---
# System prepended metadata

title: 1519. Number of Nodes in the Sub-Tree With the Same Label
tags: [leetcode]

---

# 1519. Number of Nodes in the Sub-Tree With the Same Label
###### tags: `leetcode`
## Description
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:
![](https://i.imgur.com/Rhz3oU7.png)

>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:
![](https://i.imgur.com/hsPRCqH.png)

>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:
![](https://i.imgur.com/qlWlOk3.png)

>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.

## Solution
- This is a DFS problem that should accumulate the count from the leaf to the root
- Because the given information about the tree is the `edges`, transform them into a adjancent list
```cpp=
adjList.resize(n);
for (auto &i : edges)
{
    adjList[i[0]].push_back(i[1]);
    adjList[i[1]].push_back(i[0]);
}
```
- Then for the `DFS`, calculate the current count for all the alphabet and let the one that finish iteration with the answer of the current accumulated result of the alphabet the index has
```cpp=
for (auto &i : adjList[idx])
{
    if (i != prev)
    {
        temp = dfs(i, idx, edges, ans, labels);
        transform(cur.begin(), cur.end(), temp.begin(), cur.begin(), plus<int>());
    }

}
cur[labels[idx] - 'a']++;
ans[idx] = cur[labels[idx] - 'a'];
```
- When passing the vector and the string, remember to pass them with the reference in order to speed up
    - In this case, I did not use reference with string and got TLE several time