最大子序列求和问题（1）-解法之一分治法

/**
* 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));
}
}