HDU 2845 Beans (DP)
2014-12-13 18:11
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Beans
Time Limit:1000MS Memory Limit:32768KB 64bit IO Format:%I64d & %I64u
Submit Status Practice HDU 2845
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.
![](http://acm.hdu.edu.cn/data/images/convip1-1001-1.JPG)
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
思路:
STEP_1:先以行为单位来算,设DP数组存的是以此位置为起点能得到的最大值,在此前提下,DP[i][j]因为相邻的不能走,所以要么加上DP[i][j + 2],要么加上DP[i][j + 3] (假设不越界),取最大的那个就好。从右往左依次计算这一行每个元素的DP值,记录下最大的,放到DP[i][0]里。
STEP_2:重复第一步,只不过对象换成了DP数组里每行0号单元的值,因为此单元放的是此行内的最大值。从上往下,每次选定一行后设此行为最终答案里最下面那行,因为选定一行之后它的上面和下面那一行就废掉了,所以每一行要么加上它上面第二行,要么加上它上面第三行。同理,记录下最大值,最大值即答案。(实际上答案不是最后一行就是倒数第二行,因为没有负数,只会越加越大,不过只有1行的时候就会越界,虽然HDU上的数据貌似没1行的)。
Time Limit:1000MS Memory Limit:32768KB 64bit IO Format:%I64d & %I64u
Submit Status Practice HDU 2845
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
思路:
STEP_1:先以行为单位来算,设DP数组存的是以此位置为起点能得到的最大值,在此前提下,DP[i][j]因为相邻的不能走,所以要么加上DP[i][j + 2],要么加上DP[i][j + 3] (假设不越界),取最大的那个就好。从右往左依次计算这一行每个元素的DP值,记录下最大的,放到DP[i][0]里。
STEP_2:重复第一步,只不过对象换成了DP数组里每行0号单元的值,因为此单元放的是此行内的最大值。从上往下,每次选定一行后设此行为最终答案里最下面那行,因为选定一行之后它的上面和下面那一行就废掉了,所以每一行要么加上它上面第二行,要么加上它上面第三行。同理,记录下最大值,最大值即答案。(实际上答案不是最后一行就是倒数第二行,因为没有负数,只会越加越大,不过只有1行的时候就会越界,虽然HDU上的数据貌似没1行的)。
#include<stdio.h> #include<stdlib.h> #include<string.h> #define MAX 200105 int main(void) { int n,m; int max,temp_1,temp_2,ans; while(scanf("%d%d",&n,&m) != EOF) { int dp[n + 10][m + 10]; memset(dp,0,sizeof(dp)); for(int i = 1;i <= n;i ++) for(int j = 1;j <= m;j ++) scanf("%d",&dp[i][j]); for(int i = 1;i <= n;i ++) { max = dp[i][m]; for(int j = m;j >= 1;j --) { dp[i][j] += dp[i][j + 2] > dp[i][j + 3] ? dp[i][j + 2] : dp[i][j + 3]; max = max > dp[i][j] ? max : dp[i][j]; } dp[i][0] = max; } max = dp[1][0]; dp[3][0] += dp[1][0]; for(int i = 4;i <= n;i ++) { dp[i][0] += dp[i - 2][0] > dp[i - 3][0] ? dp[i - 2][0] : dp[i - 3][0]; max = max > dp[i][0] ? max : dp[i][0]; } printf("%d\n",max); } return 0; }
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