Maximum Subarray

Posted 2021-03-21 flagyuri

Description

Given an array of integers, find a contiguous subarray which has the largest sum.

The subarray should contain at least one number.

Example

Example1:

Input: [−2,2,−3,4,−1,2,1,−5,3]
Output: 6
Explanation: the contiguous subarray [4,−1,2,1] has the largest sum = 6.

Example2:

Input: [1,2,3,4]
Output: 10
Explanation: the contiguous subarray [1,2,3,4] has the largest sum = 10.

Challenge

Can you do it in time complexity O(n)?

思路：使用前缀和。

public class Solution {
    /**
     * @param nums: A list of integers
     * @return: A integer indicate the sum of max subarray
     */
     public int maxSubArray(int[] A) {
        if (A == null || A.length == 0){
            return 0;
        }
        //max记录全局最大值，sum记录前i个数的和，minSum记录前i个数中0-k的最小值
        int max = Integer.MIN_VALUE, sum = 0, minSum = 0;
        for (int i = 0; i < A.length; i++) {
            sum += A[i];
            max = Math.max(max, sum - minSum);
            minSum = Math.min(minSum, sum);
        }

        return max;
    }
}