53. Maximum Subarray(寫1186順便複習一下這道題的兩種寫法)

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

Example:

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

Follow up:

If you have figured out the O(n) solution, try coding another solution using the divide and conquer approach, which is more subtle.

數學歸納法的寫法

class Solution {
    public int maxSubArray(int[] nums) {
        if (nums.length == 0) return 0;
        int[] end = new int[nums.length];
        end[0] = nums[0];
        int res = end[0];
        for (int i = 1; i < nums.length; i++) {
            end[i] = Math.max(end[i-1] + nums[i], nums[i]);
            res = Math.max(res, end[i]);
        }
        return res;
    }
}

兩個index的總sum之差爲subarray sum. 有點像dp

class Solution {
    public int maxSubArray(int[] nums) {
        int result = Integer.MIN_VALUE, pre = 0;
        for (int i = 0 ; i < nums.length; i++) {
            if (pre >= 0) {
                pre += nums[i];
                result = Math.max(result, pre);
            } else {
                pre = nums[i];
                result = Math.max(result, nums[i]);
            }
        }
        return result;
    }
}