Maximum subarray problem brute force complexity

问题

What is the runtime/memory complexity of the Maximum subarray problem using brute force?

Can they be optimized more? Especially the memory complexity?

Thanks,

回答1:

Brute force is Omega(n^2). Using Divide and conquer you can do it with Theta(n lg n) complexity. Further details are available in many books such as Introduction to Algorithms, or in various resources on the Web, such as this lecture.

回答2:

As suggested in this answer you can use Kadane's algorithm which has O(n) complexity. An implementation in Java:

public int[] kadanesAlgorithm (int[] array) {
        int start_old = 0;
        int start = 0;
        int end = 0;
        int found_max = 0;

        int max = array[0];

        for(int i = 0; i<array.length; i++) {
            max = Math.max(array[i], max + array[i]);
            found_max = Math.max(found_max, max);
            if(max < 0)
                start = i+1;
            else if(max == found_max) {
                start_old=start;
                end = i;
                }
        }

        return Arrays.copyOfRange(array, start_old, end+1);
    }

来源：https://stackoverflow.com/questions/5649754/maximum-subarray-problem-brute-force-complexity