53. Maximum Subarray

Question

LeetCode Problem

Given an integer array nums , find the subarray with the largest sum, and return its sum .
Example 1:

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

Example 2:

Input: nums = [1] Output: 1 Explanation: The subarray [1] has the largest sum 1.

Example 3:

Input: nums = [5,4,-1,7,8] Output: 23 Explanation: The subarray [5,4,-1,7,8] has the largest sum 23.

Constraints:

• 1 <= nums.length <= 10 5
• -10 4 <= nums[i] <= 10 4
  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.

Solutions

Use DP

• dp數組定義：dp[i]是位在i時，最大的子數組總和。
• 遞推公式：dp[i] = max(dp[i-1] + nums[i], nums[i])

int maxSubarray(vector<int>& nums) {
	int m = nums.size();
	vector<int> dp(m, 0);
	int maxSum = nums[0];
	dp[0] = nums[0];
	for (int i = 1; i < m; ++i) {
		dp[i] = max(dp[i-1] + nums[i], nums[i]);
		maxSum = max(maxSum, dp[i]);
	}
	return maxSum;
}