链接：https://www.nowcoder.com/acm/contest/141/A
来源：牛客网
PACM Team
时间限制：C/C++ 1秒，其他语言2秒
空间限制：C/C++ 262144K，其他语言524288K
Special Judge, 64bit IO Format: %lld
题目描述
Eddy was a contestant participating in ACM ICPC contests. ACM is short for Algorithm, Coding, Math. Since in the ACM contest, the most important knowledge is about algorithm, followed by coding(implementation ability), then math. However, in the ACM ICPC World Finals 2018, Eddy failed to solve a physics equation, which pushed him away from a potential medal.
Since then on, Eddy found that physics is actually the most important thing in the contest. Thus, he wants to form a team to guide the following contestants to conquer the PACM contests(PACM is short for Physics, Algorithm, Coding, Math).
There are N candidate groups each composed of pi physics experts, ai algorithm experts, ci coding experts, mi math experts. For each group, Eddy can either invite all of them or none of them. If i-th team is invited, they will bring gi knowledge points which is calculated by Eddy's magic formula. Eddy believes that the higher the total knowledge points is, the better a team could place in a contest. But, Eddy doesn't want too many experts in the same area in the invited groups. Thus, the number of invited physics experts should not exceed P, and A for algorithm experts, C for coding experts, M for math experts.
Eddy is still busy in studying Physics. You come to help him to figure out which groups should be invited such that they doesn't exceed the constraint and will bring the most knowledge points in total.
输入描述:
The first line contains a positive integer N indicating the number of candidate groups.
Each of following N lines contains five space-separated integer pi, ai, ci, mi, gi indicating that i-th team consists of pi physics experts, ai algorithm experts, ci coding experts, mi math experts, and will bring gi knowledge points.
The last line contains four space-separated integer P, A, C, M indicating the maximum possible number of physics experts, algorithm experts, coding experts, and math experts, respectively.
1 ≤ N ≤ 36
0 ≤ pi,ai,ci,mi,gi ≤ 36
0 ≤ P, A, C, M ≤ 36
输出描述:
The first line should contain a non-negative integer K indicating the number of invited groups.
The second line should contain K space-separated integer indicating the index of invited groups(groups are indexed from 0).
You can output index in any order as long as each index appears at most once. If there are multiple way to reach the most total knowledge points, you can output any one of them. If none of the groups will be invited, you could either output one line or output a blank line in the second line.示例1
输入
2
1 0 2 1 10
1 0 2 1 21
1 0 2 1输出
1
1示例2
输入
1
2 1 1 0 31
1 0 2 1输出
0题意：n组物品 每组物品 有四种类型的物品 pi,ai,ci,mi, 背包价值 为gi (物品只能一组一组的装 不可分开装)
有一个背包 最多可以装四种类型的物品的个数为 P, A, C, M 求背包的最大可载价值为时 选了多少组物品 每组物品的序号为
思路：简单的01背包 +路径记录 （二维dp变为四维dp)
AC代码：
#include <cstdio>
#include <iostream>
#define N 40
using namespace std;
int n, P, A, C, M, p[N], a[N], c[N], m[N], g[N], f[N][N][N][N];
bool h[N][N][N][N][N];
int main()
{
ios::sync_with_stdio(0);
cin.tie(0);//加快读入速度
cin >> n;
for(int i = 1; i <= n; i ++) cin >> p[i] >> a[i] >> c[i] >> m[i] >> g[i];
cin >> P >> A >> C >> M;
for(int i = 1; i <= n; i++)//每个物品进行01背包
for(int jp = P; jp >= p[i]; jp --)
for(int ja = A; ja >= a[i]; ja --)
for(int jc = C; jc >= c[i]; jc --)
for(int jm = M; jm >= m[i]; jm --)
if (f[jp - p[i]][ja - a[i]][jc - c[i]][jm - m[i]] + g[i] > f[jp][ja][jc][jm])
{
f[jp][ja][jc][jm] = f[jp - p[i]][ja - a[i]][jc - c[i]][jm - m[i]] + g[i];
h[i][jp][ja][jc][jm] = 1;//路径标记
}
int ans[N];
int cc=0;
for(int i = n; i >= 1; i --)
if (h[i][P][A][C][M])
{
ans[++ cc] = i - 1;
P -= p[i];
A -= a[i];
C -= c[i];
M -= m[i];
}
cout << cc << endl;//组数 //倒推回去
for(int i = cc; i >= 1; i --) cout << ans[i] << ' ';//逆序输出 即为一开始的背包路径顺序
return 0;
}