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

## Problem Link

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

- C++

`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;

}

};