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

https://leetcode.com/problems/number-of-nodes-in-the-sub-tree-with-the-same-label/

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]

Example 4:

Input: n = 6, edges = [[0,1],[0,2],[1,3],[3,4],[4,5]], labels = "cbabaa"
Output: [1,2,1,1,2,1]

Example 5:

Input: n = 7, edges = [[0,1],[1,2],[2,3],[3,4],[4,5],[5,6]], labels = "aaabaaa"
Output: [6,5,4,1,3,2,1]

Constraints:

• 1 <= n <= 10^5

• edges.length == n - 1

• edges[i].length == 2

• 0 <= ai, bi < n

• ai != bi

• labels.length == n

• labels is consisting of only of lower-case English letters.

对树上每个结点统计它和它子树上与它的值相同的结点数目，值范围为[a, z]。树非按层统计结点=>DFS/分治。假设每个子节点对应的树对每个值在该子树的频次已经统计完毕，将频率汇总并对该结点的值频次加一，返回。

class Solution:
    def countSubTrees(self, n: int, edges: List[List[int]], labels: str) -> List[int]:
        g, res = collections.defaultdict(list), [0] * n
        for (a, b) in edges:
            g[a].append(b)
            g[b].append(a)
        def dfs(i, last, g, labels, res):
            cnt = collections.Counter()
            for nei in g[i]:
                if nei == last: continue
                cnt += dfs(nei, i, g, labels, res)
            cnt[labels[i]] += 1
            res[i] = cnt[labels[i]]
            return cnt

        dfs(0, -1, g, labels, res)
        return res