hdoj To The Max 1081 (二维DP)
2015-11-30 21:34
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To The Max
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)Total Submission(s): 10290 Accepted Submission(s): 4950
[align=left]Problem Description[/align]
Given a two-dimensional array of positive and negative integers, a sub-rectangle is any contiguous sub-array of size 1 x 1 or greater located within the whole array. The sum of a rectangle is the sum of all the elements in that rectangle.
In this problem the sub-rectangle with the largest sum is referred to as the maximal sub-rectangle.
As an example, the maximal sub-rectangle of the array:
0 -2 -7 0
9 2 -6 2
-4 1 -4 1
-1 8 0 -2
is in the lower left corner:
9 2
-4 1
-1 8
and has a sum of 15.
[align=left]Input[/align]
The input consists of an N x N array of integers. The input begins with a single positive integer N on a line by itself, indicating the size of the square two-dimensional array. This is followed by N 2 integers separated by whitespace
(spaces and newlines). These are the N 2 integers of the array, presented in row-major order. That is, all numbers in the first row, left to right, then all numbers in the second row, left to right, etc. N may be as large as 100. The numbers in the array will
be in the range [-127,127].
[align=left]Output[/align]
Output the sum of the maximal sub-rectangle.
[align=left]Sample Input[/align]
4
0 -2 -7 0 9 2 -6 2
-4 1 -4 1 -1
8 0 -2
[align=left]Sample Output[/align]
15
#include<stdio.h> #include<string.h> #include<math.h> #include<algorithm> using namespace std; int map[200][200]; int n,m,mm; void find(int x) { int t=0; int i,j; for(i=0;i<n;i++) { if(t>0) t+=map[x][i]; else t=map[x][i]; mm=max(mm,t); } } int main() { int i,j,k; while(scanf("%d",&n)!=EOF) { memset(map,0,sizeof(map)); for(i=0;i<n;i++) for(j=0;j<n;j++) scanf("%d",&map[i][j]); mm=map[0][0]; for(i=0;i<n;i++) { find(i); for(j=i+1;j<n;j++) { for(k=0;k<n;k++) { map[i][k]+=map[j][k]; } find(i); } } printf("%d\n",mm); } return 0; }
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