Description
https://leetcode.com/problems/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 <= 3 * 104-105 <= nums[i] <= 105
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.
Explanation
The contiguous subarray which has the largest sum starts from the contiguous subarray which has the smallest sum.
Python Solution
class Solution:
def maxSubArray(self, nums: List[int]) -> int:
if not nums:
return 0
prefix_sum = 0
max_sum = -sys.maxsize
min_sum = sys.maxsize
for num in nums:
prefix_sum += num
max_sum = max(max_sum, prefix_sum, prefix_sum - min_sum)
min_sum = min(min_sum, prefix_sum)
return max_sum- Time complexity: O(N)
- Space complexity: O(1)
It is a best solution found that very popular and helpful:
https://www.youtube.com/watch?v=Ut7q0TS6sfY&ab_channel=EricProgramming
/* Java solution */
class Solution {
public int maxSubArray(int[] nums) {
int max_so_far = nums[0];
int max_ending_here = nums[0];
for (int i=1;i<nums.length;i++) {
max_ending_here = Math.max(nums[i] + max_ending_here, nums[i]);
max_so_far = Math.max(max_ending_here, max_so_far);
}
return max_so_far;
}
}