Minimum Size Subarray Sum

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] <= 105

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)).
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class Solution {
public:
    int minSubArrayLen(int target, vector<int>& nums) {
        //variable size sliding window
        int i = 0;
        int j = 0;
        int sum = 0;
        int minim = INT_MAX;
        int n = nums.size();
        while(j<n){
            sum+=nums[j];
            if(sum<target){
                j++;
            }
            else if(sum>=target){
                while(sum>=target){
                    //step1: update minim 
                    minim = min(minim, j-i+1);
                    //step2: try to reduce the size of window even further after removing ans contributed by arr[i]
                    sum-=nums[i];
                    i++;
                }
                j++;
            }
        }
        if(minim==INT_MAX) return 0;
        return minim;
    }
};