Jiry Matchings
시간 제한6초메모리 제한512 MB
가중치가 있는 트리에서 각 k=1부터 n-1까지 정확히 k개의 간선을 고르는 매칭의 최대 총 가중치를 구하고, 불가능하면 "?"를 출력한다.
문제
Ruyi Ji has a tree where the vertices are numbered by integers from 1 to n and each edge has a weight.
For each k ≤ (n − 1), he asked you to find the largest total weight of a matching with k edges if it exists.
입력
The first line of input contains one integer n: the number of vertices in the tree (2 ≤ n ≤ 200 000).
Each of the next n−1 lines contains three integers ui, vi, wi, describing an edge from ui to vi with weight wi in the tree (1 ≤ ui, vi ≤ n, ui ≠ vi, −109 ≤ wi ≤ 109).
It is guaranteed that the given graph is a tree.
출력
Output n − 1 integers: the largest weights of the matchings with 1, 2, . . . , n − 1 edges. If there is no such matching for the current k, print “?” instead.
힌트
In the first sample, with k = 1 you should take edge (2, 3) with weight 5. And with k = 2 you should take two edges, (2, 4) and (3, 5), with total weight 6. There are no matchings with a greater number of edges