LeetCode 53. Maximum Subarray (Kadane Algorithm)

 53. Maximum Subarray

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

A subarray is a contiguous part of an array.

 

Example 1:

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

Example 2:

Input: nums = [1]
Output: 1

Example 3:

Input: nums = [5,4,-1,7,8]
Output: 23

 

Constraints:

• 1 <= nums.length <= 105
• -104 <= nums[i] <= 104

 

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.

	class Solution {
	public:
	/*
	Framework DP
	1. function
	dp[i]: max sub array's sum, till end at i index
	max(dp[i]): answer
	2. relation
	dp[i] = max(dp[i-1] + nums[i], nums[i])
	3. base
	dp[0] = nums[0]
	*/
	int maxSubArray(vector<int>& nums) {
	int n = nums.size();
	vector<int> dp(n);
	dp[0] = nums[0];
	int ans = max(INT_MIN, dp[0]);
	for(int i = 1; i < n; i++){
	dp[i] = max(dp[i-1] + nums[i], nums[i]);
	ans = max(ans, dp[i]);
	}
	return ans;
	}
	};

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