最大子序列的和（四种算法）

三重循环

public static int maxSubSum(int[] a) {
    
    
        int maxSum = 0;
        for (int i = 0; i < a.length; i++)
            for (int j = i; j < a.length; j++) {
    
    
                int thisSum = 0;
                for (int k = i; k <= j; k++)
                    thisSum += a[k];
                if (thisSum > maxSum)
                    maxSum = thisSum;
            }
        return maxSum;
    }

二重循环

public static int maxSubSum(int[] a) {
    
    
        int maxSum = 0;
        for (int i = 0; i < a.length; i++) {
    
    
            int thisSum = 0;
            for (int j = i; j < a.length; j++) {
    
    
                thisSum += a[j];
                if (thisSum > maxSum)
                    maxSum = thisSum;
            }
        }
        return maxSum;
    }

递归

private static int maxSumRec(int[] a, int left, int right) {
    
    
        if (left == right)
            if (a[left] > 0)
                return a[left];
            else
                return 0;
        int center = (left + right) / 2;
        int maxLeftSum = maxSumRec(a, left, center);
        int maxRightSum = maxSumRec(a, center+1, right);

        int maxLeftBorderSum = 0, leftBorderSum = 0;
        for (int i = center; i >= left; i--) {
    
    
            leftBorderSum += a[i];
            if (leftBorderSum > maxLeftBorderSum)
                maxLeftBorderSum = leftBorderSum;
        }

        int maxRightBorderSum = 0, rightBorderSum = 0;
        for (int i = center + 1; i <= right; i++) {
    
    
            rightBorderSum += a[i];
            if (rightBorderSum > maxRightBorderSum)
                maxRightBorderSum = rightBorderSum;
        }

        return max(maxLeftSum, maxRightSum, maxLeftBorderSum + maxRightBorderSum);

    }
    public static int maxSubSum(int[] a) {
    
    
        return maxSumRec(a, 0, a.length - 1);
    }
    public static int max (int maxLeftSum, int maxRightSum, int sum) {
    
    
        if (maxLeftSum > maxRightSum)
            if (maxLeftSum > sum)
                return maxLeftSum;
            else
                return sum;
        else
            if (maxRightSum > sum)
                return maxRightSum;
            else
                return sum;
    }

消去负数

public static int maxSubSum(int[] a) {
    
    
        int maxSum = 0, thisSum = 0;
        for (int j = 0; j < a.length; j++) {
    
    
            thisSum += a[j];
            if (thisSum > maxSum)
                maxSum = thisSum;
            else if (thisSum < 0)
                thisSum = 0;
        }
        return maxSum;
    }