330 Patching Array

Given a sorted positive integer array nums and an integer n, add/patch elements to the array such that any number in 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:

nums = [1, 3], n = 6
Return 1.

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:

nums = [1, 5, 10], n = 20
Return 2.
The two patches can be [2, 4].

Example 3:

nums = [1, 2, 2], n = 5
Return 0.

Solution

class Solution {
public:
    int minPatches(vector<int>& nums, int n) {
        int nn = nums.size();
        int res = 0, i = 0;
        long max = 0;
        while ( true ) {
            if ( max >= n ) break;
            if ( i >= nn or nums[i] > max+1 ) {
                res++;
                max = 2*max+1;
            }
            else max += nums[i++];
        }
        return res;
    }
};

Notes
Pay attention to overflow!