330_Patching_Array.cpp

/*
330. Patching Array
Given a sorted integer array nums and an integer n, add/patch elements to the array such that any number in the range [1, n] inclusive can be formed by the sum of some elements in the array.
Return the minimum number of patches required.
Example 1:
Input: nums = [1,3], n = 6
Output: 1
Explanation:
Combinations of nums are [1], [3], [1,3], which form possible sums of: 1, 3, 4.
Now if we add/patch 2 to nums, the combinations are: [1], [2], [3], [1,3], [2,3], [1,2,3].
Possible sums are 1, 2, 3, 4, 5, 6, which now covers the range [1, 6].
So we only need 1 patch.
Example 2:
Input: nums = [1,5,10], n = 20
Output: 2
Explanation: The two patches can be [2, 4].
Example 3:
Input: nums = [1,2,2], n = 5
Output: 0
Constraints:
1 <= nums.length <= 1000
1 <= nums[i] <= 104
nums is sorted in ascending order.
1 <= n <= 231 - 1
*/
class Solution {
public:
    int minPatches(vector<int>& nums, int n) {
        long missing = 1;
        int patches = 0;
        int index = 0;

        while (missing <= n) {
            if (index < nums.size() && nums[index] <= missing) {
                missing += nums[index];
                index++;
            } else {
                missing += missing;
                patches++;
            }
        }

        return patches;
    }
};