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To solve this problem using the Disjoint Set Union (DSU) approach, we aim to union nodes based on their parent-child relationships. A valid tree should follow these rules:
Time Complexity: O(n), where n is the number of nodes, due to each union and find operation being nearly constant with path compression.
Space Complexity: O(n) for the parent array.
1var validateBinaryTreeNodes = function(n, leftChild, rightChild) {
2 const parent = Array.from({ length: n }, (_, index) => index);
3 const find = (x) => {
4 if (parent[x] !== x) {
5 parent[x] = find(parent[x]);
6 }
7 return parent[x];
8 };
9
10 const union = (x, y) => {
11 const rootX = find(x);
12 const rootY = find(y);
13 if (rootX === rootY) return false;
14 parent[rootY] = rootX;
15 return true;
16 };
17
18 const hasParent = new Array(n).fill(0);
19
20 for (let i = 0; i < n; ++i) {
21 if (leftChild[i] !== -1) {
22 if (hasParent[leftChild[i]] === 1 || !union(i, leftChild[i])) {
23 return false;
24 }
25 hasParent[leftChild[i]] = 1;
26 }
27 if (rightChild[i] !== -1) {
28 if (hasParent[rightChild[i]] === 1 || !union(i, rightChild[i])) {
29 return false;
30 }
31 hasParent[rightChild[i]] = 1;
32 }
33 }
34
35 return hasParent.filter(parent => parent === 0).length === 1;
36};The JavaScript variation employs similar structures to monitor the tree integrity. Using find and union functions, this approach enforces the hierarchical conditions of nodes along with a snapshot of their root relations. In JavaScript, this procedural logic ensures the union-find checks can prevent improper cycles or multiple root scenarios.
This approach involves calculating the in-degree of each node and checking connectivity via a DFS. The key aspects of a tree like single-root presence and cycle-checking can be managed by:
Time Complexity: O(n), since each node and its immediate edges are evaluated once in each step, including in-drives calculations and DFS.
Space Complexity: O(n) for holding visited tracking and in-degree counts.
The Java version checks for a single node with inDegree zero, identifying it as the root. Nodes are structured as positions within two arrays/lists representing binary tree branches. The DFS aims to explore all nodes in one pass, validating complete connectivity without omitted nodes.