{"id":2794,"date":"2025-06-09T08:45:43","date_gmt":"2025-06-09T08:45:43","guid":{"rendered":"https:\/\/diznr.com\/?p=2794"},"modified":"2025-06-09T08:45:43","modified_gmt":"2025-06-09T08:45:43","slug":"aad-hindi-all-pair-shortest-path-in-hindi-floyd-warshall-algorithm-with-example-practical","status":"publish","type":"post","link":"https:\/\/www.reilsolar.com\/pdf\/aad-hindi-all-pair-shortest-path-in-hindi-floyd-warshall-algorithm-with-example-practical\/","title":{"rendered":"AAD Hindi &#8211; All Pair Shortest Path in hindi Floyd-Warshall Algorithm With Practical Example"},"content":{"rendered":"<p>AAD Hindi &#8211; All Pair Shortest Path in hindi Floyd-Warshall Algorithm With Practical Example<\/p>\n<p>[fvplayer id=&#8221;117&#8243;]<\/p>\n<h3 data-start=\"0\" data-end=\"96\"><strong data-start=\"4\" data-end=\"94\">\u00a0All Pair Shortest Path (Floyd-Warshall Algorithm) &#8211; Explained in Hindi with Example<\/strong><\/h3>\n<p data-start=\"98\" data-end=\"339\"><strong data-start=\"98\" data-end=\"126\">Floyd-Warshall Algorithm<\/strong> \u090f\u0915 <strong data-start=\"130\" data-end=\"155\">\u0921\u093e\u092f\u0928\u0947\u092e\u093f\u0915 \u092a\u094d\u0930\u094b\u0917\u094d\u0930\u093e\u092e\u093f\u0902\u0917<\/strong> \u0906\u0927\u093e\u0930\u093f\u0924 \u090f\u0932\u094d\u0917\u094b\u0930\u093f\u0926\u092e \u0939\u0948 \u091c\u094b <strong data-start=\"179\" data-end=\"217\">\u0938\u092d\u0940 \u091c\u094b\u0921\u093c\u0940 (All Pair) \u0936\u0949\u0930\u094d\u091f\u0947\u0938\u094d\u091f \u092a\u093e\u0925<\/strong> \u0928\u093f\u0915\u093e\u0932\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u092a\u094d\u0930\u092f\u094b\u0917 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 \u092f\u0939 \u090f\u0932\u094d\u0917\u094b\u0930\u093f\u0926\u092e <strong data-start=\"267\" data-end=\"314\">\u0917\u094d\u0930\u093e\u092b \u092e\u0947\u0902 \u0938\u092d\u0940 \u0928\u094b\u0921\u094d\u0938 \u0915\u0947 \u092c\u0940\u091a \u0938\u092c\u0938\u0947 \u091b\u094b\u091f\u093e \u0930\u093e\u0938\u094d\u0924\u093e<\/strong> \u0916\u094b\u091c\u0928\u0947 \u092e\u0947\u0902 \u092e\u0926\u0926 \u0915\u0930\u0924\u093e \u0939\u0948\u0964<\/p>\n<h2 data-start=\"346\" data-end=\"391\"><strong data-start=\"349\" data-end=\"389\">\u00a0Floyd-Warshall Algorithm \u0915\u093e \u092a\u0930\u093f\u091a\u092f<\/strong><\/h2>\n<p data-start=\"392\" data-end=\"638\">\u00a0\u092f\u0939 <strong data-start=\"397\" data-end=\"434\">\u0921\u093e\u092f\u0930\u0947\u0915\u094d\u091f\u0947\u0921 (Directed) \u0935\u0947\u091f\u0947\u0921 \u0917\u094d\u0930\u093e\u092b<\/strong> \u092a\u0930 \u0915\u093e\u092e \u0915\u0930\u0924\u093e \u0939\u0948\u0964<br data-start=\"450\" data-end=\"453\" \/>\u00a0\u092f\u0939 <strong data-start=\"458\" data-end=\"522\">\u0928\u0947\u0917\u0947\u091f\u093f\u0935 \u0935\u0947\u091f \u090f\u091c (Negative Weight Edge) \u0915\u094b \u092d\u0940 \u0939\u0948\u0902\u0921\u0932 \u0915\u0930 \u0938\u0915\u0924\u093e \u0939\u0948<\/strong> (\u0932\u0947\u0915\u093f\u0928 <strong data-start=\"530\" data-end=\"548\">\u0928\u0947\u0917\u0947\u091f\u093f\u0935 \u0938\u093e\u0907\u0915\u093f\u0932<\/strong> \u0915\u094b \u0928\u0939\u0940\u0902)\u0964<br data-start=\"558\" data-end=\"561\" \/>\u00a0\u0907\u0938\u0915\u093e \u091f\u093e\u0907\u092e \u0915\u0949\u092e\u094d\u092a\u094d\u0932\u0947\u0915\u094d\u0938\u093f\u091f\u0940 <strong data-start=\"588\" data-end=\"597\">O(N\u00b3)<\/strong> \u0939\u094b\u0924\u0940 \u0939\u0948, \u091c\u0939\u093e\u0901 <strong data-start=\"612\" data-end=\"635\">N = \u0928\u094b\u0921\u094d\u0938 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e<\/strong>\u0964<\/p>\n<h3 data-start=\"645\" data-end=\"683\"><strong data-start=\"648\" data-end=\"681\">\u00a0\u090f\u0932\u094d\u0917\u094b\u0930\u093f\u0926\u092e \u0915\u0940 \u092e\u0941\u0916\u094d\u092f \u0905\u0935\u0927\u093e\u0930\u0923\u093e<\/strong><\/h3>\n<p data-start=\"684\" data-end=\"806\">\u00a0\u092e\u093e\u0928 \u0932\u0940\u091c\u093f\u090f \u0915\u093f \u0939\u092e\u093e\u0930\u0947 \u092a\u093e\u0938 <strong data-start=\"711\" data-end=\"734\">N \u0928\u094b\u0921\u094d\u0938 \u0915\u093e \u090f\u0915 \u0917\u094d\u0930\u093e\u092b<\/strong> \u0939\u0948\u0964<br data-start=\"738\" data-end=\"741\" \/>\u00a0\u090f\u0915 <strong data-start=\"748\" data-end=\"798\">\u0921\u093f\u0938\u094d\u091f\u0947\u0902\u0938 \u092e\u0948\u091f\u094d\u0930\u093f\u0915\u094d\u0938 (Distance Matrix) \u092c\u0928\u093e\u0924\u0947 \u0939\u0948\u0902<\/strong>, \u091c\u0939\u093e\u0901<\/p>\n<ul data-start=\"810\" data-end=\"1022\">\n<li data-start=\"810\" data-end=\"863\"><strong data-start=\"812\" data-end=\"861\">dist[i][j] = i \u0938\u0947 j \u0924\u0915 \u091c\u093e\u0928\u0947 \u0915\u0940 \u0938\u092c\u0938\u0947 \u091b\u094b\u091f\u0940 \u0926\u0942\u0930\u0940<\/strong><\/li>\n<li data-start=\"867\" data-end=\"1022\"><strong data-start=\"869\" data-end=\"928\">\u0905\u0917\u0930 \u0915\u094b\u0908 \u0921\u093e\u092f\u0930\u0947\u0915\u094d\u091f \u090f\u091c \u0928\u0939\u0940\u0902 \u0939\u0948, \u0924\u094b Infinity (INF) \u0932\u0947\u0924\u0947 \u0939\u0948\u0902<\/strong><br data-start=\"928\" data-end=\"931\" \/>\u00a0\u0905\u092c \u0939\u092e <strong data-start=\"941\" data-end=\"977\">\u0939\u0930 \u0928\u094b\u0921 k \u0915\u094b \u0907\u0902\u091f\u0930\u092e\u0940\u0921\u093f\u090f\u091f \u0928\u094b\u0921 \u092e\u093e\u0928\u0915\u0930<\/strong> \u0938\u092d\u0940 \u0928\u094b\u0921\u094d\u0938 \u0915\u0947 \u092c\u0940\u091a \u0915\u0947 \u0930\u093e\u0938\u094d\u0924\u0947 \u0905\u092a\u0921\u0947\u091f \u0915\u0930\u0924\u0947 \u0939\u0948\u0902:<\/li>\n<\/ul>\n<div class=\"contain-inline-size rounded-md border-[0.5px] border-token-border-medium relative bg-token-sidebar-surface-primary dark:bg-gray-950\">\n<div class=\"overflow-y-auto p-4\" dir=\"ltr\"><code class=\"!whitespace-pre\">dist[i][j] = <span class=\"hljs-built_in\">min<\/span>(dist[i][j], dist[i][k] + dist[k][j])<br \/>\n<\/code><\/div>\n<\/div>\n<p data-start=\"1094\" data-end=\"1203\">\u00a0\u092f\u0939 \u092a\u094d\u0930\u094b\u0938\u0947\u0938 <strong data-start=\"1109\" data-end=\"1139\">\u0939\u0930 \u0928\u094b\u0921 \u0915\u094b \u0907\u0902\u091f\u0930\u092e\u0940\u0921\u093f\u090f\u091f \u092e\u093e\u0928\u0915\u0930<\/strong> \u0924\u092c \u0924\u0915 \u0926\u094b\u0939\u0930\u093e\u0924\u0947 \u0939\u0948\u0902, \u091c\u092c \u0924\u0915 \u0915\u093f \u0939\u092e \u0938\u092d\u0940 \u0936\u0949\u0930\u094d\u091f\u0947\u0938\u094d\u091f \u092a\u093e\u0925 \u0928 \u0928\u093f\u0915\u093e\u0932 \u0932\u0947\u0902\u0964<\/p>\n<h3 data-start=\"1210\" data-end=\"1236\"><strong data-start=\"1213\" data-end=\"1236\">\u00a0\u0909\u0926\u093e\u0939\u0930\u0923 (Example)<\/strong><\/h3>\n<h3 data-start=\"1237\" data-end=\"1279\"><strong data-start=\"1241\" data-end=\"1277\">\u092e\u093e\u0928 \u0932\u0940\u091c\u093f\u090f \u0939\u092e\u093e\u0930\u0947 \u092a\u093e\u0938 \u092f\u0939 \u0917\u094d\u0930\u093e\u092b \u0939\u0948:<\/strong><\/h3>\n<div class=\"contain-inline-size rounded-md border-[0.5px] border-token-border-medium relative bg-token-sidebar-surface-primary dark:bg-gray-950\">\n<div class=\"overflow-y-auto p-4\" dir=\"ltr\"><code class=\"!whitespace-pre\">      (<span class=\"hljs-selector-tag\">A<\/span>)<br \/>\n\/   \\<br \/>\n<span class=\"hljs-number\">4<\/span>     <span class=\"hljs-number\">1<\/span><br \/>\n\/       \\<br \/>\n(<span class=\"hljs-selector-tag\">B<\/span>) --- <span class=\"hljs-number\">2<\/span> --- (C)<br \/>\n<\/code><\/div>\n<\/div>\n<h3 data-start=\"1357\" data-end=\"1386\"><strong data-start=\"1361\" data-end=\"1386\">\u0935\u0947\u091f\u0947\u0921 \u090f\u0921\u094d\u091c \u092e\u0948\u091f\u094d\u0930\u093f\u0915\u094d\u0938:<\/strong><\/h3>\n<table data-start=\"1387\" data-end=\"1476\">\n<thead data-start=\"1387\" data-end=\"1404\">\n<tr data-start=\"1387\" data-end=\"1404\">\n<th data-start=\"1387\" data-end=\"1391\"><\/th>\n<th data-start=\"1391\" data-end=\"1395\">A<\/th>\n<th data-start=\"1395\" data-end=\"1399\">B<\/th>\n<th data-start=\"1399\" data-end=\"1404\">C<\/th>\n<\/tr>\n<\/thead>\n<tbody data-start=\"1423\" data-end=\"1476\">\n<tr data-start=\"1423\" data-end=\"1440\">\n<td>A<\/td>\n<td>0<\/td>\n<td>4<\/td>\n<td>1<\/td>\n<\/tr>\n<tr data-start=\"1441\" data-end=\"1458\">\n<td>B<\/td>\n<td>\u221e<\/td>\n<td>0<\/td>\n<td>2<\/td>\n<\/tr>\n<tr data-start=\"1459\" data-end=\"1476\">\n<td>C<\/td>\n<td>\u221e<\/td>\n<td>\u221e<\/td>\n<td>0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h3 data-start=\"1483\" data-end=\"1530\"><strong data-start=\"1486\" data-end=\"1530\">\u00a0Python \u0915\u094b\u0921 (Floyd-Warshall Algorithm)<\/strong><\/h3>\n<div class=\"contain-inline-size rounded-md border-[0.5px] border-token-border-medium relative bg-token-sidebar-surface-primary dark:bg-gray-950\">\n<div class=\"overflow-y-auto p-4\" dir=\"ltr\">\n<p><code class=\"!whitespace-pre language-python\"><span class=\"hljs-keyword\">import<\/span> sys<\/code><\/p>\n<p><span class=\"hljs-comment\"># Define number of vertices<\/span><br \/>\nN = <span class=\"hljs-number\">3<\/span><\/p>\n<p><span class=\"hljs-comment\"># Infinity value (for no direct path)<\/span><br \/>\nINF = sys.maxsize<\/p>\n<p><span class=\"hljs-comment\"># Graph adjacency matrix (distance representation)<\/span><br \/>\ndist = [<br \/>\n[<span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">4<\/span>, <span class=\"hljs-number\">1<\/span>],<br \/>\n[INF, <span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">2<\/span>],<br \/>\n[INF, INF, <span class=\"hljs-number\">0<\/span>]<br \/>\n]<\/p>\n<p><span class=\"hljs-comment\"># Floyd-Warshall Algorithm<\/span><br \/>\n<span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title function_\">floyd_warshall<\/span>():<br \/>\n<span class=\"hljs-keyword\">global<\/span> dist<br \/>\n<span class=\"hljs-keyword\">for<\/span> k <span class=\"hljs-keyword\">in<\/span> <span class=\"hljs-built_in\">range<\/span>(N): <span class=\"hljs-comment\"># Intermediate node<\/span><br \/>\n<span class=\"hljs-keyword\">for<\/span> i <span class=\"hljs-keyword\">in<\/span> <span class=\"hljs-built_in\">range<\/span>(N): <span class=\"hljs-comment\"># Source node<\/span><br \/>\n<span class=\"hljs-keyword\">for<\/span> j <span class=\"hljs-keyword\">in<\/span> <span class=\"hljs-built_in\">range<\/span>(N): <span class=\"hljs-comment\"># Destination node<\/span><br \/>\n<span class=\"hljs-keyword\">if<\/span> dist[i][k] != INF <span class=\"hljs-keyword\">and<\/span> dist[k][j] != INF:<br \/>\ndist[i][j] = <span class=\"hljs-built_in\">min<\/span>(dist[i][j], dist[i][k] + dist[k][j])<\/p>\n<p><span class=\"hljs-comment\"># Run algorithm<\/span><br \/>\nfloyd_warshall()<\/p>\n<p><span class=\"hljs-comment\"># Print final shortest path matrix<\/span><br \/>\n<span class=\"hljs-built_in\">print<\/span>(<span class=\"hljs-string\">&#8220;All-Pair Shortest Path Matrix:&#8221;<\/span>)<br \/>\n<span class=\"hljs-keyword\">for<\/span> row <span class=\"hljs-keyword\">in<\/span> dist:<br \/>\n<span class=\"hljs-built_in\">print<\/span>(row)<\/p>\n<\/div>\n<\/div>\n<h3 data-start=\"2248\" data-end=\"2293\"><strong data-start=\"2251\" data-end=\"2293\">\u0906\u0909\u091f\u092a\u0941\u091f (Final Shortest Path Matrix)<\/strong><\/h3>\n<div class=\"contain-inline-size rounded-md border-[0.5px] border-token-border-medium relative bg-token-sidebar-surface-primary dark:bg-gray-950\">\n<div class=\"overflow-y-auto p-4\" dir=\"ltr\"><code class=\"!whitespace-pre\"><span class=\"hljs-keyword\">All<\/span><span class=\"hljs-selector-tag\">-Pair<\/span> <span class=\"hljs-selector-tag\">Shortest<\/span> <span class=\"hljs-selector-tag\">Path<\/span> <span class=\"hljs-selector-tag\">Matrix<\/span>:<br \/>\n<span class=\"hljs-selector-attr\">[0, 3, 1]<\/span><br \/>\n<span class=\"hljs-selector-attr\">[INF, 0, 2]<\/span><br \/>\n<span class=\"hljs-selector-attr\">[INF, INF, 0]<\/span><br \/>\n<\/code><\/div>\n<\/div>\n<p data-start=\"2369\" data-end=\"2573\"><strong data-start=\"2372\" data-end=\"2388\">Explanation:<\/strong><br data-start=\"2388\" data-end=\"2391\" \/><code data-start=\"2393\" data-end=\"2400\">A \u2192 B<\/code> \u0915\u093e \u0936\u0949\u0930\u094d\u091f\u0947\u0938\u094d\u091f \u092a\u093e\u0925: <strong data-start=\"2419\" data-end=\"2424\">3<\/strong> (A \u2192 C \u2192 B)<br data-start=\"2436\" data-end=\"2439\" \/><code data-start=\"2441\" data-end=\"2448\">A \u2192 C<\/code> \u0915\u093e \u0936\u0949\u0930\u094d\u091f\u0947\u0938\u094d\u091f \u092a\u093e\u0925: <strong data-start=\"2467\" data-end=\"2472\">1<\/strong><br data-start=\"2472\" data-end=\"2475\" \/><code data-start=\"2477\" data-end=\"2484\">B \u2192 C<\/code> \u0915\u093e \u0936\u0949\u0930\u094d\u091f\u0947\u0938\u094d\u091f \u092a\u093e\u0925: <strong data-start=\"2503\" data-end=\"2508\">2<\/strong><br data-start=\"2508\" data-end=\"2511\" \/><code data-start=\"2513\" data-end=\"2520\">B \u2192 A<\/code> \u0914\u0930 <code data-start=\"2524\" data-end=\"2538\">C \u2192 A, C \u2192 B<\/code> \u0915\u0947 \u0932\u093f\u090f <strong data-start=\"2546\" data-end=\"2565\">\u0915\u094b\u0908 \u0930\u093e\u0938\u094d\u0924\u093e \u0928\u0939\u0940\u0902<\/strong> (INF)<\/p>\n<h3 data-start=\"2580\" data-end=\"2620\"><strong data-start=\"2583\" data-end=\"2618\">\u00a0\u091f\u093e\u0907\u092e \u0914\u0930 \u0938\u094d\u092a\u0947\u0938 \u0915\u0949\u092e\u094d\u092a\u094d\u0932\u0947\u0915\u094d\u0938\u093f\u091f\u0940<\/strong><\/h3>\n<p data-start=\"2621\" data-end=\"2705\"><strong data-start=\"2623\" data-end=\"2643\">Time Complexity:<\/strong> <code data-start=\"2644\" data-end=\"2651\">O(N\u00b3)<\/code><br data-start=\"2651\" data-end=\"2654\" \/><strong data-start=\"2656\" data-end=\"2677\">Space Complexity:<\/strong> <code data-start=\"2678\" data-end=\"2685\">O(N\u00b2)<\/code> (Distance Matrix)<\/p>\n<h3 data-start=\"2712\" data-end=\"2770\"><strong data-start=\"2715\" data-end=\"2770\">\u00a0Floyd-Warshall Algorithm \u0915\u0947 \u0909\u092a\u092f\u094b\u0917 (Applications)<\/strong><\/h3>\n<p data-start=\"2771\" data-end=\"2930\"><strong data-start=\"2773\" data-end=\"2809\">\u0928\u0947\u091f\u0935\u0930\u094d\u0915 \u0930\u0942\u091f\u093f\u0902\u0917 (Network Routing)<\/strong><br data-start=\"2809\" data-end=\"2812\" \/><strong data-start=\"2814\" data-end=\"2861\">\u092e\u0948\u092a\u094d\u0938 \u0914\u0930 \u0928\u0947\u0935\u093f\u0917\u0947\u0936\u0928 \u0938\u093f\u0938\u094d\u091f\u092e (Google Maps, GPS)<\/strong><br data-start=\"2861\" data-end=\"2864\" \/><strong data-start=\"2866\" data-end=\"2891\">\u0938\u094b\u0936\u0932 \u0928\u0947\u091f\u0935\u0930\u094d\u0915 \u090f\u0928\u093e\u0932\u093f\u0938\u093f\u0938<\/strong><br data-start=\"2891\" data-end=\"2894\" \/><strong data-start=\"2896\" data-end=\"2928\">\u0921\u0947\u091f\u093e \u0938\u0947\u0902\u091f\u0930 \u0914\u0930 \u092a\u0948\u0915\u0947\u091f \u0938\u094d\u0935\u093f\u091a\u093f\u0902\u0917<\/strong><\/p>\n<h3 data-start=\"2937\" data-end=\"2968\"><strong data-start=\"2940\" data-end=\"2968\">\u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937 (Conclusion)<\/strong><\/h3>\n<ul data-start=\"2969\" data-end=\"3221\">\n<li data-start=\"2969\" data-end=\"3070\"><strong data-start=\"2971\" data-end=\"2999\">Floyd-Warshall Algorithm<\/strong> \u0938\u092d\u0940 \u0928\u094b\u0921\u094d\u0938 \u0915\u0947 \u092c\u0940\u091a <strong data-start=\"3017\" data-end=\"3037\">\u0938\u092c\u0938\u0947 \u091b\u094b\u091f\u093e \u0930\u093e\u0938\u094d\u0924\u093e<\/strong> \u0928\u093f\u0915\u093e\u0932\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u092c\u0939\u0941\u0924 \u0909\u092a\u092f\u094b\u0917\u0940 \u0939\u0948\u0964<\/li>\n<li data-start=\"3071\" data-end=\"3150\">\u092f\u0939 <strong data-start=\"3076\" data-end=\"3101\">\u0921\u093e\u092f\u0928\u0947\u092e\u093f\u0915 \u092a\u094d\u0930\u094b\u0917\u094d\u0930\u093e\u092e\u093f\u0902\u0917<\/strong> \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0924\u093e \u0939\u0948 \u0914\u0930 <strong data-start=\"3122\" data-end=\"3147\">O(N\u00b3) \u0938\u092e\u092f \u092e\u0947\u0902 \u091a\u0932\u0924\u093e \u0939\u0948<\/strong>\u0964<\/li>\n<li data-start=\"3151\" data-end=\"3221\"><strong data-start=\"3153\" data-end=\"3218\">\u0928\u0947\u0917\u0947\u091f\u093f\u0935 \u0935\u0947\u091f \u0915\u094b \u0939\u0948\u0902\u0921\u0932 \u0915\u0930 \u0938\u0915\u0924\u093e \u0939\u0948, \u0932\u0947\u0915\u093f\u0928 \u0928\u0947\u0917\u0947\u091f\u093f\u0935 \u0938\u093e\u0907\u0915\u093f\u0932 \u0915\u094b \u0928\u0939\u0940\u0902<\/strong>\u0964<\/li>\n<\/ul>\n<h3 data-start=\"3228\" data-end=\"3309\" data-is-last-node=\"\" data-is-only-node=\"\">\u00a0<strong data-start=\"3235\" data-end=\"3309\" data-is-last-node=\"\">\u0915\u094d\u092f\u093e \u0906\u092a Bellman-Ford Algorithm \u092f\u093e Dijkstra Algorithm \u092d\u0940 \u0938\u092e\u091d\u0928\u093e \u091a\u093e\u0939\u0947\u0902\u0917\u0947?<\/strong><\/h3>\n<h3><a href=\"https:\/\/www.bgsbu.ac.in\/btechdit\/ITE_Syllabus_20_Apr_2021.pdf\" target=\"_blank\" rel=\"noopener\">AAD Hindi &#8211; All Pair Shortest Path in hindi Floyd-Warshall Algorithm With Practical Example<\/a><\/h3>\n<p>Here\u2019s a complete explanation of the <strong>Floyd-Warshall Algorithm<\/strong> (All Pair Shortest Path) in <strong>Hindi<\/strong> with a <strong>practical example<\/strong>, perfect for <strong>B.Tech, BCA, GATE, or competitive exams<\/strong> under <strong>AAD (Advanced Algorithm Design)<\/strong>.<\/p>\n<hr \/>\n<h2>\ud83e\udde0 <strong>Floyd-Warshall Algorithm (All-Pairs Shortest Path) \u2013 \u0939\u093f\u0902\u0926\u0940 \u092e\u0947\u0902<\/strong><\/h2>\n<h3>\ud83d\udd37 <strong>\u0915\u094d\u092f\u093e \u0939\u0948 Floyd-Warshall Algorithm?<\/strong><\/h3>\n<p>Floyd-Warshall \u090f\u0915 <strong>Dynamic Programming<\/strong> \u0906\u0927\u093e\u0930\u093f\u0924 \u090f\u0932\u094d\u0917\u094b\u0930\u093f\u0925\u094d\u092e \u0939\u0948 \u091c\u093f\u0938\u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u090f\u0915 \u0917\u094d\u0930\u093e\u092b \u0915\u0947 <strong>\u0938\u092d\u0940 \u0928\u094b\u0921\u094d\u0938 \u0915\u0947 \u092c\u0940\u091a \u0915\u0940 \u0938\u092c\u0938\u0947 \u091b\u094b\u091f\u0940 \u0926\u0942\u0930\u0940<\/strong> (All-Pairs Shortest Path) \u0916\u094b\u091c\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/p>\n<hr \/>\n<h2>\ud83d\udccc <strong>Algorithm \u0915\u093e \u0909\u0926\u094d\u0926\u0947\u0936\u094d\u092f:<\/strong><\/h2>\n<ul>\n<li>Directed \u092f\u093e Undirected \u0917\u094d\u0930\u093e\u092b \u092e\u0947\u0902<\/li>\n<li>Negative weights \u0939\u094b \u0938\u0915\u0924\u0947 \u0939\u0948\u0902, \u0932\u0947\u0915\u093f\u0928 <strong>Negative cycle \u0928\u0939\u0940\u0902 \u0939\u094b\u0928\u093e \u091a\u093e\u0939\u093f\u090f<\/strong>\u0964<\/li>\n<li>\u0938\u092d\u0940 vertex pairs (i, j) \u0915\u0947 \u0932\u093f\u090f shortest distance \u0928\u093f\u0915\u093e\u0932\u0924\u093e \u0939\u0948\u0964<\/li>\n<\/ul>\n<hr \/>\n<h2>\ud83d\udcda <strong>\u090f\u0932\u094d\u0917\u094b\u0930\u093f\u0926\u092e \u0915\u0940 \u0938\u094d\u091f\u0947\u092a\u094d\u0938 (\u0939\u093f\u0902\u0926\u0940 \u092e\u0947\u0902)<\/strong><\/h2>\n<p>\u092e\u093e\u0928 \u0932\u0940\u091c\u093f\u090f \u0939\u092e\u093e\u0930\u0947 \u092a\u093e\u0938 n nodes \u0935\u093e\u0932\u093e \u090f\u0915 \u0917\u094d\u0930\u093e\u092b \u0939\u0948\u0964 \u0939\u092e \u090f\u0915 <strong>Distance Matrix (D)<\/strong> \u092c\u0928\u093e\u090f\u0902\u0917\u0947, \u091c\u0939\u093e\u0901:<\/p>\n<ul>\n<li>\u092f\u0926\u093f <span class=\"katex\">i==ji == j<\/span>, \u0924\u094b <span class=\"katex\">D[i][j]=0D[i][j] = 0<\/span><\/li>\n<li>\u092f\u0926\u093f <span class=\"katex\">ii<\/span> \u0938\u0947 <span class=\"katex\">jj<\/span> \u0915\u0947 \u092c\u0940\u091a edge \u0939\u0948, \u0924\u094b <span class=\"katex\">D[i][j]=weightD[i][j] = weight<\/span><\/li>\n<li>\u0928\u0939\u0940\u0902 \u0939\u0948 \u0924\u094b <span class=\"katex\">D[i][j]=\u221eD[i][j] = \u221e<\/span><\/li>\n<\/ul>\n<p>\u0905\u092c \u0939\u092e \u0924\u0940\u0928 nested loops \u091a\u0932\u093e\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<pre><code class=\"language-pseudo\">for k = 1 to n:\n   for i = 1 to n:\n      for j = 1 to n:\n         if D[i][j] &gt; D[i][k] + D[k][j]:\n             D[i][j] = D[i][k] + D[k][j]\n<\/code><\/pre>\n<p>\u092f\u0939 \u091a\u0947\u0915 \u0915\u0930\u0924\u093e \u0939\u0948 \u0915\u093f \u0915\u094d\u092f\u093e i \u0938\u0947 j \u0915\u0940 current distance \u0938\u0947 \u092c\u0947\u0939\u0924\u0930 \u0930\u093e\u0938\u094d\u0924\u093e k \u0915\u0947 through \u0939\u094b \u0938\u0915\u0924\u093e \u0939\u0948\u0964<\/p>\n<hr \/>\n<h2>\ud83e\uddea <strong>Practical Example:<\/strong><\/h2>\n<p>\u092e\u093e\u0928 \u0932\u0940\u091c\u093f\u090f \u0939\u092e\u093e\u0930\u0947 \u092a\u093e\u0938 4 vertex \u0939\u0948\u0902 \u0914\u0930 \u0928\u0940\u091a\u0947 \u0926\u093f\u092f\u093e \u0917\u092f\u093e weighted graph \u0939\u0948:<\/p>\n<pre><code>Graph Matrix (Adjacency):\n      0   3   \u221e   7\n      8   0   2   \u221e\n      5   \u221e   0   1\n      2   \u221e   \u221e   0\n<\/code><\/pre>\n<p>\u0907\u0938\u0947 \u0939\u092e Distance Matrix D \u092e\u093e\u0928\u0924\u0947 \u0939\u0948\u0902\u0964 \u0905\u092c \u0939\u092e Floyd-Warshall \u090f\u0932\u094d\u0917\u094b\u0930\u093f\u0926\u094d\u092e \u0932\u0917\u093e\u0924\u0947 \u0939\u0948\u0902\u0964<\/p>\n<h3>\ud83d\udd01 Update \u0939\u094b\u0924\u093e \u0930\u0939\u0947\u0917\u093e \u091c\u0948\u0938\u0947:<\/h3>\n<ul>\n<li>k = 1: All paths through node 1<\/li>\n<li>k = 2: All paths through node 2<\/li>\n<li>&#8230;<\/li>\n<li>k = n: Final shortest paths between all nodes<\/li>\n<\/ul>\n<p>\ud83d\udc49 \u0905\u0902\u0924\u093f\u092e Matrix \u0938\u092d\u0940 node pairs \u0915\u0947 \u092c\u0940\u091a \u0915\u0940 <strong>minimum distances<\/strong> \u0915\u094b \u0926\u0930\u094d\u0936\u093e\u0924\u0940 \u0939\u0948\u0964<\/p>\n<hr \/>\n<h2>\ud83d\udcca Final Output (Shortest Distance Matrix):<\/h2>\n<p>(After applying Floyd-Warshall)<\/p>\n<pre><code>    0   3   5   6\n    7   0   2   3\n    5   8   0   1\n    2   5   7   0\n<\/code><\/pre>\n<hr \/>\n<h2>\ud83d\udccc Time Complexity:<\/h2>\n<p><span class=\"katex\">O(n3)O(n^3)<\/span><\/p>\n<hr \/>\n<h2>\ud83d\udd10 Key Points:<\/h2>\n<table>\n<thead>\n<tr>\n<th>\u0935\u093f\u0936\u0947\u0937\u0924\u093e<\/th>\n<th>\u0935\u093f\u0935\u0930\u0923<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Input<\/td>\n<td>Weighted graph (matrix)<\/td>\n<\/tr>\n<tr>\n<td>Allowed Weights<\/td>\n<td>Positive or Negative<\/td>\n<\/tr>\n<tr>\n<td>Not Allowed<\/td>\n<td>Negative Cycles<\/td>\n<\/tr>\n<tr>\n<td>Complexity<\/td>\n<td><span class=\"katex\">O(n3)O(n^3)<\/span><\/td>\n<\/tr>\n<tr>\n<td>Technique<\/td>\n<td>Dynamic Programming<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<hr \/>\n<h2>\ud83d\udd04 Need Extra Help?<\/h2>\n<p>Would you like:<\/p>\n<ul>\n<li>\ud83d\udcdd Floyd-Warshall \u0915\u093e <strong>step-by-step Hindi PDF notes<\/strong>?<\/li>\n<li>\ud83c\udfa5 <strong>Hindi video explanation<\/strong> with animated graph?<\/li>\n<li>\ud83e\uddea A <strong>live code implementation in Python or C++<\/strong>?<\/li>\n<\/ul>\n<p>Just tell me and I\u2019ll provide the exact format you need!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>AAD Hindi &#8211; All Pair Shortest Path in hindi Floyd-Warshall Algorithm With Practical Example [fvplayer id=&#8221;117&#8243;] \u00a0All Pair Shortest Path (Floyd-Warshall Algorithm) &#8211; Explained in Hindi with Example Floyd-Warshall Algorithm \u090f\u0915 \u0921\u093e\u092f\u0928\u0947\u092e\u093f\u0915 \u092a\u094d\u0930\u094b\u0917\u094d\u0930\u093e\u092e\u093f\u0902\u0917 \u0906\u0927\u093e\u0930\u093f\u0924 \u090f\u0932\u094d\u0917\u094b\u0930\u093f\u0926\u092e \u0939\u0948 \u091c\u094b \u0938\u092d\u0940 \u091c\u094b\u0921\u093c\u0940 (All Pair) \u0936\u0949\u0930\u094d\u091f\u0947\u0938\u094d\u091f \u092a\u093e\u0925 \u0928\u093f\u0915\u093e\u0932\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u092a\u094d\u0930\u092f\u094b\u0917 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 \u092f\u0939 \u090f\u0932\u094d\u0917\u094b\u0930\u093f\u0926\u092e \u0917\u094d\u0930\u093e\u092b \u092e\u0947\u0902 \u0938\u092d\u0940 [&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-2794","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\/2794","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=2794"}],"version-history":[{"count":0,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/2794\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/media?parent=2794"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/categories?post=2794"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/tags?post=2794"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}