{"id":105966,"date":"2025-04-14T09:06:36","date_gmt":"2025-04-14T04:36:36","guid":{"rendered":"https:\/\/nabfollower.com\/blog\/breadth-first-search-bfs-algorithm-3lmh\/"},"modified":"2025-04-14T09:06:36","modified_gmt":"2025-04-14T04:36:36","slug":"breadth-first-search-bfs-algorithm-3lmh","status":"publish","type":"post","link":"https:\/\/nabfollower.com\/blog\/breadth-first-search-bfs-algorithm-3lmh\/","title":{"rendered":"\ud83d\udd0d \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062c\u0633\u062a\u062c\u0648\u06cc Wredth-First (BFS)"},"content":{"rendered":"<div data-article-id=\"2405381\" id=\"article-body\">\n<p><strong>\ud83e\udde0 \u0627\u06cc\u0646 \u0631\u0627 \u062a\u0635\u0648\u0631 \u06a9\u0646\u06cc\u062f:<\/strong><br \/>\u0634\u0645\u0627 \u062f\u0631 \u067e\u06cc\u0686 \u0648 \u062e\u0645 \u0627\u062a\u0627\u0642 \u0647\u0633\u062a\u06cc\u062f. \u0634\u0645\u0627 \u0645\u06cc \u062e\u0648\u0627\u0647\u06cc\u062f \u06a9\u0648\u062a\u0627\u0647\u062a\u0631\u06cc\u0646 \u0631\u0627\u0647 \u0631\u0627 \u067e\u06cc\u062f\u0627 \u06a9\u0646\u06cc\u062f. \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u0627\u0632 \u0627\u062a\u0627\u0642 \u0627\u0648\u0644 \u0634\u0631\u0648\u0639 \u0645\u06cc \u06a9\u0646\u06cc\u062f \u060c \u062a\u0645\u0627\u0645 \u0627\u062a\u0627\u0642 \u0647\u0627\u06cc \u0645\u062c\u0627\u0648\u0631 \u0631\u0627 \u0628\u0631\u0631\u0633\u06cc \u06a9\u0646\u06cc\u062f \u060c \u0633\u067e\u0633 \u0628\u0647 \u0644\u0627\u06cc\u0647 \u0628\u0639\u062f\u06cc \u0627\u062a\u0627\u0642 \u0647\u0627 \u0628\u0631\u0648\u06cc\u062f \u0648 \u062a\u0627 \u0631\u0633\u06cc\u062f\u0646 \u0628\u0647 \u062e\u0631\u0648\u062c\u06cc \u060c \u06af\u0633\u062a\u0631\u0634 \u062f\u0647\u06cc\u062f.<br \/>\u0627\u06cc\u0646 \u062c\u0633\u062a\u062c\u0648\u06cc \u0648\u0633\u0639\u062a \u0627\u0648\u0644 (BFS) \u0627\u0633\u062a-\u0634\u0645\u0627 \u0644\u0627\u06cc\u0647 \u0628\u0631 \u0631\u0648\u06cc \u0644\u0627\u06cc\u0647 \u060c \u0633\u0637\u062d \u0628\u0631 \u0627\u0633\u0627\u0633 \u0633\u0637\u062d \u0631\u0627 \u06a9\u0634\u0641 \u0645\u06cc \u06a9\u0646\u06cc\u062f.<\/p>\n<p><strong>bs BFS \u0686\u06cc\u0633\u062a\u061f<\/strong><br \/>Wreadth-First Search (BFS) \u06cc\u06a9 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0627\u0633\u0627\u0633\u06cc \u0646\u0645\u0648\u062f\u0627\u0631 Traversal \u0627\u0633\u062a \u06a9\u0647 \u0633\u0637\u062d \u06af\u0631\u0647 \u0647\u0627 \u0631\u0627 \u0628\u0631 \u0627\u0633\u0627\u0633 \u0633\u0637\u062d \u0628\u0631\u0631\u0633\u06cc \u0645\u06cc \u06a9\u0646\u062f. \u0627\u06cc\u0646 \u0627\u0645\u0631 \u0628\u0647 \u0648\u06cc\u0698\u0647 \u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u06a9\u0648\u062a\u0627\u0647\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u062f\u0631 \u0646\u0645\u0648\u062f\u0627\u0631\u0647\u0627\u06cc \u0628\u062f\u0648\u0646 \u0648\u0632\u0646\u06cc \u0645\u0641\u06cc\u062f \u0627\u0633\u062a.<br \/>\u0628\u0647 \u0627\u06cc\u0646 \u0641\u06a9\u0631 \u06a9\u0646\u06cc\u062f \u0645\u0627\u0646\u0646\u062f \u06a9\u0627\u0648\u0634 \u062f\u0631 \u06cc\u06a9 \u062f\u0631\u062e\u062a \u0628\u0647 \u0635\u0648\u0631\u062a \u0627\u0641\u0642\u06cc: \u0634\u0645\u0627 \u0642\u0628\u0644 \u0627\u0632 \u0631\u0641\u062a\u0646 \u0628\u0647 \u067e\u0633\u0631 \u0639\u0645\u0648\u06cc \u062e\u0648\u062f \u060c \u0647\u0645\u0647 \u062e\u0648\u0627\u0647\u0631 \u0648 \u0628\u0631\u0627\u062f\u0631\u0647\u0627\u06cc \u062e\u0648\u062f \u0631\u0627 \u0628\u0631\u0631\u0633\u06cc \u0645\u06cc \u06a9\u0646\u06cc\u062f!<\/p>\n<p><strong>\ud83e\udde0 \u0686\u06af\u0648\u0646\u0647 \u06a9\u0627\u0631 \u0645\u06cc \u06a9\u0646\u062f<\/strong><br \/>1. \u0627\u0632 \u06cc\u06a9 \u06af\u0631\u0647 \u0634\u0631\u0648\u0639 \u06a9\u0646\u06cc\u062f (\u0645\u062b\u0644\u0627\u064b \u06af\u0631\u0647 0).<br \/>2. \u0627\u0632 \u06cc\u06a9 \u0635\u0641 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0646\u06cc\u062f \u062a\u0627 \u0628\u0647 \u062e\u0627\u0637\u0631 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u06cc\u062f &#8220;\u0686\u0647 \u0686\u06cc\u0632\u06cc \u0628\u0631\u0627\u06cc \u0628\u0627\u0632\u062f\u06cc\u062f \u0628\u0639\u062f\u06cc&#8221;.<br \/>3. \u0628\u0627\u0632\u062f\u06cc\u062f \u0627\u0632[] \u0622\u0631\u0627\u06cc\u0647 \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u0628\u0627\u0632\u062f\u06cc\u062f\u0647\u0627\u06cc \u062e\u0648\u062f \u0631\u0627 \u062a\u06a9\u0631\u0627\u0631 \u0646\u0645\u06cc \u06a9\u0646\u06cc\u062f.<br \/>4. \u0628\u0631\u0627\u06cc \u0647\u0631 \u06af\u0631\u0647:<br \/>\u0647\u0645\u0633\u0627\u06cc\u06af\u0627\u0646 \u0628\u06cc \u0646\u0638\u06cc\u0631 \u062e\u0648\u062f \u0631\u0627 \u0628\u0647 \u0635\u0641 \u0627\u0636\u0627\u0641\u0647 \u06a9\u0646\u06cc\u062f.<br \/>\u06cc\u06a9\u06cc \u06cc\u06a9\u06cc \u0627\u0632 \u0622\u0646\u0647\u0627 \u0628\u0627\u0632\u062f\u06cc\u062f \u06a9\u0646\u06cc\u062f.<br \/>\ud83d\udce5queue \u0646\u0638\u0645 \u0631\u0627 \u062a\u0636\u0645\u06cc\u0646 \u0645\u06cc \u06a9\u0646\u062f &#8211; \u0627\u0648\u0644 \u060c \u0627\u0648\u0644. \u0645\u0646\u0627\u0633\u0628 \u0628\u0631\u0627\u06cc \u0633\u0637\u062d \u0633\u0637\u062d <br \/>\u0633\u0641\u0631<\/p>\n<p><strong>\ud83e\udd1d \u0645\u0648\u0627\u0631\u062f \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u062f\u0631 \u062f\u0646\u06cc\u0627\u06cc \u0648\u0627\u0642\u0639\u06cc<\/strong><br \/>\u067e\u06cc\u0634\u0646\u0647\u0627\u062f\u0627\u062a \u0634\u0628\u06a9\u0647 \u0627\u062c\u062a\u0645\u0627\u0639\u06cc (\u0686\u0647 \u06a9\u0633\u06cc 1 \u062f\u0648\u0633\u062a \u0627\u0632 \u062f\u0648\u0633\u062a \u0634\u0645\u0627 \u062f\u0648\u0631 \u0627\u0633\u062a\u061f)<br \/>\u062e\u0632\u06cc\u062f\u0646<br \/>\u06a9\u0648\u062a\u0627\u0647\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u062f\u0631 \u0646\u0645\u0648\u062f\u0627\u0631\u0647\u0627\u06cc \u0628\u062f\u0648\u0646 \u0648\u0632\u0646\u06cc<br \/>\u0634\u0628\u06a9\u0647 \u0647\u0627\u06cc \u0647\u0645\u062a\u0627 \u0628\u0647 \u0647\u0645\u0633\u0627\u0644\u0627\u0646 <\/p>\n<p><strong>\ud83d\udd04 \u0645\u062b\u0627\u0644 \u0627\u062c\u0631\u0627\u06cc \u062e\u0634\u06a9 (\u0646\u0645\u0648\u062f\u0627\u0631)<\/strong><\/p>\n<p><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/media2.dev.to\/dynamic\/image\/width=800%2Cheight=%2Cfit=scale-down%2Cgravity=auto%2Cformat=auto\/https%3A%2F%2Fdev-to-uploads.s3.amazonaws.com%2Fuploads%2Farticles%2Fonfz00f1z87nefhrvtzz.png\" alt=\"\u0634\u0631\u062d \u062a\u0635\u0648\u06cc\u0631\" loading=\"lazy\" width=\"675\" height=\"210\" title=\"\"><\/p>\n<p><strong>order \u0633\u0641\u0627\u0631\u0634 Traversal:<\/strong> 1 \u2192 2 \u2192 3 \u2192 4 \u2192 5<br \/><strong>\u2705 \u062a\u0648\u0636\u06cc\u062d<\/strong>:<br \/>\u0627\u0632 \u06af\u0631\u0647 1 \u2192 \u0647\u0645\u0633\u0627\u06cc\u06af\u0627\u0646 Enqueue 2 \u0648 3 \u0634\u0631\u0648\u0639 \u06a9\u0646\u06cc\u062f<br \/>\u0628\u0647 2 \u2192 Enqueue 4 \u0645\u0631\u0627\u062c\u0639\u0647 \u06a9\u0646\u06cc\u062f<br \/>\u0628\u0647 3 \u2192 Enqueue 5 \u0645\u0631\u0627\u062c\u0639\u0647 \u06a9\u0646\u06cc\u062f<br \/>\u0628\u0627\u0632\u062f\u06cc\u062f \u0627\u0632 4 (\u0642\u0628\u0644\u0627\u064b \u0627\u0636\u0627\u0641\u0647 \u0634\u062f\u0647)<br \/>\u0628\u0627\u0632\u062f\u06cc\u062f \u0627\u0632 5<br \/>\u0635\u0641 \u062e\u0627\u0644\u06cc \u0645\u06cc \u0634\u0648\u062f.<\/p>\n<div class=\"highlight js-code-highlight\">\n<pre class=\"highlight plaintext\"><code>#include <iostream>\n#include <vector>\n#include <queue>\nusing namespace std;\n\nvector<int> bfsOfGraph(int V, vector<int> adj[]) {\n    vector<int> bfs;\n    vector<bool> visited(V, false);\n    queue<int> q;\n\n    \/\/ Start BFS from node 0\n    q.push(0);\n    visited[0] = true;\n\n    while (!q.empty()) {\n        int node = q.front();\n        q.pop();\n        bfs.push_back(node);\n\n        for (int neighbor : adj[node]) {\n            if (!visited[neighbor]) {\n                visited[neighbor] = true;\n                q.push(neighbor);\n            }\n        }\n    }\n\n    return bfs;\n}\n\nint main() {\n    int V = 5;\n    vector<int> adj[V];\n\n    \/\/ Undirected Graph Example\n    adj[0] = {1, 2};\n    adj[1] = {0, 3};\n    adj[2] = {0, 4};\n    adj[3] = {1};\n    adj[4] = {2};\n\n    vector<int> result = bfsOfGraph(V, adj);\n\n    cout &lt;&lt; \"BFS Traversal: \";\n    for (int node : result)\n        cout &lt;&lt; node &lt;&lt; \" \";\n    cout &lt;&lt; endl;\n\n    return 0;\n}\n\n<\/int><\/int><\/int><\/bool><\/int><\/int><\/int><\/queue><\/vector><\/iostream><\/code><\/pre>\n<div class=\"highlight__panel js-actions-panel\">\n<div class=\"highlight__panel-action js-fullscreen-code-action\">\n    <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"20px\" height=\"20px\" viewbox=\"0 0 24 24\" class=\"highlight-action crayons-icon highlight-action--fullscreen-on\"><title>\u062d\u0627\u0644\u062a \u062a\u0645\u0627\u0645 \u0635\u0641\u062d\u0647 \u0631\u0627 \u0648\u0627\u0631\u062f \u06a9\u0646\u06cc\u062f<\/title>\n    <path d=\"M16 3h6v6h-2V5h-4V3zM2 3h6v2H4v4H2V3zm18 16v-4h2v6h-6v-2h4zM4 19h4v2H2v-6h2v4z\"\/>\n<\/svg><\/p>\n<p>    <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"20px\" height=\"20px\" viewbox=\"0 0 24 24\" class=\"highlight-action crayons-icon highlight-action--fullscreen-off\"><title>\u0627\u0632 \u062d\u0627\u0644\u062a \u062a\u0645\u0627\u0645 \u0635\u0641\u062d\u0647 \u062e\u0627\u0631\u062c \u0634\u0648\u06cc\u062f<\/title>\n    <path d=\"M18 7h4v2h-6V3h2v4zM8 9H2V7h4V3h2v6zm10 8v4h-2v-6h6v2h-4zM8 15v6H6v-4H2v-2h6z\"\/>\n<\/svg><\/p>\n<\/div>\n<\/div>\n<\/div>\n<p><strong>\ud83d\udcc8 \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646 \u0648 \u0641\u0636\u0627<\/strong><br \/><strong>\u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc<\/strong>: o (v + e)<br \/><strong>\u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0641\u0636\u0627<\/strong>: o (v)<br \/>\u062c\u0627\u06cc\u06cc \u06a9\u0647 V \u062a\u0639\u062f\u0627\u062f \u0631\u0627\u0633 \u0647\u0627 \u0648 E \u062a\u0639\u062f\u0627\u062f \u0644\u0628\u0647 \u0647\u0627 \u0627\u0633\u062a.<\/p>\n<p><strong>\ud83e\uddca \u063a\u0630\u0627\u06cc \u0627\u0635\u0644\u06cc<\/strong><br \/>BFS \u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u06a9\u0648\u062a\u0627\u0647\u062a\u0631\u06cc\u0646 \u0645\u0633\u06cc\u0631 (\u062f\u0631 \u0646\u0645\u0648\u062f\u0627\u0631\u0647\u0627\u06cc \u0628\u062f\u0648\u0646 \u0648\u0632\u0646\u06cc) \u0628\u0633\u06cc\u0627\u0631 \u0639\u0627\u0644\u06cc \u0627\u0633\u062a.<br \/>\u0627\u0632 \u06cc\u06a9 \u0635\u0641 \u0628\u0631\u0627\u06cc \u0639\u0628\u0648\u0631 \u0627\u0632 \u0633\u0637\u062d \u0628\u0647 \u0633\u0637\u062d \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc \u06a9\u0646\u062f.<br \/>\u0627\u06cc\u062f\u0647 \u0622\u0644 \u0648\u0642\u062a\u06cc \u0645\u06cc \u062e\u0648\u0627\u0647\u06cc\u062f \u0627\u0628\u062a\u062f\u0627 \u0647\u0645\u0647 \u0686\u06cc\u0632 \u0646\u0632\u062f\u06cc\u06a9 \u062e\u0648\u062f \u0631\u0627 \u06a9\u0634\u0641 \u06a9\u0646\u06cc\u062f.<\/p>\n<\/p><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\ud83e\udde0 \u0627\u06cc\u0646 \u0631\u0627 \u062a\u0635\u0648\u0631 \u06a9\u0646\u06cc\u062f:\u0634\u0645\u0627 \u062f\u0631 \u067e\u06cc\u0686 \u0648 \u062e\u0645 \u0627\u062a\u0627\u0642 \u0647\u0633\u062a\u06cc\u062f. \u0634\u0645\u0627 \u0645\u06cc \u062e\u0648\u0627\u0647\u06cc\u062f \u06a9\u0648\u062a\u0627\u0647\u062a\u0631\u06cc\u0646 \u0631\u0627\u0647 \u0631\u0627 \u067e\u06cc\u062f\u0627 \u06a9\u0646\u06cc\u062f. \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u0627\u0632 \u0627\u062a\u0627\u0642 \u0627\u0648\u0644 \u0634\u0631\u0648\u0639 \u0645\u06cc \u06a9\u0646\u06cc\u062f \u060c \u062a\u0645\u0627\u0645 \u0627\u062a\u0627\u0642 \u0647\u0627\u06cc \u0645\u062c\u0627\u0648\u0631 \u0631\u0627 \u0628\u0631\u0631\u0633\u06cc \u06a9\u0646\u06cc\u062f \u060c \u0633\u067e\u0633 \u0628\u0647 \u0644\u0627\u06cc\u0647 \u0628\u0639\u062f\u06cc \u0627\u062a\u0627\u0642 \u0647\u0627 \u0628\u0631\u0648\u06cc\u062f \u0648 \u062a\u0627 \u0631\u0633\u06cc\u062f\u0646 \u0628\u0647 \u062e\u0631\u0648\u062c\u06cc \u060c \u06af\u0633\u062a\u0631\u0634 \u062f\u0647\u06cc\u062f.\u0627\u06cc\u0646 \u062c\u0633\u062a\u062c\u0648\u06cc \u0648\u0633\u0639\u062a \u0627\u0648\u0644 (BFS) \u0627\u0633\u062a-\u0634\u0645\u0627 &hellip;<\/p>\n","protected":false},"author":2,"featured_media":105967,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":"","footnotes":""},"categories":[339],"tags":[],"class_list":["post-105966","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-dev"],"_links":{"self":[{"href":"https:\/\/nabfollower.com\/blog\/wp-json\/wp\/v2\/posts\/105966","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/nabfollower.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/nabfollower.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/nabfollower.com\/blog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/nabfollower.com\/blog\/wp-json\/wp\/v2\/comments?post=105966"}],"version-history":[{"count":0,"href":"https:\/\/nabfollower.com\/blog\/wp-json\/wp\/v2\/posts\/105966\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/nabfollower.com\/blog\/wp-json\/wp\/v2\/media\/105967"}],"wp:attachment":[{"href":"https:\/\/nabfollower.com\/blog\/wp-json\/wp\/v2\/media?parent=105966"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/nabfollower.com\/blog\/wp-json\/wp\/v2\/categories?post=105966"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/nabfollower.com\/blog\/wp-json\/wp\/v2\/tags?post=105966"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}