HDU 2845 Beans （DP）

[align=left]Problem Description[/align]
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 ?

[align=left]Input[/align]
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.

[align=left]Output[/align]
For each case, you just output the MAX qualities you can eat and then get.

[align=left]Sample Input[/align]

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

[align=left]Sample Output[/align]

242

题目能够看成是一个二维的，每一维的解法都是一个DP的过程。也就是一个数组，取第i个数就不能取与他相邻的数。求和最大。

能够设两个数组d[i],f[i]为别表示第i个数取或者不取时的和最大。

d[i] = f[i-1]+a[i] , f[i] = max(f[i-1],d[i-1]) 。

f[1] = 0, d[1] = a[1] .

#include <stdio.h>
#include <string.h>
#include <algorithm>
#include <math.h>
using namespace std;
typedef long long LL;
const int MAX=0x3f3f3f3f;
const int maxn = 200005;
int n, m;
int d[maxn], f[maxn], a[maxn], b[maxn];
int DP(int *c, int len) {
d[1] = c[1], f[1] = 0;
for(int i = 1; i <= len; i++) {
d[i] = f[i-1] + c[i];
f[i] = max(f[i-1], d[i-1]);
}
return max(f[len], d[len]);
}
int main()
{
while(~scanf("%d%d", &n, &m)) {
for(int i = 1; i <= n; i++) {
for(int j = 1; j <= m; j++)
scanf("%d", &a[j]);
b[i] = DP(a, m);
}
printf("%d\n", DP(b, n));
}
return 0;
}