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

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:

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 <= 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.

 

Solutions

Solution: Depth-First Search

• Time complexity: O(n)
• Space complexity: O(n)

 

JavaScript

/**
 * @param {number} n
 * @param {number[][]} edges
 * @param {string} labels
 * @return {number[]}
 */
const countSubTrees = function (n, edges, labels) {
  const result = [];
  const visited = new Set([0]);
  const edgesMap = edges.reduce((map, [a, b]) => {
    const edgeA = map.get(a) ?? [];
    const edgeB = map.get(b) ?? [];

    edgeA.push(b);
    edgeB.push(a);
    map.set(a, edgeA);
    return map.set(b, edgeB);
  }, new Map());

  const countEdges = node => {
    const label = labels[node];
    const targetEdges = edgesMap.get(node) ?? [];
    const countMap = targetEdges.reduce(
      (map, edge) => {
        if (visited.has(edge)) return map;
        visited.add(edge);
        const currentCountMap = countEdges(edge);

        currentCountMap.forEach((value, key) => {
          const count = map.get(key) ?? 0;
          map.set(key, count + value);
        });
        return map;
      },
      new Map([[label, 1]]),
    );

    result[node] = countMap.get(label);
    return countMap;
  };

  countEdges(0);
  return result;
};