Patching Array - Implementation

Here is the solution:

function minPatches(nums, n)
 patches := 0
 miss := 1
 i := 0
 while miss <= n
 if i < length(nums) and nums[i] <= miss then
 miss := miss + nums[i]
 i := i + 1
 else
 miss := miss + miss
 patches := patches + 1
 return patches

Time: $O(m + \log n)$ where $m$ is array length. Space: $O(1)$.

Either use an existing number to extend range, or patch with $miss$ to double the range. Doubling means $O(\log n)$ patches at most.