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209. Minimum Size Subarray Sum

Difficulty Topics

Description

Given an array of positive integers nums and a positive integer target, return the minimal length of a contiguous subarray [numsl, numsl+1, ..., numsr-1, numsr] of which the sum is greater than or equal to target. If there is no such subarray, return 0 instead.

 

Example 1:

Input: target = 7, nums = [2,3,1,2,4,3]
Output: 2
Explanation: The subarray [4,3] has the minimal length under the problem constraint.

Example 2:

Input: target = 4, nums = [1,4,4]
Output: 1

Example 3:

Input: target = 11, nums = [1,1,1,1,1,1,1,1]
Output: 0

 

Constraints:

  • 1 <= target <= 109
  • 1 <= nums.length <= 105
  • 1 <= nums[i] <= 104

 

Follow up: If you have figured out the O(n) solution, try coding another solution of which the time complexity is O(n log(n)).

Solution

minimum-size-subarray-sum.py
class Solution:
    def minSubArrayLen(self, target: int, nums: List[int]) -> int:
        n = len(nums)
        total = sum(nums)

        if total < target: return 0

        left, right = 1, n

        def good(k):
            s = 0

            for i, x in enumerate(nums):
                if i >= k:
                    s -= nums[i - k]
                s += x

                if s >= target: return True

            return False

        while left < right:
            mid = left + (right - left) // 2

            if good(mid):
                right = mid
            else:
                left = mid + 1

        return left