maxSubArray

Description:

Find the contiguous subarray within an array (containing at least one number) which has the largest sum.

For example, given the array [-2,1,-3,4,-1,2,1,-5,4],
the contiguous subarray [4,-1,2,1] has the largest sum = 6.

Thoughts:

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.

there is my java code:

package easy.array;
 
public class MaxSubArray {
    public int maxSubArray(int[] nums){
        int maxsofar = nums[0];
        int maxtotal = nums[0];
        for(int i = 1; i< nums.length;i++){
            maxsofar = Math.max(maxsofar+nums[i], nums[i]);
            maxtotal = Math.max(maxtotal, maxsofar);
        }
        return maxtotal;
    }
 
    public static void main(String[] args){
        int[] nums = new int[]{-2, 1, -3, 4, -1, 2, 1, -5, 4};
        MaxSubArray max = new MaxSubArray();
        int num = max.maxSubArray(nums);
        System.out.println(num);
    }
}