209. Minimum Size Subarray Sum

1. Description

Given an array of positive integers nums and a positive integer target, return the minimal length of a subarray whose sum is greater than or equal to target. If there is no such subarray, return 0 instead.

2. Example

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

3. Constraints

• 1 <= target <= 10$^{9}$
• 1 <= nums.length <= 10$^{5}$
• 1 <= nums[i] <= 10$^{5}$

4. Solutions

Sliding Window

n = nums.size()
Time complexity: O(n)
Space complexity: O(1)

class Solution {
public:
    int minSubArrayLen(const int target, const vector<int> &nums) {
        const int n = nums.size();
        int length = numeric_limits<int>::max(), sum = 0;
        for (int left = 0, right = 0; right < n; ++right) {
            sum += nums[right];

            while (sum - nums[left] >= target) {
                sum -= nums[left];
                ++left;
            }

            if (sum >= target) {
                length = min(length, right - left + 1);
            }
        }

        return length == numeric_limits<int>::max() ? 0 : length;
    }
};