{"id":2792,"date":"2025-06-17T08:39:53","date_gmt":"2025-06-17T08:39:53","guid":{"rendered":"https:\/\/diznr.com\/?p=2792"},"modified":"2025-06-17T08:39:53","modified_gmt":"2025-06-17T08:39:53","slug":"traveling-salesman-problem-in-hindi-using-dynamic-programming-with-example-practical","status":"publish","type":"post","link":"https:\/\/www.reilsolar.com\/pdf\/traveling-salesman-problem-in-hindi-using-dynamic-programming-with-example-practical\/","title":{"rendered":"Traveling Salesman Problem In Hindi Using Dynamic Programming  With Practical Example"},"content":{"rendered":"<p>Traveling Salesman Problem In Hindi Using Dynamic Programming With Practical Example<\/p>\n<p>[fvplayer id=&#8221;115&#8243;]<\/p>\n<p class=\"\" data-start=\"0\" data-end=\"168\">\u092f\u0939\u093e\u0901 <strong data-start=\"5\" data-end=\"41\">Traveling Salesman Problem (TSP)<\/strong> \u0915\u094b <strong data-start=\"45\" data-end=\"68\">Dynamic Programming<\/strong> \u0926\u094d\u0935\u093e\u0930\u093e \u0939\u0932 \u0915\u0930\u0928\u0947 \u0915\u0940 \u0939\u093f\u0902\u0926\u0940 \u092e\u0947\u0902 \u0935\u093f\u0938\u094d\u0924\u0943\u0924 \u0935\u094d\u092f\u093e\u0916\u094d\u092f\u093e \u0926\u0940 \u0917\u0908 \u0939\u0948, \u091c\u093f\u0938\u092e\u0947\u0902 \u090f\u0915 <strong data-start=\"134\" data-end=\"155\">\u092a\u094d\u0930\u0948\u0915\u094d\u091f\u093f\u0915\u0932 \u0909\u0926\u093e\u0939\u0930\u0923<\/strong> \u092d\u0940 \u0936\u093e\u092e\u093f\u0932 \u0939\u0948:<\/p>\n<hr class=\"\" data-start=\"170\" data-end=\"173\" \/>\n<h2 class=\"\" data-start=\"175\" data-end=\"223\"><strong data-start=\"178\" data-end=\"223\">Traveling Salesman Problem (TSP) \u0915\u094d\u092f\u093e \u0939\u0948?<\/strong><\/h2>\n<p class=\"\" data-start=\"225\" data-end=\"371\">Traveling Salesman Problem (TSP) \u090f\u0915 \u0915\u094d\u0932\u093e\u0938\u093f\u0915\u0932 \u0915\u0902\u092a\u094d\u092f\u0942\u091f\u0930 \u0938\u093e\u0907\u0902\u0938 \u0914\u0930 \u0911\u092a\u094d\u091f\u093f\u092e\u093e\u0907\u091c\u0947\u0936\u0928 \u0915\u0940 \u0938\u092e\u0938\u094d\u092f\u093e \u0939\u0948 \u091c\u093f\u0938\u092e\u0947\u0902 \u090f\u0915 \u0938\u0947\u0932\u094d\u0938\u092e\u0948\u0928 \u0915\u094b \u0915\u0908 \u0936\u0939\u0930\u094b\u0902 \u0915\u093e \u0926\u094c\u0930\u093e \u0915\u0930\u0928\u093e \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0909\u0938\u0947:<\/p>\n<ol data-start=\"373\" data-end=\"490\">\n<li class=\"\" data-start=\"373\" data-end=\"406\">\n<p class=\"\" data-start=\"376\" data-end=\"406\">\u0939\u0930 \u0936\u0939\u0930 \u092e\u0947\u0902 <strong data-start=\"387\" data-end=\"397\">\u090f\u0915 \u092c\u093e\u0930<\/strong> \u091c\u093e\u0928\u093e \u0939\u0948\u0964<\/p>\n<\/li>\n<li class=\"\" data-start=\"407\" data-end=\"449\">\n<p class=\"\" data-start=\"410\" data-end=\"449\">\u0905\u0902\u0924 \u092e\u0947\u0902 <strong data-start=\"418\" data-end=\"433\">\u0936\u0941\u0930\u0941\u0906\u0924\u0940 \u0936\u0939\u0930<\/strong> \u092a\u0930 \u0935\u093e\u092a\u0938 \u0906\u0928\u093e \u0939\u0948\u0964<\/p>\n<\/li>\n<li class=\"\" data-start=\"450\" data-end=\"490\">\n<p class=\"\" data-start=\"453\" data-end=\"490\"><strong data-start=\"453\" data-end=\"470\">\u0915\u0941\u0932 \u0926\u0942\u0930\u0940\/\u0932\u093e\u0917\u0924<\/strong> \u0928\u094d\u092f\u0942\u0928\u0924\u092e \u0939\u094b\u0928\u0940 \u091a\u093e\u0939\u093f\u090f\u0964<\/p>\n<\/li>\n<\/ol>\n<hr class=\"\" data-start=\"492\" data-end=\"495\" \/>\n<h2 class=\"\" data-start=\"497\" data-end=\"567\"><strong data-start=\"500\" data-end=\"567\">Dynamic Programming \u0926\u094d\u0935\u093e\u0930\u093e TSP \u0915\u094b \u0939\u0932 \u0915\u0930\u0928\u093e (Held-Karp Algorithm)<\/strong><\/h2>\n<p class=\"\" data-start=\"569\" data-end=\"662\">Dynamic Programming TSP \u0915\u094b <strong data-start=\"596\" data-end=\"611\">O(n\u00b2 * 2\u207f)<\/strong> \u0938\u092e\u092f \u092e\u0947\u0902 \u0939\u0932 \u0915\u0930\u0924\u093e \u0939\u0948, \u091c\u0939\u093e\u0901 <strong data-start=\"637\" data-end=\"642\">n<\/strong> \u0936\u0939\u0930\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0939\u0948\u0964<\/p>\n<p class=\"\" data-start=\"664\" data-end=\"697\">\u0939\u092e \u090f\u0915 \u0938\u094d\u091f\u0947\u091f <code data-start=\"676\" data-end=\"687\">(mask, i)<\/code> \u0930\u0916\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<ul data-start=\"698\" data-end=\"803\">\n<li class=\"\" data-start=\"698\" data-end=\"781\">\n<p class=\"\" data-start=\"700\" data-end=\"781\"><strong data-start=\"700\" data-end=\"708\">mask<\/strong>: \u092c\u093e\u0907\u0928\u0930\u0940 \u0930\u093f\u092a\u094d\u0930\u0947\u091c\u0947\u0902\u091f\u0947\u0936\u0928 \u092c\u0924\u093e\u0924\u093e \u0939\u0948 \u0915\u093f \u0915\u094c\u0928-\u0915\u094c\u0928 \u0938\u0947 \u0936\u0939\u0930 \u0935\u093f\u091c\u093c\u093f\u091f \u0915\u093f\u090f \u091c\u093e \u091a\u0941\u0915\u0947 \u0939\u0948\u0902\u0964<\/p>\n<\/li>\n<li class=\"\" data-start=\"782\" data-end=\"803\">\n<p class=\"\" data-start=\"784\" data-end=\"803\"><strong data-start=\"784\" data-end=\"789\">i<\/strong>: \u0935\u0930\u094d\u0924\u092e\u093e\u0928 \u0936\u0939\u0930\u0964<\/p>\n<\/li>\n<\/ul>\n<h3 class=\"\" data-start=\"805\" data-end=\"824\"><strong data-start=\"809\" data-end=\"824\">DP Formula:<\/strong><\/h3>\n<div class=\"contain-inline-size rounded-md border-[0.5px] border-token-border-medium relative bg-token-sidebar-surface-primary\">\n<div class=\"flex items-center text-token-text-secondary px-4 py-2 text-xs font-sans justify-between h-9 bg-token-sidebar-surface-primary dark:bg-token-main-surface-secondary select-none rounded-t-[5px]\">bash<\/div>\n<div class=\"sticky top-9\">\n<div class=\"absolute end-0 bottom-0 flex h-9 items-center pe-2\">\n<div class=\"bg-token-sidebar-surface-primary text-token-text-secondary dark:bg-token-main-surface-secondary flex items-center rounded-sm px-2 font-sans text-xs\"><button class=\"flex gap-1 items-center select-none px-4 py-1\" aria-label=\"Copy\">Copy<\/button><span class=\"\" data-state=\"closed\"><button class=\"flex items-center gap-1 px-4 py-1 select-none\">Edit<\/button><\/span><\/div>\n<\/div>\n<\/div>\n<div class=\"overflow-y-auto p-4\" dir=\"ltr\"><code class=\"whitespace-pre!\">dp[mask][i] = min(dp[mask ^ (1 &lt;&lt; <span class=\"hljs-string\">i)][j] + cost[j][i<\/span>])<br \/>\n<\/code><\/div>\n<\/div>\n<p class=\"\" data-start=\"890\" data-end=\"953\">\u091c\u0939\u093e\u0901 <code data-start=\"895\" data-end=\"898\">j<\/code> \u0939\u0930 \u0935\u094b \u0936\u0939\u0930 \u0939\u0948 \u091c\u094b <code data-start=\"915\" data-end=\"921\">mask<\/code> \u092e\u0947\u0902 \u092a\u0939\u0932\u0947 \u0938\u0947 \u0935\u093f\u091c\u093c\u093f\u091f \u0915\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948\u0964<\/p>\n<hr class=\"\" data-start=\"955\" data-end=\"958\" \/>\n<h2 class=\"\" data-start=\"960\" data-end=\"995\">\u2705 <strong data-start=\"965\" data-end=\"995\">\u0909\u0926\u093e\u0939\u0930\u0923 (Practical Example)<\/strong><\/h2>\n<p class=\"\" data-start=\"997\" data-end=\"1073\">\u092e\u093e\u0928 \u0932\u0940\u091c\u093f\u090f 4 \u0936\u0939\u0930 \u0939\u0948\u0902: A, B, C, D<br data-start=\"1028\" data-end=\"1031\" \/>\u0939\u092e \u0909\u0928\u094d\u0939\u0947\u0902 0, 1, 2, 3 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u092e\u093e\u0928\u0924\u0947 \u0939\u0948\u0902\u0964<\/p>\n<h3 class=\"\" data-start=\"1075\" data-end=\"1112\"><strong data-start=\"1079\" data-end=\"1112\">Distance Matrix (Cost Table):<\/strong><\/h3>\n<div class=\"_tableContainer_16hzy_1\">\n<div class=\"_tableWrapper_16hzy_14 group flex w-fit flex-col-reverse\">\n<table class=\"w-fit min-w-(--thread-content-width)\" data-start=\"1114\" data-end=\"1317\">\n<thead data-start=\"1114\" data-end=\"1147\">\n<tr data-start=\"1114\" data-end=\"1147\">\n<th data-start=\"1114\" data-end=\"1118\" data-col-size=\"sm\"><\/th>\n<th data-start=\"1118\" data-end=\"1125\" data-col-size=\"sm\">A(0)<\/th>\n<th data-start=\"1125\" data-end=\"1132\" data-col-size=\"sm\">B(1)<\/th>\n<th data-start=\"1132\" data-end=\"1139\" data-col-size=\"sm\">C(2)<\/th>\n<th data-start=\"1139\" data-end=\"1147\" data-col-size=\"sm\">D(3)<\/th>\n<\/tr>\n<\/thead>\n<tbody data-start=\"1182\" data-end=\"1317\">\n<tr data-start=\"1182\" data-end=\"1215\">\n<td data-start=\"1182\" data-end=\"1186\" data-col-size=\"sm\">A<\/td>\n<td data-start=\"1186\" data-end=\"1193\" data-col-size=\"sm\">0<\/td>\n<td data-col-size=\"sm\" data-start=\"1193\" data-end=\"1200\">10<\/td>\n<td data-col-size=\"sm\" data-start=\"1200\" data-end=\"1207\">15<\/td>\n<td data-col-size=\"sm\" data-start=\"1207\" data-end=\"1215\">20<\/td>\n<\/tr>\n<tr data-start=\"1216\" data-end=\"1249\">\n<td data-start=\"1216\" data-end=\"1220\" data-col-size=\"sm\">B<\/td>\n<td data-start=\"1220\" data-end=\"1227\" data-col-size=\"sm\">10<\/td>\n<td data-start=\"1227\" data-end=\"1234\" data-col-size=\"sm\">0<\/td>\n<td data-col-size=\"sm\" data-start=\"1234\" data-end=\"1241\">35<\/td>\n<td data-col-size=\"sm\" data-start=\"1241\" data-end=\"1249\">25<\/td>\n<\/tr>\n<tr data-start=\"1250\" data-end=\"1283\">\n<td data-start=\"1250\" data-end=\"1254\" data-col-size=\"sm\">C<\/td>\n<td data-start=\"1254\" data-end=\"1261\" data-col-size=\"sm\">15<\/td>\n<td data-start=\"1261\" data-end=\"1268\" data-col-size=\"sm\">35<\/td>\n<td data-start=\"1268\" data-end=\"1275\" data-col-size=\"sm\">0<\/td>\n<td data-col-size=\"sm\" data-start=\"1275\" data-end=\"1283\">30<\/td>\n<\/tr>\n<tr data-start=\"1284\" data-end=\"1317\">\n<td data-start=\"1284\" data-end=\"1288\" data-col-size=\"sm\">D<\/td>\n<td data-start=\"1288\" data-end=\"1295\" data-col-size=\"sm\">20<\/td>\n<td data-start=\"1295\" data-end=\"1302\" data-col-size=\"sm\">25<\/td>\n<td data-start=\"1302\" data-end=\"1309\" data-col-size=\"sm\">30<\/td>\n<td data-start=\"1309\" data-end=\"1317\" data-col-size=\"sm\">0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"sticky end-(--thread-content-margin) h-0 self-end select-none\">\n<div class=\"absolute end-0 flex items-end\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<p class=\"\" data-start=\"1319\" data-end=\"1412\">\u0939\u092e\u0947\u0902 \u0936\u0939\u0930 A \u0938\u0947 \u0936\u0941\u0930\u0942 \u0939\u094b\u0915\u0930 \u0938\u092d\u0940 \u0936\u0939\u0930\u094b\u0902 \u092e\u0947\u0902 \u091c\u093e\u0915\u0930 \u092b\u093f\u0930 \u0938\u0947 A \u0932\u094c\u091f\u0928\u093e \u0939\u0948, \u0914\u0930 \u0915\u0941\u0932 \u0926\u0942\u0930\u0940 \u0928\u094d\u092f\u0942\u0928\u0924\u092e \u0939\u094b\u0928\u0940 \u091a\u093e\u0939\u093f\u090f\u0964<\/p>\n<hr class=\"\" data-start=\"1414\" data-end=\"1417\" \/>\n<h2 class=\"\" data-start=\"1419\" data-end=\"1458\">\ud83e\udde0 <strong data-start=\"1425\" data-end=\"1458\">\u0938\u094d\u091f\u0947\u092a-\u092c\u093e\u092f-\u0938\u094d\u091f\u0947\u092a \u0939\u0932 (Using DP)<\/strong><\/h2>\n<p class=\"\" data-start=\"1460\" data-end=\"1485\">\u0939\u092e \u090f\u0915 DP table \u092c\u0928\u093e\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<div class=\"contain-inline-size rounded-md border-[0.5px] border-token-border-medium relative bg-token-sidebar-surface-primary\">\n<div class=\"flex items-center text-token-text-secondary px-4 py-2 text-xs font-sans justify-between h-9 bg-token-sidebar-surface-primary dark:bg-token-main-surface-secondary select-none rounded-t-[5px]\">python<\/div>\n<div class=\"sticky top-9\">\n<div class=\"absolute end-0 bottom-0 flex h-9 items-center pe-2\">\n<div class=\"bg-token-sidebar-surface-primary text-token-text-secondary dark:bg-token-main-surface-secondary flex items-center rounded-sm px-2 font-sans text-xs\"><button class=\"flex gap-1 items-center select-none px-4 py-1\" aria-label=\"Copy\">Copy<\/button><span class=\"\" data-state=\"closed\"><button class=\"flex items-center gap-1 px-4 py-1 select-none\">Edit<\/button><\/span><\/div>\n<\/div>\n<\/div>\n<div class=\"overflow-y-auto p-4\" dir=\"ltr\"><code class=\"whitespace-pre! language-python\"><span class=\"hljs-keyword\">from<\/span> functools <span class=\"hljs-keyword\">import<\/span> lru_cache<\/p>\n<p><span class=\"hljs-comment\"># \u0926\u0942\u0930\u0940 \u092e\u0948\u091f\u094d\u0930\u093f\u0915\u094d\u0938<\/span><br \/>\ncost = [<br \/>\n    [<span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">10<\/span>, <span class=\"hljs-number\">15<\/span>, <span class=\"hljs-number\">20<\/span>],<br \/>\n    [<span class=\"hljs-number\">10<\/span>, <span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">35<\/span>, <span class=\"hljs-number\">25<\/span>],<br \/>\n    [<span class=\"hljs-number\">15<\/span>, <span class=\"hljs-number\">35<\/span>, <span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">30<\/span>],<br \/>\n    [<span class=\"hljs-number\">20<\/span>, <span class=\"hljs-number\">25<\/span>, <span class=\"hljs-number\">30<\/span>, <span class=\"hljs-number\">0<\/span>]<br \/>\n]<\/p>\n<p>N = <span class=\"hljs-number\">4<\/span>  <span class=\"hljs-comment\"># \u0936\u0939\u0930\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e<\/span><br \/>\nALL_VISITED = (<span class=\"hljs-number\">1<\/span> &lt;&lt; N) - <span class=\"hljs-number\">1<\/span>  <span class=\"hljs-comment\"># \u0938\u092d\u0940 \u0936\u0939\u0930 \u0935\u093f\u091c\u093f\u091f \u0915\u093f\u090f \u0917\u090f (1111 in binary)<\/span><\/p>\n<p><span class=\"hljs-meta\">@lru_cache(<span class=\"hljs-params\"><span class=\"hljs-literal\">None<\/span><\/span><\/span>)<br \/>\n<span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title function_\">tsp<\/span>(<span class=\"hljs-params\">mask, pos<\/span>):<br \/>\n    <span class=\"hljs-keyword\">if<\/span> mask == ALL_VISITED:<br \/>\n        <span class=\"hljs-keyword\">return<\/span> cost[pos][<span class=\"hljs-number\">0<\/span>]  <span class=\"hljs-comment\"># \u0935\u093e\u092a\u0938 A \u092a\u0930 \u0932\u094c\u091f\u0947\u0902<\/span><\/p>\n<p>    ans = <span class=\"hljs-built_in\">float<\/span>(<span class=\"hljs-string\">'inf'<\/span>)<br \/>\n    <span class=\"hljs-keyword\">for<\/span> city <span class=\"hljs-keyword\">in<\/span> <span class=\"hljs-built_in\">range<\/span>(N):<br \/>\n        <span class=\"hljs-keyword\">if<\/span> (mask &amp; (<span class=\"hljs-number\">1<\/span> &lt;&lt; city)) == <span class=\"hljs-number\">0<\/span>:<br \/>\n            newAns = cost[pos][city] + tsp(mask | (<span class=\"hljs-number\">1<\/span> &lt;&lt; city), city)<br \/>\n            ans = <span class=\"hljs-built_in\">min<\/span>(ans, newAns)<br \/>\n    <span class=\"hljs-keyword\">return<\/span> ans<\/p>\n<p><span class=\"hljs-comment\"># \u0936\u0941\u0930\u0942\u0906\u0924 A (0) \u0938\u0947<\/span><br \/>\n<span class=\"hljs-built_in\">print<\/span>(<span class=\"hljs-string\">\"Minimum cost:\"<\/span>, tsp(<span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">0<\/span>))<br \/>\n<\/code><\/div>\n<\/div>\n<h3 class=\"\" data-start=\"2117\" data-end=\"2132\"><strong data-start=\"2121\" data-end=\"2132\">Output:<\/strong><\/h3>\n<div class=\"contain-inline-size rounded-md border-[0.5px] border-token-border-medium relative bg-token-sidebar-surface-primary\">\n<div class=\"flex items-center text-token-text-secondary px-4 py-2 text-xs font-sans justify-between h-9 bg-token-sidebar-surface-primary dark:bg-token-main-surface-secondary select-none rounded-t-[5px]\">yaml<\/div>\n<div class=\"sticky top-9\">\n<div class=\"absolute end-0 bottom-0 flex h-9 items-center pe-2\">\n<div class=\"bg-token-sidebar-surface-primary text-token-text-secondary dark:bg-token-main-surface-secondary flex items-center rounded-sm px-2 font-sans text-xs\"><button class=\"flex gap-1 items-center select-none px-4 py-1\" aria-label=\"Copy\">Copy<\/button><span class=\"\" data-state=\"closed\"><button class=\"flex items-center gap-1 px-4 py-1 select-none\">Edit<\/button><\/span><\/div>\n<\/div>\n<\/div>\n<div class=\"overflow-y-auto p-4\" dir=\"ltr\"><code class=\"whitespace-pre!\"><span class=\"hljs-attr\">Minimum cost:<\/span> <span class=\"hljs-number\">80<\/span><br \/>\n<\/code><\/div>\n<\/div>\n<hr class=\"\" data-start=\"2159\" data-end=\"2162\" \/>\n<h2 class=\"\" data-start=\"2164\" data-end=\"2209\">\ud83d\udd01 <strong data-start=\"2170\" data-end=\"2209\">\u0938\u092e\u091d\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0938\u0930\u0932 \u092d\u093e\u0937\u093e \u092e\u0947\u0902 \u0935\u094d\u092f\u093e\u0916\u094d\u092f\u093e:<\/strong><\/h2>\n<ul data-start=\"2211\" data-end=\"2417\">\n<li class=\"\" data-start=\"2211\" data-end=\"2237\">\n<p class=\"\" data-start=\"2213\" data-end=\"2237\">\u0939\u092e\u0928\u0947 \u0936\u0939\u0930 A \u0938\u0947 \u0936\u0941\u0930\u0941\u0906\u0924 \u0915\u0940\u0964<\/p>\n<\/li>\n<li class=\"\" data-start=\"2238\" data-end=\"2293\">\n<p class=\"\" data-start=\"2240\" data-end=\"2293\">\u0939\u0930 \u092c\u093e\u0930 \u090f\u0915 \u0928\u092f\u093e \u0936\u0939\u0930 \u091a\u0941\u0928\u0924\u0947 \u0939\u0948\u0902 \u091c\u094b \u0905\u092d\u0940 \u0924\u0915 \u0935\u093f\u091c\u093f\u091f \u0928\u0939\u0940\u0902 \u0939\u0941\u0906\u0964<\/p>\n<\/li>\n<li class=\"\" data-start=\"2294\" data-end=\"2360\">\n<p class=\"\" data-start=\"2296\" data-end=\"2360\">\u092b\u093f\u0930 \u0930\u093f\u0915\u0930\u094d\u0938\u093f\u0935 \u0924\u0930\u0940\u0915\u0947 \u0938\u0947 \u092c\u093e\u0915\u0940 \u0936\u0939\u0930\u094b\u0902 \u0915\u093e \u0938\u092c\u0938\u0947 \u091b\u094b\u091f\u093e \u0930\u093e\u0938\u094d\u0924\u093e \u0922\u0942\u0902\u0922\u0924\u0947 \u0939\u0948\u0902\u0964<\/p>\n<\/li>\n<li class=\"\" data-start=\"2361\" data-end=\"2417\">\n<p class=\"\" data-start=\"2363\" data-end=\"2417\">\u0905\u0902\u0924 \u092e\u0947\u0902, \u0938\u092d\u0940 \u0936\u0939\u0930 \u0935\u093f\u091c\u093f\u091f \u0939\u094b \u091c\u093e\u090f\u0901 \u0924\u094b \u0935\u093e\u092a\u0938 A \u092a\u0930 \u0932\u094c\u091f\u0924\u0947 \u0939\u0948\u0902\u0964<\/p>\n<\/li>\n<\/ul>\n<hr class=\"\" data-start=\"2419\" data-end=\"2422\" \/>\n<h2 class=\"\" data-start=\"2424\" data-end=\"2443\">\ud83c\udfaf <strong data-start=\"2430\" data-end=\"2443\">\u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937:<\/strong><\/h2>\n<ul data-start=\"2445\" data-end=\"2643\">\n<li class=\"\" data-start=\"2445\" data-end=\"2569\">\n<p class=\"\" data-start=\"2447\" data-end=\"2569\">TSP \u090f\u0915 \u0915\u0920\u093f\u0928 \u0938\u092e\u0938\u094d\u092f\u093e \u0939\u0948 \u0932\u0947\u0915\u093f\u0928 Dynamic Programming (Held-Karp) \u0926\u094d\u0935\u093e\u0930\u093e \u091b\u094b\u091f\u093e \u0907\u0928\u092a\u0941\u091f \u0939\u094b\u0928\u0947 \u092a\u0930 \u0907\u0938\u0947 \u0915\u0941\u0936\u0932\u0924\u093e\u092a\u0942\u0930\u094d\u0935\u0915 \u0939\u0932 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964<\/p>\n<\/li>\n<li class=\"\" data-start=\"2570\" data-end=\"2643\">\n<p class=\"\" data-start=\"2572\" data-end=\"2643\">\u092f\u0939 \u0930\u0942\u091f \u0911\u092a\u094d\u091f\u093f\u092e\u093e\u0907\u091c\u0947\u0936\u0928, \u0932\u0949\u091c\u093f\u0938\u094d\u091f\u093f\u0915\u094d\u0938, \u0914\u0930 \u0921\u093f\u0932\u0940\u0935\u0930\u0940 \u0938\u093f\u0938\u094d\u091f\u092e \u092e\u0947\u0902 \u092c\u0939\u0941\u0924 \u0909\u092a\u092f\u094b\u0917\u0940 \u0939\u0948\u0964<\/p>\n<\/li>\n<\/ul>\n<hr class=\"\" data-start=\"2645\" data-end=\"2648\" \/>\n<p class=\"\" data-start=\"2650\" data-end=\"2768\">\u0905\u0917\u0930 \u0906\u092a \u091a\u093e\u0939\u0947\u0902, \u0924\u094b \u092e\u0948\u0902 \u0907\u0938\u0915\u093e <strong data-start=\"2676\" data-end=\"2705\">\u092a\u093e\u092f\u0925\u0928 \u0915\u094b\u0921 \u0915\u093e \u0935\u093f\u091c\u0941\u0905\u0932\u093e\u0907\u091c\u0947\u0936\u0928<\/strong>, <strong data-start=\"2707\" data-end=\"2722\">C++ \u0938\u0902\u0938\u094d\u0915\u0930\u0923<\/strong>, \u092f\u093e <strong data-start=\"2727\" data-end=\"2746\">\u0917\u094d\u0930\u093e\u092b\u093f\u0915\u0932 \u0909\u0926\u093e\u0939\u0930\u0923<\/strong> \u092d\u0940 \u0924\u0948\u092f\u093e\u0930 \u0915\u0930 \u0938\u0915\u0924\u093e \u0939\u0942\u0901\u0964<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Traveling Salesman Problem In Hindi Using Dynamic Programming With Practical Example [fvplayer id=&#8221;115&#8243;] \u092f\u0939\u093e\u0901 Traveling Salesman Problem (TSP) \u0915\u094b Dynamic Programming \u0926\u094d\u0935\u093e\u0930\u093e \u0939\u0932 \u0915\u0930\u0928\u0947 \u0915\u0940 \u0939\u093f\u0902\u0926\u0940 \u092e\u0947\u0902 \u0935\u093f\u0938\u094d\u0924\u0943\u0924 \u0935\u094d\u092f\u093e\u0916\u094d\u092f\u093e \u0926\u0940 \u0917\u0908 \u0939\u0948, \u091c\u093f\u0938\u092e\u0947\u0902 \u090f\u0915 \u092a\u094d\u0930\u0948\u0915\u094d\u091f\u093f\u0915\u0932 \u0909\u0926\u093e\u0939\u0930\u0923 \u092d\u0940 \u0936\u093e\u092e\u093f\u0932 \u0939\u0948: Traveling Salesman Problem (TSP) \u0915\u094d\u092f\u093e \u0939\u0948? Traveling Salesman Problem (TSP) \u090f\u0915 \u0915\u094d\u0932\u093e\u0938\u093f\u0915\u0932 \u0915\u0902\u092a\u094d\u092f\u0942\u091f\u0930 \u0938\u093e\u0907\u0902\u0938 \u0914\u0930 \u0911\u092a\u094d\u091f\u093f\u092e\u093e\u0907\u091c\u0947\u0936\u0928 [&hellip;]<\/p>\n","protected":false},"author":71,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12],"tags":[],"class_list":["post-2792","post","type-post","status-publish","format-standard","hentry","category-algorithm-analysis-and-design"],"_links":{"self":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/2792","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/users\/71"}],"replies":[{"embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/comments?post=2792"}],"version-history":[{"count":0,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/2792\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/media?parent=2792"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/categories?post=2792"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/tags?post=2792"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}