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:

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

Solution

Approach 1: Greedy.

Code (Python)

Approach 1:

Code (C++)

Approach 1:

class Solution {
public:
    int minPatches(vector<int>& nums, int n) {
        int count = 0;
        long max = 0;
        int i = 0;
        while (max < n)
        {
            if (i == nums.size() || max + 1 < nums[i])
            {
                count++;
                max += max + 1;
            }
            else
            {
                max += nums[i];
                i++;
            }
        }
        return count;
    }
};