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"""
53. Maximum Subarray
Easy
Given an integer array nums, find the contiguous subarray (containing at least one number) which has the largest sum and return its sum.
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.
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 = [0]
Output: 0
Example 4:
Input: nums = [-1]
Output: -1
Example 5:
Input: nums = [-2147483647]
Output: -2147483647
Constraints:
1 <= nums.length <= 2 * 10^4
-2^31 <= nums[i] <= 2^31 - 1
"""
from typing import List
import math
"""
DP (dynamic programming) using Kadane's algorithm
cur_sum[i] = max(nums[i], nums[i]+cur_sum[i-1])
^ ^
don't use cur_sum[i-1] use cur_sum[i-1]
time O(N)
space O(1)
"""
class Solution:
def maxSubArray(self, nums: List[int]) -> int:
best_sum = -math.inf
cur_sum = -math.inf
for num in nums:
cur_sum = max(num, cur_sum + num)
best_sum = max(best_sum, cur_sum)
return best_sum
def main():
sol = Solution()
assert sol.maxSubArray([-2,1,-3,4,-1,2,1,-5,4]) == 6, 'fails'
assert sol.maxSubArray([1]) == 1, 'fails'
assert sol.maxSubArray([0]) == 0, 'fails'
assert sol.maxSubArray([-1]) == -1, 'fails'
assert sol.maxSubArray([-2147483647]) == -2147483647, 'fails'
if __name__ == '__main__':
main()