Maximum Subarray

Quesiton

from lintcode

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

Notice
The subarray should contain at least one number.

Example
Given the array [−2,2,−3,4,−1,2,1,−5,3], the contiguous subarray [4,−1,2,1] has the largest sum = 6.

Idea

Math trick. Sum from x to y = (sum from 0 - y) - (sum from 0 to x - 1)

public class Solution {
    /**
     * @param nums: A list of integers
     * @return: A integer indicate the sum of max subarray
     */
    public int maxSubArray(int[] nums) {
        if (nums.length == 0) return 0;
        
        int max = Integer.MIN_VALUE;
        int sum = 0;
        int minSum = 0;
        for (int i = 0; i < nums.length; i++) {
            // sum of 0-index to i-index elements
            sum += nums[i];
            
            // FORMULA
            // e.g.
            // sum(3 to 6) = sum(0 to 6) - sum(0 to 2)
            // to maximize subarray, gonna minimize the subtraction
            int subArraySum = sum - minSum;
            
            // update the subarray sum which has the smallest sum
            // from 0th to x-th 
            minSum = Math.min(minSum, sum);
            
            max = Math.max(max, subArraySum);
        }
        return max;
    }
}