Starship Troopers
Problem Description
You, the leader of Starship Troopers, are sent to destroy a base of the bugs. The base is built underground. It is actually a huge cavern, which consists of many rooms connected with tunnels. Each room is occupied by some bugs, and their brains hide in some of the rooms. Scientists have just developed a new weapon and want to experiment it on some brains. Your task is to destroy the whole base, and capture as many brains as possible.
To kill all the bugs is always easier than to capture their brains. A map is drawn for you, with all the rooms marked by the amount of bugs inside, and the possibility of containing a brain. The cavern's structure is like a tree in such a way that there is one unique path leading to each room from the entrance. To finish the battle as soon as possible, you do not want to wait for the troopers to clear a room before advancing to the next one, instead you have to leave some troopers at each room passed to fight all the bugs inside. The troopers never re-enter a room where they have visited before.
A starship trooper can fight against 20 bugs. Since you do not have enough troopers, you can only take some of the rooms and let the nerve gas do the rest of the job. At the mean time, you should maximize the possibility of capturing a brain. To simplify the problem, just maximize the sum of all the possibilities of containing brains for the taken rooms. Making such a plan is a difficult job. You need the help of a computer.
Input
The input contains several test cases. The first line of each test case contains two integers N (0 < N <= 100) and M (0 <= M <= 100), which are the number of rooms in the cavern and the number of starship troopers you have, respectively. The following N lines give the description of the rooms. Each line contains two non-negative integers -- the amount of bugs inside and the possibility of containing a brain, respectively. The next N - 1 lines give the description of tunnels. Each tunnel is described by two integers, which are the indices of the two rooms it connects. Rooms are numbered from 1 and room 1 is the entrance to the cavern.
The last test case is followed by two -1's.
Output
For each test case, print on a single line the maximum sum of all the possibilities of containing brains for the taken rooms.
Sample Input
5 1050 1040 1040 2065 3070 301 21 32 42 51 120 7-1 -1
Sample Output
507
Author
XU, Chuan
Source
题目类型：树形背包
算法分析：dp[i][j]表示j个士兵占领以i为根节点的子树所能够获得最大概率，则状态转移方程为dp[i][j] = max (dp[i][j], dp[i][k] + dp[son][j-k])，其中son为i的直接子节点。初始化dp数组全为0，最后输出dp[1][m]即可，注意dp[i][j]在计算前需要先按照类似完全背包的方法初始化
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/************************************************* Author :supermaker Created Time :2015/11/28 16:13:32 File Location :C:\Users\abcd\Desktop\TheEternalPoet **************************************************/ #pragma comment(linker, "/STACK:102400000,102400000") #include <set> #include <bitset> #include <list> #include <map> #include <stack> #include <queue> #include <deque> #include <string> #include <vector> #include <ios> #include <iostream> #include <fstream> #include <sstream> #include <iomanip> #include <algorithm> #include <utility> #include <complex> #include <numeric> #include <functional> #include <cmath> #include <ctime> #include <climits> #include <cstdarg> #include <cstdio> #include <cstdlib> #include <cstring> #include <cctype> #include <cassert> using namespace std; #define CFF freopen ("aaa.txt", "r", stdin) #define CPPFF ifstream cin ("aaa.txt") #define DB(ccc) cout << #ccc << " = " << ccc << endl #define PB push_back #define MP(A, B) make_pair(A, B) typedef long long LL; typedef unsigned long long ULL; typedef double DB; typedef pair <int, int> PII; typedef pair <int, bool> PIB; const int INF = 0x7F7F7F7F; const int MOD = 1e9 + 7; const double EPS = 1e-10; const double PI = 2 * acos (0.0); const int maxn = 1e5 + 6666; int c[166], p[166], g[166][166], dp[166][166], n, m; bool vis[166]; void dfs (int cur) { vis[cur] = true; for (int i = c[cur]; i <= m; i++) dp[cur][i] = p[cur]; for (int i = 1; i <= n; i++) { if (g[cur][i] == 1 && !vis[i]) { dfs (i); for (int j = m; j >= c[cur]; j--) for (int k = 1; k <= j - c[cur]; k++) dp[cur][j] = max (dp[cur][j], dp[cur][j-k] + dp[i][k]); } } } int main() { //CFF; //CPPFF; while (scanf ("%d %d", &n, &m) != EOF) { if (n == -1 && m == -1) break; for (int i = 1; i <= n; i++) { scanf ("%d%d", &c[i], &p[i]); if (c[i] % 20 == 0) c[i] /= 20; else c[i] = c[i] / 20 + 1; } memset (g, 0, sizeof (g)); for (int i = 1; i <= n - 1; i++) { int u, v; scanf ("%d %d", &u, &v); g[u][v] = g[v][u] = 1; } if (m == 0) { puts ("0"); continue; } memset (vis, false, sizeof (vis)); memset (dp, 0, sizeof (dp)); dfs (1); printf ("%d\n", dp[1][m]); } return 0; } |