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1519 - Number of Nodes in the Sub-Tree With the Same Label (Medium)

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

Problem Statement​

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 <= 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 lowercase English letters.

Approach 1: DFS​

Written by @wingkwong
class Solution {
public:
    vector<int> countSubTrees(int n, vector<vector<int>>& edges, string labels) {
        vector<int> ans(n);
        vector<vector<int>> g(n);
        for (auto x : edges) {
			// x[0] can go to x[1]
            g[x[0]].push_back(x[1]);
			// x[1] can go to x[0]
            g[x[1]].push_back(x[0]);
        }
        // u = current vertex
        // p = parent vertex
        function<vector<int>(int, int)> dfs = [&] (int u, int p) {
            // count each label in the subtree
            vector<int> cnt(26);
            // init the current label
            cnt[labels[u] - 'a'] = 1;
            // traverse the children of u
            for (auto v : g[u]) {
                // if v is not same as p
                if (p ^ v) {
                    // get the count of labels in subtree
                    vector<int> cnt2 = dfs(v, u);
                    // add it back to cnt
                    for (int i = 0; i < 26; i++) cnt[i] += cnt2[i];
                }
            }
            // set the answer
            ans[u] = cnt[labels[u] - 'a'];
            return cnt;
        };
        dfs(0, -1);
        return ans;
    }
};