POJ - 3661 Running

Posted 2020-10-01 西北会法语

The cows are trying to become better athletes, so Bessie is running on a track for exactly N (1 ≤ N ≤ 10,000) minutes. During each minute, she can choose to either run or rest for the whole minute.

The ultimate distance Bessie runs, though, depends on her ‘exhaustion factor‘, which starts at 0. When she chooses to run in minute i, she will run exactly a distance of D_i (1 ≤ D_i ≤ 1,000) and her exhaustion factor will increase by 1 -- but must never be allowed to exceed M (1 ≤ M ≤ 500). If she chooses to rest, her exhaustion factor will decrease by 1 for each minute she rests. She cannot commence running again until her exhaustion factor reaches 0. At that point, she can choose to run or rest.

At the end of the N minute workout, Bessie‘s exaustion factor must be exactly 0, or she will not have enough energy left for the rest of the day.

Find the maximal distance Bessie can run.

Input

* Line 1: Two space-separated integers: N and M
* Lines 2..N+1: Line i+1 contains the single integer: D_i

Output

* Line 1: A single integer representing the largest distance Bessie can run while satisfying the conditions.
　

Sample Input

5 2
5
3
4
2
10

Sample Output

9

属于动态规划，dp【i】【j】代表前i分钟，疲劳值是j所能跑的最大长度。

 1 #include<iostream>
 2 #include<cstdio>
 3 #include<cstring>
 4 #include<cmath>
 5 
 6 using namespace std;
 7 
 8 
 9 int dp[10005][505],n,m,a[10005];
10 
11 int main()
12 {
13     int i,j;
14     scanf("%d%d",&n,&m);
15         for(i=1;i<=n;i++)
16             scanf("%d",&a[i]);
17         memset(dp,0,sizeof(dp));
18         for(i=1;i<=n;i++)
19         {
20             for(j=1;j<=m;j++)
21                 dp[i][j]=dp[i-1][j-1]+a[i];
22             dp[i][0]=dp[i-1][0];
23             for(int k=1;k<=m&&i>=k;k++)
24                 dp[i][0]=max(dp[i][0],dp[i-k][k]);
25         }
26         printf("%d\n",dp[n][0]);
27     return 0;
28 }