Minimum Time to Collect All Apples in a Tree
Given an undirected tree consisting of n vertices numbered from 0 to n - 1, where some vertices have apples, you spend 1 second to walk over one edge of the tree.
Return the minimum time in seconds you have to spend to collect all apples in the tree, starting at vertex 0 and coming back to this vertex.
The edges of the undirected tree are given in the array edges, where edges[i] = [ai, bi] means that there exists an edge connecting the vertices ai and bi. Additionally, there is a boolean array hasApple, where hasApple[i] = true means that vertex i has an apple; otherwise, it does not have any apple.
Example 1
Input
n = 7, edges = [[0,1],[0,2],[1,4],[1,5],[2,3],[2,6]], hasApple = [false,false,true,false,true,true,false]Output
8The figure above represents the given tree where red vertices have an apple, and one optimal path to collect all apples is shown by the green arrows.
Example 2
Input
n = 7, edges = [[0,1],[0,2],[1,4],[1,5],[2,3],[2,6]], hasApple = [false,false,true,false,false,true,false]Output
6The figure above represents the given tree where red vertices have an apple, and one optimal path to collect all apples is shown by the green arrows.
Constraints
- 1 <= n <= 10^5
- edges.length == n - 1
- edges[i].length == 2
- 0 <= ai < bi <= n - 1
- hasApple.length == n