LeetCode 53. Maximum Subarray

Question

Given an integer array nums, find the contiguous subarray (containing at least one number) which has the largest sum and return its sum.

A subarray is a contiguous part of an array.

Example 1:

Input: nums = [-2,1,-3,4,-1,2,1,-5,4]
Output: 6
Explanation: [4,-1,2,1] has the largest sum = 6.

Example 2:

Input: nums = [1]
Output: 1

Example 3:

Input: nums = [5,4,-1,7,8]
Output: 23

Constraints:

• 1 <= nums.length <= 105
• -104 <= nums[i] <= 104

Source: https://leetcode.com/problems/maximum-subarray/

Solution

For subarray sum problems, prefix sum is a powerful tool. The sum of any subarray can be calculated by two prefix sums. And for a subarray ending with index i, its sum must be the difference between prefixSums[i] and the min prefix sum before i. The idea is similar to LeetCode 121. Best Time to Buy and Sell Stock.

public int maxSubArray(int[] nums) {
    int len = nums.length;
    // prefixSums[i] represents the sum of nums[0, i)
    int[] prefixSums = new int[len + 1];
    prefixSums[0] = 0;
    for (int i = 0; i < len; i++) {
        prefixSums[i + 1] = prefixSums[i] + nums[i];
    }

    int minPrefix = 0;
    int maxSubarray = Integer.MIN_VALUE;
    for (int i = 1; i <= len; i++) {
        maxSubarray = Math.max(maxSubarray, prefixSums[i] - minPrefix);
        minPrefix = Math.min(minPrefix, prefixSums[i]);
    }
    return maxSubarray;
}