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

Medium

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 <code>edgesi = a_i, b_i</code>, which means there is an edge between nodes <code>a_i</code> and <code>b_i</code> in the tree.

Return an array of size n where ans[i] is the number of nodes in the subtree of the <code>i^th</code> 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:

• <code>1 <= n <= 10⁵</code>

• edges.length == n - 1

• edges[i].length == 2

• <code>0 <= a_i, b_i< n</code>

• <code>a_i != b_i</code>

• labels.length == n

• labels is consisting of only of lowercase English letters.