01背包 Codeforces Round #267 (Div. 2) C. George and Job

题目传送门

 /*
     题意：选择k个m长的区间，使得总和最大
     01背包：dp[i][j] 表示在i的位置选或不选[i-m+1, i]这个区间，当它是第j个区间。
         01背包思想，状态转移方程：dp[i][j] = max (dp[i-1][j], dp[i-m][j-1] + sum[i] - sum[i-m]);
         在两个for循环，每一次dp[i][j]的值都要更新
 */
 #include <cstdio>
 #include <cstring>
 #include <algorithm>
 #include <cmath>
 using namespace std;

 typedef long long ll;
 const int MAXN = 5e3 + ;
 const int INF = 0x3f3f3f3f;
 ll a[MAXN];
 ll sum[MAXN];
 ll dp[MAXN][MAXN];

 int main(void)        //Codeforces Round #267 (Div. 2) C. George and Job
 {
     int n, m, k;
     while (scanf ("%d%d%d", &n, &m, &k) == )
     {
         memset (sum, , sizeof (sum));
         for (int i=; i<=n; ++i)    {scanf ("%I64d", &a[i]);    sum[i] = sum[i-] + a[i];}

         ll ans = ;
         for (int i=m; i<=n; ++i)
         {
             ll tmp = sum[i] - sum[i-m];
             for (int j=; j<=k; ++j)
             {
                 dp[i][j] = max (dp[i-][j], dp[i-m][j-] + tmp);
             }
             ans = max (ans, dp[i][k]);
         }

         printf ("%I64d\n", ans);
     }

     return ;
 }

 /*
 5 2 1
 1 2 3 4 5
 7 1 3
 2 10 7 18 5 33 0
 */