Validate Binary Tree Nodes — LeetCode 1361 Python Solution

The problem

You have n binary tree nodes numbered from 0 to n - 1 where node i has two children leftChild[i] and rightChild[i], return true if and only if all the given nodes form exactly one valid binary tree. If node i has no left child then leftChild[i] will equal -1, similarly for the right child.

Example

Input

n = 4, leftChild = [1,-1,3,-1], rightChild = [2,-1,-1,-1]

Output

true

Python solution

class Solution:
    def validateBinaryTreeNodes(
        self, n: int, leftChild: List[int], rightChild: List[int]
    ) -> bool:
        def find(x: int) -> int:
            if p[x] != x:
                p[x] = find(p[x])
            return p[x]

        p = list(range(n))
        vis = [False] * n
        for i, (a, b) in enumerate(zip(leftChild, rightChild)):
            for j in (a, b):
                if j != -1:
                    if vis[j] or find(i) == find(j):
                        return False
                    p[find(i)] = find(j)
                    vis[j] = True
                    n -= 1
        return n == 1

Complexity

Pattern: Union-Find

Merge groups and ask whether two things are connected, both in near-constant time. LeetCode 1361. Validate Binary Tree Nodes is filed here because LeetCode tags it Union Find, which is the vocabulary this hub collects.

The union-find guide has the Python template for the pattern and the 83 LeetCode problems that use it.

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