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.
Constraints:
- 1 <= nums.length <= 10^5
- -10^4 <= nums[i] <= 10^4
Examples:
Input: [-2,1,-3,4,-1,2,1,-5,4]
Output: 6
Explanation: The subarray [4,-1,2,1] has the largest sum 6.
Solutions
Kadane's Algorithm
Time: O(n)Space: O(1)
Kadane's algorithm scans the entire array and at each position finds the maximum sum of the subarray ending at that position.
def maxSubArray(nums):
max_so_far = nums[0]; max_ending_here = nums[0]; for i in range(1, len(nums)):
max_ending_here = max(nums[i], max_ending_here + nums[i]); max_so_far = max(max_so_far, max_ending_here); return max_so_farFollow-up:
What if the input array is empty?
