同：最大子序和 https://www.cnblogs.com/liujinhui/p/15574312.html

描述
输入一个长度为n的整型数组array，数组中的一个或连续多个整数组成一个子数组。求所有子数组的和的最大值。

 

 

方法1：双层循环、暴力求解【运行超时】

public class Solution {
    public int FindGreatestSumOfSubArray(int[] array) {
        int maxRes = Integer.MIN_VALUE;
        for(int i = 0; i < array.length; i++) {
            int sum = 0;
            for(int j = i; j < array.length; j++) {
                sum += array[j];
                maxRes = Math.max(maxRes, sum);
            }
        }
        return maxRes;
    }
}

方法2：动态规划

public class Solution {
    public int FindGreatestSumOfSubArray(int[] array) {
        int[] dp = new int[array.length];
        dp[0] = array[0];
        int maxRes = dp[0];
        for(int i = 1; i < array.length; i++) {
            dp[i] = Math.max(dp[i - 1] + array[i], array[i]); //递推公式
            maxRes = Math.max(maxRes, dp[i]);
        }
        return maxRes;
    }
}

方法3：动态规划优化

public class Solution {
    public int FindGreatestSumOfSubArray(int[] array) {
        int maxRes = array[0];
        int fi = maxRes;
        for(int i = 1; i < array.length; i++) {
            fi = Math.max(fi + array[i], array[i]);
            maxRes = Math.max(maxRes, fi);
        }
        return maxRes;
    }
}

方法4：贪心，sum>0就相加，否则等于当前数

public class Solution {
    public int FindGreatestSumOfSubArray(int[] array) {
        int maxRes = array[0];
        int sum = 0;
        for(int i = 0; i < array.length; i++) {
            if(sum > 0) {
                sum += array[i];
            } else {
                sum = array[i];
            }
            maxRes = Math.max(maxRes, sum);
        }
        return maxRes;
    }
}