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1519. Number of Nodes in the Sub-Tree With the Same Label

You are given a tree (i.e. a connected, undirected graph that has no cycles) consisting of n nodes numbered from 0 to n - 1 and exactly n - 1 edges. The root of the tree is the node 0, and each node of the tree has a label which is a lower-case character given in the string labels (i.e. The node with the number i has the label labels[i]).

The edges array is given on the form edges[i] = [ai, bi], which means there is an edge between nodes ai and bi in the tree.

Return an array of size n where ans[i] is the number of nodes in the subtree of the ith node which have the same label as node i.

A subtree of a tree T is the tree consisting of a node in T and all of its descendant nodes.

Example 1:

Input: n = 7, edges = [[0,1],[0,2],[1,4],[1,5],[2,3],[2,6]], labels = "abaedcd"
Output: [2,1,1,1,1,1,1]
Explanation: Node 0 has label 'a' and its sub-tree has node 2 with label 'a' as well, thus the answer is 2. Notice that any node is part of its sub-tree.
Node 1 has a label 'b'. The sub-tree of node 1 contains nodes 1,4 and 5, as nodes 4 and 5 have different labels than node 1, the answer is just 1 (the node itself).

Example 2:

Input: n = 4, edges = [[0,1],[1,2],[0,3]], labels = "bbbb"
Output: [4,2,1,1]
Explanation: The sub-tree of node 2 contains only node 2, so the answer is 1.
The sub-tree of node 3 contains only node 3, so the answer is 1.
The sub-tree of node 1 contains nodes 1 and 2, both have label 'b', thus the answer is 2.
The sub-tree of node 0 contains nodes 0, 1, 2 and 3, all with label 'b', thus the answer is 4.

Example 3:

Input: n = 5, edges = [[0,1],[0,2],[1,3],[0,4]], labels = "aabab"
Output: [3,2,1,1,1]

Constraints:

  • 1 <= n <= 105
  • edges.length == n - 1
  • edges[i].length == 2
  • 0 <= ai, bi < n
  • ai != bi
  • labels.length == n
  • labels is consisting of only of lowercase English letters.

Solutions (Python)

1. Solution

class Solution:
    def countSubTrees(self, n: int, edges: List[List[int]], labels: str) -> List[int]:
        children = [set() for _ in range(n)]
        parent = [-1] * n
        stack = [0]
        count = [[0] * 26 for _ in range(n)]
        ans = [0] * n

        for (a, b) in edges:
            children[a].add(b)
            children[b].add(a)

        while stack != []:
            i = stack.pop()

            for j in children[i]:
                children[j].remove(i)
                parent[j] = i
                stack.append(j)

        stack = [i for i in range(n) if len(children[i]) == 0]

        while stack != []:
            i = stack.pop()

            count[i][ord(labels[i]) - 97] += 1
            ans[i] = count[i][ord(labels[i]) - 97]

            if parent[i] != -1:
                for j in range(26):
                    count[parent[i]][j] += count[i][j]
                children[parent[i]].remove(i)
                if len(children[parent[i]]) == 0:
                    stack.append(parent[i])

        return ans