{"id":11383,"date":"2025-12-24T16:55:39","date_gmt":"2025-12-24T11:25:39","guid":{"rendered":"https:\/\/namastedev.com\/blog\/?p=11383"},"modified":"2026-01-11T21:12:53","modified_gmt":"2026-01-11T15:42:53","slug":"kruskal-and-union-find-code","status":"publish","type":"post","link":"https:\/\/namastedev.com\/blog\/kruskal-and-union-find-code\/","title":{"rendered":"Kruskal and Union Find Code"},"content":{"rendered":"\n<!-- Shortest Path in unweighted graph -->\n<!-- PrismJS for Syntax Highlighting -->\n<link href=\"https:\/\/cdn.jsdelivr.net\/npm\/prismjs@1.29.0\/themes\/prism-tomorrow.min.css\" rel=\"stylesheet\">\n<script src=\"https:\/\/cdn.jsdelivr.net\/npm\/prismjs@1.29.0\/prism.min.js\"><\/script>\n<script src=\"https:\/\/cdn.jsdelivr.net\/npm\/prismjs@1.29.0\/plugins\/autoloader\/prism-autoloader.min.js\"><\/script>\n\n<style>\n.wp_blog_theme {\n  --primary: #E58C32;\n  --secondary: #030302;\n  --light-bg: #fef9f4;\n  --text-dark: #2d2d2d;\n  --tab-radius: 12px;\n  --shadow: 0 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white;\n  font-weight: bold;\n  cursor: pointer;\n  border: none;\n  box-shadow: var(--shadow);\n  transition: background 0.3s, transform 0.2s;\n}\n\n.wp_blog_toggle-btn:hover {\n  background: #cc772e;\n}\n\n.wp_blog_theme.dark-mode .wp_blog_code-tabs-container {\n  background: #1e1e1e;\n}\n<\/style>\n\n<div class=\"wp_blog_container wp_blog_theme\">\n  <button id=\"blogNotesThemeToggle\" class=\"wp_blog_toggle-btn\">\ud83c\udf19<\/button>\n  <h1 class=\"wp_blog_main-heading\"><\/h1>\n\n  <div class=\"wp_blog_explanation\">\n            <h2>Example:<\/h2>\n            <img decoding=\"async\" src=\"https:\/\/namastedev.com\/blog\/wp-content\/uploads\/2025\/12\/Screenshot-2025-12-24-at-4.10.41-PM.png\" alt=\"\">\n\n        <ul>\n            <p><strong>Sorted Edges:<\/strong><\/p>\n            <li> 1 \u2192 0, 1 <\/li>\n            <li> 2 \u2192 3, 2 <\/li>\n            <li> 3 \u2192 4, 3 <\/li>\n            <li> 2 \u2192 5, 6 <\/li>\n            <li> 2 \u2192 4, 7 <\/li>\n            <li> 0 \u2192 2, 8 <\/li>\n            <li> 1 \u2192 2, 9<\/li>\n            <li> 4 \u2192 5, 10 <\/li>\n        <\/ul>\n\n                <h2>Exploring Edges<\/h2>\n        <ul>\n            <li><strong>1 \u2192 0, 1<\/strong><\/li>\n            <img decoding=\"async\" src=\"https:\/\/namastedev.com\/blog\/wp-content\/uploads\/2025\/12\/Screenshot-2025-12-24-at-4.25.48-PM.png\" alt=\"\">\n\n            <li><strong>2 \u2192 3, 2<\/strong><\/li>\n            <img decoding=\"async\" src=\"https:\/\/namastedev.com\/blog\/wp-content\/uploads\/2025\/12\/Screenshot-2025-12-24-at-4.28.32-PM.png\" alt=\"\">            \n            \n            <li><strong>3 \u2192 4, 3<\/strong><\/li>\n            <img decoding=\"async\" src=\"https:\/\/namastedev.com\/blog\/wp-content\/uploads\/2025\/12\/Screenshot-2025-12-24-at-4.30.54-PM.png\" alt=\"\">\n\n            <li><strong>2 \u2192 5, 6<\/strong><\/li>\n            <img decoding=\"async\" src=\"https:\/\/namastedev.com\/blog\/wp-content\/uploads\/2025\/12\/Screenshot-2025-12-24-at-4.34.00-PM.png\" alt=\"\">\n            \n            <li><strong>2 \u2192 4, 7<\/li><\/strong><code> Cycle Detected (Skip)<\/code><\/li>\n\n            <li><strong>0 \u2192 2, 8<\/strong><\/li>\n            <img decoding=\"async\" src=\"https:\/\/namastedev.com\/blog\/wp-content\/uploads\/2025\/12\/Screenshot-2025-12-24-at-4.36.14-PM.png\" alt=\"\">\n        \n            <li><strong>1 \u2192 2, 9<\/li><\/strong><code> Cycle Detected (Skip)<\/code><\/li>\n\n            <li><strong>4 \u2192 5, 10<\/li><\/strong><code> Cycle Detected (Skip)<\/code><\/li>\n        \n        <p><strong>MST => 1 + 2 + 3 + 6 + 8 => 20<\/strong><\/p>\n        <\/ul>\n\n    <h2>Code<\/h2>\n  <div class=\"wp_blog_code-tabs-container\">\n      <div class=\"wp_blog_code-tabs-header\">\n      <button class=\"wp_blog_code-tab-button active\" data-lang=\"js\">JavaScript<\/button>\n      <button class=\"wp_blog_code-tab-button\" data-lang=\"py\">Python<\/button>\n      <button class=\"wp_blog_code-tab-button\" data-lang=\"java\">Java<\/button>\n      <button class=\"wp_blog_code-tab-button\" data-lang=\"cpp\">C++<\/button>\n      <button class=\"wp_blog_code-tab-button\" data-lang=\"c\">C<\/button>\n      <button class=\"wp_blog_code-tab-button\" data-lang=\"cs\">C#<\/button>\n    <\/div>\n    <div class=\"wp_blog_code-tab-content active\" data-lang=\"js\">\n      <pre>\nclass UnionFind {\n    constructor(n) {\n        this.parent = new Array(n).fill(0).map((_, i) => i);\n        this.rank = new Array(n).fill(0);\n    }\n\n    \/\/ finds the root of node x\n    find(x) {\n        if(this.parent[x] !== x) {\n            this.parent[x] = this.find(this.parent[x]);\n        }\n        return this.parent[x];\n    }\n\n    union(x, y){\n        let rootX = this.find(x);\n        let rootY = this.find(y);\n        \/\/ cycle Detected\n        if(rootX === rootY) return false;\n        \n        \/\/ union based on rank\n        if(this.rank[rootX] > this.rank[rootY]) {\n            this.parent[rootY] = rootX;\n        }\n        else if(this.rank[rootY] > this.rank[rootX]) {\n            this.parent[rootX] = rootY;\n        }\n        else {\n            this.parent[rootY] = rootX;\n            this.rank[rootX]++;\n        }\n        return true;\n    }\n}\n\n\/\/ Kruskal Algorithm\nfunction Kruskal(n, edges) {\n    \/\/ sort the edges based on weights\n    edges.sort((a, b) => a[2] - b[2]);\n\n    let uf = new UnionFind(n);\n    let mstCost = 0;\n\n    for(let [x, y, w] of edges) {\n        if (uf.union(x, y)) {\n            mstCost = mstCost + w;\n        } \n    }\n    return mstCost;\n}\n\nconst edges = [\n    [0, 1, 4], [0, 2, 4], [1, 2, 2],\n    [2, 3, 3], [2, 5, 2], [2, 4, 4],\n    [3, 4, 3], [5, 4, 3]\n];\n\nconsole.log(Kruskal(6, edges));\n<\/pre>\n    <\/div>\n\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"py\">\n    <pre>\n  class UnionFind:\n    def __init__(self, n):\n        self.parent = list(range(n))\n        self.rank = [0] * n\n\n    def find(self, x):\n        if self.parent[x] != x:\n            self.parent[x] = self.find(self.parent[x])\n        return self.parent[x]\n\n    def union(self, x, y):\n        rootX = self.find(x)\n        rootY = self.find(y)\n\n        if rootX == rootY:\n            return False\n\n        if self.rank[rootX] > self.rank[rootY]:\n            self.parent[rootY] = rootX\n        elif self.rank[rootY] > self.rank[rootX]:\n            self.parent[rootX] = rootY\n        else:\n            self.parent[rootY] = rootX\n            self.rank[rootX] += 1\n        return True\n\n\ndef kruskal(n, edges):\n    edges.sort(key=lambda x: x[2])\n    uf = UnionFind(n)\n    mst_cost = 0\n\n    for x, y, w in edges:\n        if uf.union(x, y):\n            mst_cost += w\n\n    return mst_cost\n\n\nedges = [\n    [0, 1, 4], [0, 2, 4], [1, 2, 2],\n    [2, 3, 3], [2, 5, 2], [2, 4, 4],\n    [3, 4, 3], [5, 4, 3]\n]\n\nprint(kruskal(6, edges))\n\n    <\/pre>\n    <\/div>\n\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"java\">\n    <pre>\nimport java.util.*;\n\nclass UnionFind {\n    int[] parent, rank;\n\n    UnionFind(int n) {\n        parent = new int[n];\n        rank = new int[n];\n        for (int i = 0; i < n; i++)\n            parent[i] = i;\n    }\n\n    int find(int x) {\n        if (parent[x] != x)\n            parent[x] = find(parent[x]);\n        return parent[x];\n    }\n\n    boolean union(int x, int y) {\n        int rootX = find(x);\n        int rootY = find(y);\n\n        if (rootX == rootY) return false;\n\n        if (rank[rootX] > rank[rootY])\n            parent[rootY] = rootX;\n        else if (rank[rootY] > rank[rootX])\n            parent[rootX] = rootY;\n        else {\n            parent[rootY] = rootX;\n            rank[rootX]++;\n        }\n        return true;\n    }\n}\n\npublic class KruskalMST {\n\n    public static int kruskal(int n, int[][] edges) {\n        Arrays.sort(edges, Comparator.comparingInt(a -> a[2]));\n        UnionFind uf = new UnionFind(n);\n        int mstCost = 0;\n\n        for (int[] e : edges) {\n            if (uf.union(e[0], e[1]))\n                mstCost += e[2];\n        }\n        return mstCost;\n    }\n\n    public static void main(String[] args) {\n        int[][] edges = {\n            {0,1,4},{0,2,4},{1,2,2},\n            {2,3,3},{2,5,2},{2,4,4},\n            {3,4,3},{5,4,3}\n        };\n\n        System.out.println(kruskal(6, edges));\n    }\n}\n    <\/pre>\n    <\/div>\n\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"cpp\">\n  <pre>\n#include &lt;bits\/stdc++.h&gt;\nusing namespace std;\n\nclass UnionFind {\n    vector<int> parent, rank;\n\npublic:\n    UnionFind(int n) {\n        parent.resize(n);\n        rank.resize(n, 0);\n        for (int i = 0; i < n; i++)\n            parent[i] = i;\n    }\n\n    int find(int x) {\n        if (parent[x] != x)\n            parent[x] = find(parent[x]);\n        return parent[x];\n    }\n\n    bool unite(int x, int y) {\n        int rootX = find(x);\n        int rootY = find(y);\n\n        if (rootX == rootY) return false;\n\n        if (rank[rootX] > rank[rootY])\n            parent[rootY] = rootX;\n        else if (rank[rootY] > rank[rootX])\n            parent[rootX] = rootY;\n        else {\n            parent[rootY] = rootX;\n            rank[rootX]++;\n        }\n        return true;\n    }\n};\n\nint kruskal(int n, vector<vector<int>>& edges) {\n    sort(edges.begin(), edges.end(),\n         [](auto &a, auto &b) { return a[2] < b[2]; });\n\n    UnionFind uf(n);\n    int mstCost = 0;\n\n    for (auto &#038;e : edges) {\n        if (uf.unite(e[0], e[1]))\n            mstCost += e[2];\n    }\n    return mstCost;\n}\n\nint main() {\n    vector<vector<int>> edges = {\n        {0,1,4},{0,2,4},{1,2,2},\n        {2,3,3},{2,5,2},{2,4,4},\n        {3,4,3},{5,4,3}\n    };\n\n    cout << kruskal(6, edges);\n}\n  <\/pre>\n    <\/div>\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"c\">\n      <pre>\n#include &lt;stdio.h&gt;\n#include &lt;stdlib.h&gt;\n\ntypedef struct {\n    int x, y, w;\n} Edge;\n\nint parent[100], rankArr[100];\n\nint find(int x) {\n    if (parent[x] != x)\n        parent[x] = find(parent[x]);\n    return parent[x];\n}\n\nint unionSet(int x, int y) {\n    int rootX = find(x);\n    int rootY = find(y);\n\n    if (rootX == rootY) return 0;\n\n    if (rankArr[rootX] > rankArr[rootY])\n        parent[rootY] = rootX;\n    else if (rankArr[rootY] > rankArr[rootX])\n        parent[rootX] = rootY;\n    else {\n        parent[rootY] = rootX;\n        rankArr[rootX]++;\n    }\n    return 1;\n}\n\nint cmp(const void *a, const void *b) {\n    return ((Edge*)a)->w - ((Edge*)b)->w;\n}\n\nint kruskal(int n, Edge edges[], int m) {\n    qsort(edges, m, sizeof(Edge), cmp);\n\n    for (int i = 0; i < n; i++) {\n        parent[i] = i;\n        rankArr[i] = 0;\n    }\n\n    int mstCost = 0;\n\n    for (int i = 0; i < m; i++) {\n        if (unionSet(edges[i].x, edges[i].y))\n            mstCost += edges[i].w;\n    }\n    return mstCost;\n}\n\nint main() {\n    Edge edges[] = {\n        {0,1,4},{0,2,4},{1,2,2},\n        {2,3,3},{2,5,2},{2,4,4},\n        {3,4,3},{5,4,3}\n    };\n\n    printf(\"%d\\n\", kruskal(6, edges, 8));\n    return 0;\n}\n<\/pre>\n    <\/div>\n\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"cs\">\n    <pre>\nusing System;\nusing System.Collections.Generic;\n\nclass UnionFind {\n    int[] parent, rank;\n\n    public UnionFind(int n) {\n        parent = new int[n];\n        rank = new int[n];\n        for (int i = 0; i < n; i++)\n            parent[i] = i;\n    }\n\n    public int Find(int x) {\n        if (parent[x] != x)\n            parent[x] = Find(parent[x]);\n        return parent[x];\n    }\n\n    public bool Union(int x, int y) {\n        int rootX = Find(x);\n        int rootY = Find(y);\n\n        if (rootX == rootY) return false;\n\n        if (rank[rootX] > rank[rootY])\n            parent[rootY] = rootX;\n        else if (rank[rootY] > rank[rootX])\n            parent[rootX] = rootY;\n        else {\n            parent[rootY] = rootX;\n            rank[rootX]++;\n        }\n        return true;\n    }\n}\n\nclass Program {\n    static int Kruskal(int n, List<int[]> edges) {\n        edges.Sort((a, b) => a[2] - b[2]);\n        UnionFind uf = new UnionFind(n);\n        int mstCost = 0;\n\n        foreach (var e in edges) {\n            if (uf.Union(e[0], e[1]))\n                mstCost += e[2];\n        }\n        return mstCost;\n    }\n\n    static void Main() {\n        var edges = new List<int[]> {\n            new[] {0,1,4}, new[] {0,2,4}, new[] {1,2,2},\n            new[] {2,3,3}, new[] {2,5,2}, new[] {2,4,4},\n            new[] {3,4,3}, new[] {5,4,3}\n        };\n\n        Console.WriteLine(Kruskal(6, edges));\n    }\n}\n<\/pre>\n    <\/div>\n  <\/div>\n<\/div>  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themeContainer.classList.contains(\"dark-mode\") ? \"\u2600\ufe0f\" : \"\ud83c\udf19\";\n  });\n});\n<\/script>\n\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\ud83c\udf19 Example: Sorted Edges: 1 \u2192 0, 1 2 \u2192 3, 2 3 \u2192 4, 3 2 \u2192 5, 6 2 \u2192 4, 7 0 \u2192 2, 8 1 \u2192 2, 9 4 \u2192 5, 10 Exploring Edges 1 \u2192 0, 1 2 \u2192 3, 2 3 \u2192 4, 3 2 \u2192 5, 6 2<\/p>\n","protected":false},"author":108,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[210,322,260,176,175,211,810,174,172,173],"tags":[],"class_list":["post-11383","post","type-post","status-publish","format-standard","category-algorithms","category-algorithms-and-data-structures","category-c-c-plus-plus","category-csharp","category-cplusplus","category-data-structures","category-dsa","category-java","category-javascript","category-python"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/11383","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/users\/108"}],"replies":[{"embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/comments?post=11383"}],"version-history":[{"count":2,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/11383\/revisions"}],"predecessor-version":[{"id":11450,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/11383\/revisions\/11450"}],"wp:attachment":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/media?parent=11383"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/categories?post=11383"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/tags?post=11383"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}