MaximumSumSubArray.java

/*
this problem was discussed by Jon Bentley (Sep. 1984 Vol. 27 No. 9 Communications of the ACM P885)

the paragraph below was copied from his paper (with a little modifications)

algorithm that operates on arrays: it starts at the left end (element A[1]) and scans through to the right end (element A[n]), keeping track of the maximum sum subvector seen so far. The maximum is initially A[0]. Suppose we've solved the problem for A[1 .. i - 1]; how can we extend that to A[1 .. i]? The maximum
sum in the first I elements is either the maximum sum in the first i - 1 elements (which we'll call MaxSoFar), or it is that of a subvector that ends in position i (which we'll call MaxEndingHere).

MaxEndingHere is either A[i] plus the previous MaxEndingHere, or just A[i], whichever is larger.

O(n)
O(1)

*/

public class Solution
{
    public int maxSubArray(int[] nums)
    {
        int max = nums[0], maxSoFar = nums[0];
        for(int i=1; i < nums.length; i++)
        {
            maxSoFar = maxSoFar > 0 ? maxSoFar + nums[i] : nums[i];
            max = Math.max(maxSoFar, max);
        }
        return max;
    }
}