hdu1712(01背包)
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ACboy needs your help
Time Limit: 1000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)Total Submission(s): 6054 Accepted Submission(s): 3309
Problem Description
ACboy has N courses this term, and he plans to spend at most M days on study.Of course,the profit he will gain from different course depending on the days he spend on it.How to arrange the M days for the N courses to maximize the profit?
Input
The input consists of multiple data sets. A data set starts with a line containing two positive integers N and M, N is the number of courses, M is the days ACboy has.
Next follow a matrix A[i][j], (1<=i<=N<=100,1<=j<=M<=100).A[i][j] indicates if ACboy spend j days on ith course he will get profit of value A[i][j].
N = 0 and M = 0 ends the input.
Next follow a matrix A[i][j], (1<=i<=N<=100,1<=j<=M<=100).A[i][j] indicates if ACboy spend j days on ith course he will get profit of value A[i][j].
N = 0 and M = 0 ends the input.
Output
For each data set, your program should output a line which contains the number of the max profit ACboy will gain.
Sample Input
2 21 21 32 22 12 12 33 2 13 2 10 0
Sample Output
346
题意:ACboy要花m天来复习n门课,现在告诉你他花j天在第i门课上会得到的奖励,让你给他算出最优解。
思路:01背包稍微变形一下,其实是一模一样的。
dp[i]表示花i天来复习的最优解,然后转移方程是dp[j]=max(dp[j],dp[j-k]+val[i][k]);
其实想出状态转移方程不难,我们要做的就是一一对应01背包的各种条件,显然这题m天是背包容量,花k天来复习是消耗的容量,val[i][j]则是对应的得到的价值。
#include <iostream>#include <stdio.h>#include <stdlib.h>#include<string.h>#include<algorithm>#include<math.h>#include<queue>#include<stack>using namespace std;typedef long long ll;int val[110][110],dp[110];int main(){ int m,n; while(~scanf("%d%d",&n,&m)&&m+n) { for(int i=1; i<=n; i++) for(int j=1; j<=m; j++) scanf("%d",&val[i][j]); memset(dp,0,sizeof(dp)); for(int i=1; i<=n; i++) for(int j=m; j>=0; j--) for(int k=1; k<=j; k++) dp[j]=max(dp[j],dp[j-k]+val[i][k]); printf("%d\n",dp[m]); } return 0;}
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