Add week 10 solutions: graphValidTree

Author: yolophg

graph-valid-tree/yolophg.js

@@ -0,0 +1,51 @@
+// Time Complexity: O(n)
+// Space Complexity: O(n)
+
+class Solution {
+  validTree(n, edges) {
+    // initialize Union-Find data structure
+    const parent = Array(n)
+      .fill(0)
+      .map((_, index) => index);
+    const rank = Array(n).fill(1);
+
+    // find function with path compression
+    function find(x) {
+      if (parent[x] !== x) {
+        parent[x] = find(parent[x]);
+      }
+      return parent[x];
+    }
+
+    // union function with union by rank
+    function union(x, y) {
+      const rootX = find(x);
+      const rootY = find(y);
+      if (rootX !== rootY) {
+        if (rank[rootX] > rank[rootY]) {
+          parent[rootY] = rootX;
+        } else if (rank[rootX] < rank[rootY]) {
+          parent[rootX] = rootY;
+        } else {
+          parent[rootY] = rootX;
+          rank[rootX] += 1;
+        }
+      } else {
+        // if rootX == rootY, there is a cycle
+        return false;
+      }
+      return true;
+    }
+
+    // process each edge
+    for (const [u, v] of edges) {
+      if (!union(u, v)) {
+        // if union returns false, a cycle is detected
+        return false;
+      }
+    }
+
+    // if all unions are successful, it's a valid tree
+    return true;
+  }
+}