编程之美---子矩阵之和的最大值

把二维转化为一维,再利用求最大子序列的方法求最大子矩阵.

 

#include<stdio.h>

#include<stdlib.h>

#include<string.h>

#include<assert.h>



#define max(a, b) ((a) > (b) ? (a) : (b))



const int neginf = 0x80000001;



int a[100][100] = {0};



int getMaxSum(int *b, int n)

{

	int curSum = 0;

	int maxSum = neginf;

	for(int i=0; i<n; i++)

	{

		if(curSum < 0)

			curSum = 0;

		curSum += b[i];

		maxSum = max(maxSum, curSum);

	}

	return maxSum;

}



int * getSeqMatrix(int s, int e, int n)

{

	int *b = new int[n];

	for(int i=0; i<n; i++)

		b[i] = 0;

	for(i=0; i<n; i++)

	{

		for(int j=s; j<=e; j++)

		{

			b[i] += a[j][i];

		}

	}

	return b;

}



int getMaxMatrix(int n)

{

	int curSum = 0;

	int maxSum = neginf;

	for(int i=0; i<n; i++)

	{

		for(int j=i; j<n; j++)

		{

			int *b = getSeqMatrix(i, j, n);

			curSum = getMaxSum(b, n);

			maxSum = max(curSum, maxSum);

			delete []b;

		}

	}

	return maxSum;

}



void test()

{

	int n;

	while(scanf("%d", &n)!=EOF)

	{

		if(n == 0) break;

		for(int i=0; i<n; i++)

		{

			for(int j=0; j<n; j++)

				scanf("%d", &a[i][j]);

		}

		int ret = getMaxMatrix(n);

		printf("%d\n", ret);

	}

}



int main()

{

	test();

	return 0;

}