POJ 1050 To the Max【最大子矩阵】
2012-07-31 18:28
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Description
Given a two-dimensional array of positive and negative integers, a sub-rectangle is any contiguous sub-array of size 1*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.
Input
The input consists of an N * 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].
Output
Output the sum of the maximal sub-rectangle.
Sample Input
Sample Output
Given a two-dimensional array of positive and negative integers, a sub-rectangle is any contiguous sub-array of size 1*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.
Input
The input consists of an N * 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].
Output
Output the sum of the maximal sub-rectangle.
Sample Input
4 0 -2 -7 0 9 2 -6 2 -4 1 -4 1 -1 8 0 -2
Sample Output
15
思路 | 将一维的求最大子序列的和进行加强版,同样这里采取相对暴力的方法,时间复杂度为O(N^3)的方法进行枚举每个子矩阵。 |
源码 | #include<stdio.h> #include<string.h> #define MIN -99999999 int main() { int i, j, k, f[101][101], a[101], n, mem[101]; while(scanf("%d", &n)!=EOF) { for(i=1; i<=n; i++) for(j=1; j<=n; j++) scanf("%d", &f[i][j]); int maxnum=MIN, change; memset(a, 0, sizeof(a)); for(i=1; i<=n; i++) { memset(mem, 0, sizeof(mem)); for(j=i; j<=n; j++) { for(k=1; k<=n; k++) { mem[k]+=f[j][k]; a[k]=mem[k]; } change=a[1]; for(k=2; k<=n; k++) { a[k]=a[k]>a[k]+a[k-1]?a[k]:a[k]+a[k-1]; change=a[k]>change?a[k]:change; } maxnum=maxnum>change?maxnum:change; } } printf("%d\n", maxnum); } } |
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