[LeetCode] Patching Array

From leetcode
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].

Let's look at the example 1, let curr be the current number in the arrray, cover be the maximum number the numbers being covered from 1.
When curr = 1, cover = 1;
When curr = 3, since there is gap between cover and curr, we need to fill it in, so insert 2, and update cover to 1 + 2 + 3 = 6;
Done.

Example 2.
curr = 1, cover = 1;
curr = 5, fill in the gap between 1 and 5, insert 2, cover = 1+2 = 3, gap is still there between 3 and 5, insert cover+1=4, update cover = 1+2+3=6, no gap any more, update cover = 1+2+3+5=11
curr = 10, no gap, and update cover = 11+10=21
21>20, Done.

So the two most important findings are
1) when we insert a number, the coverage will be increased by that number,
2) next insert number will be the coverage+1.

So our algorithm is following:
let cover=0, insert=0
1. go through the numbers (curr) in the list until cover >= n
  while curr > cover+1 and cover<n,
    insert cover+1
    update cover = cover + cover+1
    increase insert by 1

2. while cover < n
        insert cover+1
        update cover = cover + cover+1
        increase insert by 1