# Leetcode 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 = 6Output: 1 Explanation:Combinations of nums are , , [1,3], which form possible sums of: 1, 3, 4.Now if we add/patch 2 to nums, the combinations are: , , , [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 = 20Output: 2Explanation: The two patches can be [2, 4].`

Example 3:

`Input: nums = [1,2,2], n = 5Output: 0`

Problem Analysis:

Suppose k is the smallest number missed in nums, [1, …, k) is covered, so add the number k we can cover [1, …, 2*k), if existing nums[i] that k≤nums[i]<2*k, then we can update covering range to [1, …, 2*k+nums[i]).

Iterating the procedure and update until reaching n, we can find the minimum number of patches.

Solution:

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

Time Complexity: O(n)

Space Complexity: O(1)