HDU 5234 Happy birthday --- 三维01背包

时间:2022-06-26 07:26:39

  HDU 5234

  题目大意:给定n,m,k,以及n*m(n行m列)个数,k为背包容量,从(1,1)开始只能往下走或往右走,求到达(m,n)时能获得的最大价值

  解题思路:dp[i][j][k]表示在位置(i,j)有一个容量为k的背包所能获得的最大价值

       决策:a[i][j]处的数是否选取

       不选取: dp[i][j][k]= max(dp[i-1][j][k], dp[i][j-1][k])

       选取:首先要求k >=a[i][j],那么dp[i][j][k] = max(dp[i-1][j][k-w[i][j]], dp[i][j-1][k-w[i][j]]);

       相当于求四者的最大值,最后dp[m][n][k]即为所求结果

/* HDU 5234 Happy birthday --- 三维01背包 */
#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std; const int maxn = ;
int w[maxn][maxn];
int dp[maxn][maxn][maxn];
int n, m, V; int main()
{
#ifdef _LOCAL
freopen("D:\\input.txt", "r", stdin);
#endif //n行m列容量为V
while (scanf("%d%d%d", &n, &m, &V) == ){
for (int i = ; i <= n; ++i){
for (int j = ; j <= m; ++j){
scanf("%d", w[i] + j);
}//for(j)
}//for(i) memset(dp, , sizeof dp); for (int i = ; i <= n; ++i){
for (int j = ; j <= m; ++j){
for (int k = ; k <= V; ++k){
//w[i][j]不取的时候
int a = max(dp[i - ][j][k], dp[i][j - ][k]);
int b = ;
//k > w[i][j], w[i][j]取的时候
if (k - w[i][j] >= ){
b = max(dp[i - ][j][k - w[i][j]], dp[i][j - ][k - w[i][j]]) + w[i][j];
}
dp[i][j][k] = max(a, b);
}
}//for(j)
}//for(i) printf("%d\n", dp[n][m][V]);
} return ;
}