[USACO2002][poj1947]Rebuilding Roads（树形dp）

Rebuilding Roads
Time Limit: 1000MS Memory Limit: 30000K
Total Submissions: 8589 Accepted: 3854
Description

The cows have reconstructed Farmer John's farm, with its N barns (1 <= N <= 150, number 1..N) after the terrible earthquake last May. The cows didn't have time to rebuild any extra roads, so now there is exactly one way to get from any given barn to any other barn. Thus, the farm transportation system can be represented as a tree.

Farmer John wants to know how much damage another earthquake could do. He wants to know the minimum number of roads whose destruction would isolate a subtree of exactly P (1 <= P <= N) barns from the rest of the barns.
Input

* Line 1: Two integers, N and P

* Lines 2..N: N-1 lines, each with two integers I and J. Node I is node J's parent in the tree of roads.
Output

A single line containing the integer that is the minimum number of roads that need to be destroyed for a subtree of P nodes to be isolated.
Sample Input

11 6
1 2
1 3
1 4
1 5
2 6
2 7
2 8
4 9
4 10
4 11
Sample Output

2
Hint

[A subtree with nodes (1, 2, 3, 6, 7, 8) will become isolated if roads 1-4 and 1-5 are destroyed.]
Source

USACO 2002 February

题意：给你一颗多叉的树，然后让你删除尽量少的边，得到一颗有p个节点的子树

分析：

明显这是一道树形dp

f[i][j]表示以i为根的树，要成为j个节点的子树所需要删除的最少边数

则f[i][j]=min(f[i][j-k]+f[son][k]-2)

总结：

此题很容易考虑f[i][j]和某个f[son][k]的关系，不过这样会发现状态转移时完全搜索级的……以后遇到这种情况的树形dp时候，可以换个角度考虑以同一个节点为根的子树不同j之间的转移。