最大子矩阵

/**
 * 最大子矩阵
 * 穷举可解，复杂度太高
 * 
 * 局部动态规划
 * 参考最大子段和问题
 * 
 *
 */
public class MaxMetrics {

	public static int twoMax(int[][] a, int m, int n){
		int max = 0;
		int[] b = new int[n];
		for(int i=0; i<m; i++){
			clear(b);
			for(int j=i; j<m; j++){
				for(int k=0; k<n; k++){
					b[k] += a[j][k];
					int sum = oneMax(b, n);
					if(sum > max){
						max = sum;
					}
				}
			}
		}
		return max;
	}
	
	private static int oneMax(int[] a, int n){
		int sum = a[0];
		int max = a[0];
		for(int i=1; i<n; i++){
			if(sum >0){
				sum += a[i];
			}else{
				sum = a[i];
			}
			if(sum > max){
				max = sum;
			}
		}
		return max;
	}
	
	private static void clear(int[] a){
		for(int i=0; i<a.length; i++){
			a[i] = 0;
		}
	}
	
	/**
	 * @param args
	 */
	public static void main(String[] args) {
		int[] a1 = {1,-2,3,4,-5,-3,9,6};
		int[] a2 = {-2,-2,5,7,2,12,-9,-6};
		int[] a3 = {1,2,3,4,-5,-3,8,1};
		int[] a4 = {8,6,-3,-4,5,-3,-1,-4};
		
		int[][] a = {a1,a2,a3,a4};
		
		int max = MaxMetrics.twoMax(a, 4, 8);
		System.out.println(max);
	}

}