53. Maximum Subarray
Category: /leetcodeGiven an integer array nums, find the contiguous subarray (containing at least one number) which has the largest sum and return its sum.
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
Solution
prefix sum
T: O(n), S:O(n)
def maxSubArray(self, nums: List[int]) -> int:
for i in range(1, len(nums)):
if nums[i-1] > 0:
nums[i] += nums[i-1]
return max(nums)
Kadane’s algorithm
T: O(n), S:O(n)
def maxSubArray(self, nums: List[int]) -> int:
# Initialize our variables using the first element.
current_subarray = max_subarray = nums[0]
# Start with the 2nd element since we already used the first one.
for num in nums[1:]:
# If current_subarray is negative, throw it away.
# Otherwise, keep adding to it.
current_subarray = max(num, current_subarray + num)
max_subarray = max(max_subarray, current_subarray)
return max_subarray
