Add week 10 solutions: numberOfConnectedComponentsInAnUndirectedGraph

Author: yolophg

number-of-connected-components-in-an-undirected-graph/yolophg.js

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+// Time Complexity: O(n + m) m : number of edges
+// Space Complexity: O(n)
+
+class Solution {
+  countComponents(n, edges) {
+    // initialize the parent array where each node is its own parent initially
+    const parent = new Array(n).fill(0).map((_, index) => index);
+
+    // to find the root of a node with path compression
+    const find = (node) => {
+      if (parent[node] !== node) {
+        parent[node] = find(parent[node]);
+      }
+      return parent[node];
+    };
+
+    // to union two nodes
+    const union = (node1, node2) => {
+      const root1 = find(node1);
+      const root2 = find(node2);
+      if (root1 !== root2) {
+        parent[root1] = root2;
+      }
+    };
+
+    // union all the edges
+    for (let [a, b] of edges) {
+      union(a, b);
+    }
+
+    // count the number of unique roots
+    const uniqueRoots = new Set();
+    for (let i = 0; i < n; i++) {
+      uniqueRoots.add(find(i));
+    }
+
+    return uniqueRoots.size;
+  }
+}