
|
" #1 #2 #3 #4 #5 | Algorithm\n",
|
||||||
" --- --- --- --- --- --- | ---------\n",
|
" --- --- --- --- --- | ---------\n",
|
||||||
" 15 6 5 8 6 0 | improve_greedy\n",
|
" 16 7 7 10 0 | improve_greedy\n",
|
||||||
" 16 14 7 3 0 0 | rep_improve_nn\n",
|
" 19 15 6 0 0 | rep_improve_nn\n",
|
||||||
" 5 5 10 11 9 0 | improve_rep_nn\n",
|
" 1 1 1 4 33 | improve_divide\n",
|
||||||
" 1 1 0 1 4 33 | improve_divide\n",
|
" 2 13 14 8 3 | improve_nn\n",
|
||||||
" 1 12 9 7 8 3 | improve_nn\n",
|
" 2 4 12 18 4 | improve_mst\n"
|
||||||
" 2 2 9 10 13 4 | improve_mst\n"
|
|
||||||
]
|
]
|
||||||
}
|
}
|
||||||
],
|
],
|
||||||
"source": [
|
"source": [
|
||||||
"improved = [improve_greedy_tsp, rep_improve_nn_tsp, improve_rep_nn_tsp, \n",
|
"improved = [improve_greedy_tsp, rep_improve_nn_tsp, improve_divide_tsp, improve_nn_tsp, improve_mst_tsp]\n",
|
||||||
" improve_divide_tsp, improve_nn_tsp, improve_mst_tsp, ]\n",
|
|
||||||
"\n",
|
"\n",
|
||||||
"compare(improved)"
|
"compare(improved)"
|
||||||
]
|
]
|
||||||
@@ -2561,9 +2561,9 @@
|
|||||||
"outputs": [
|
"outputs": [
|
||||||
{
|
{
|
||||||
"data": {
|
"data": {
|
||||||
"image/png": 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truncated
|
"image/png": 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truncated
|
||||||
"text/plain": [
|
"text/plain": [
|
||||||
"<matplotlib.figure.Figure at 0x13b050b00>"
|
"<matplotlib.figure.Figure at 0x138258978>"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
@@ -2607,9 +2607,9 @@
|
|||||||
"outputs": [
|
"outputs": [
|
||||||
{
|
{
|
||||||
"data": {
|
"data": {
|
||||||
"image/png": 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truncated
|
"image/png": 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truncated
|
||||||
"text/plain": [
|
"text/plain": [
|
||||||
"<matplotlib.figure.Figure at 0x13b616080>"
|
"<matplotlib.figure.Figure at 0x1384cef28>"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
@@ -2651,9 +2651,9 @@
|
|||||||
"outputs": [
|
"outputs": [
|
||||||
{
|
{
|
||||||
"data": {
|
"data": {
|
||||||
"image/png": 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truncated
|
"image/png": 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truncated
|
||||||
"text/plain": [
|
"text/plain": [
|
||||||
"<matplotlib.figure.Figure at 0x10ea92cc0>"
|
"<matplotlib.figure.Figure at 0x10c400e48>"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
@@ -2671,9 +2671,9 @@
|
|||||||
"outputs": [
|
"outputs": [
|
||||||
{
|
{
|
||||||
"data": {
|
"data": {
|
||||||
"image/png": 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truncated
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truncated
|
||||||
"text/plain": [
|
"text/plain": [
|
||||||
"<matplotlib.figure.Figure at 0x114b05860>"
|
"<matplotlib.figure.Figure at 0x10a7fbdd8>"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
|
|||||||
Reference in new issue
Block a user