Beans

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)

Total Submission(s): 2596    Accepted Submission(s): 1279

Problem Description

Bean-eating is an interesting game, everyone owns an M*N matrix, which is filled with different qualities beans. Meantime, there is only one bean in any 1*1 grid. Now you want to eat the beans and collect the qualities, but everyone
must obey by the following rules: if you eat the bean at the coordinate(x, y), you can’t eat the beans anyway at the coordinates listed (if exiting): (x, y-1), (x, y+1), and the both rows whose abscissas are x-1 and x+1.

Now, how much qualities can you eat and then get ?

Input

There are a few cases. In each case, there are two integer M (row number) and N (column number). The next M lines each contain N integers, representing the qualities of the beans. We can make sure that the quality of bean isn‘t beyond
1000, and 1<=M*N<=200000.

Output

For each case, you just output the MAX qualities you can eat and then get.

Sample Input

4 6
11 0 7 5 13 9
78 4 81 6 22 4
1 40 9 34 16 10
11 22 0 33 39 6

Sample Output

242

Source

2009 Multi-University Training Contest 4 - Host by HDU

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这道题意思可以转换成：

对每一行，不能有间隔的取一个子序列，即取该行的最大不连续子序列和；

再从上面所有值中，取其最大不连续子序列和；就相当于隔一行取了

状态：f[i]表示取第i个元素(a[i]必取)的最大值，map[i]表示取到a[i]（可不取）时的最大值

状态转移：f[i]=map[i-2]+a[i];map[i]=max{map[i-1],f[i]};

#include <stdio.h>
#include <iostream>
using namespace std;
#define M 200001
int vis[M],map[M],dp[M],f[M];
int max(int a[],int n)                //求在a[]中最大不连续子序列和。
{
  int i;
  f[0]=map[0]=0;
  f[1]=map[1]=a[1];
  for(i=2;i<=n;i++)                   //要保证i-2不会数组越界。
  {
      f[i]=map[i-2]+a[i];                  //因为要隔一个取，所以取了a[i],就不能取a[i-1],所以最大值就是前i-2个数的最大值+a[i].
      map[i]=f[i]>map[i-1]?f[i]:map[i-1];  //如果取a[i]要更大，更新map[i]的值。
  }
 return map[n];
}
int main(int i,int j,int k)
{
    int n,m,tot,cur;
    while(scanf("%d%d",&n,&m)!=EOF&&n&&m)
    {
        for(i=1;i<=n;i++)
        {
            for(j=1;j<=m;j++)
                scanf("%d",&vis[j]);
            dp[i]=max(vis,m);
        }
    printf("%d\n",max(dp,n));
    }
    return 0;
}

HDU 2845 Beans (动规)