最大子序列求和问题（1）-解法之一分治法

（一）问题提出

求序列和的最大值

/**
 * 求最大序列和
 */
public class CMaxSumUtils {
  /*
   * 算法一
   */
	public static int maxSum(int[] a, int left, int right) {
		//当‘分’，数据项只有一项时
		if (left == right) {//递归的基准
			if(a[left] > 0) {
			    return a[left];
			} else {//如果为负，则抛弃此项数据，从后再计算
				return 0;
			}
		} 
		//‘分’
		int center = (left + right) / 2;
		//递归求解
		int maxLeftSum = maxSum(a, left, center);
		int maxRightSum = maxSum(a, center + 1, right);
		/**
		 * 例：
		 * 当子问题为[-1 2]，求得以下
		 * maxLeft=-1,maxRight=2,max横跨左右=-1 + 2
		 * 当取 3者最大解
		 */
		int maxLeftBorderSum = 0;
		int leftBorderSum = 0;
		for(int i = center; i >= left; i--) {
			leftBorderSum += a[i];
			if(leftBorderSum > maxLeftBorderSum) {
				maxLeftBorderSum = leftBorderSum;
			}
 		}
		
		int maxRightBorderSum = 0;
		int rightBorderSum = 0;
		for(int i = center + 1; i <= right; i++) {
			rightBorderSum += a[i];
			if(rightBorderSum > maxRightBorderSum) {
				maxRightBorderSum = rightBorderSum;
			}
 		}
		
		return max(maxLeftSum, maxRightSum, maxLeftBorderSum + maxRightBorderSum );
	}
	
	private static int max(int a1, int a2, int a3) {
		int max = 0;
		if(a1 > max) {
			max = a1;
		}
		if(a2 > max) {
		    max = a2;	
		}
		if(a3 > max) {
			max = a3;
		}
		return max;
	}
	
	public static void main(String[] args) {
		int[] a = {-1, 2, -7, 5};
		System.out.println(maxSum(a, 0, a.length - 1));
	}
}