Make Unique - Implementation

Here is the solution:

function minIncrementForUnique(nums)
 sort nums ascending
 moves := 0
 for i from 1 to length - 1
 if nums[i] <= nums[i-1] then
 need := nums[i-1] + 1
 moves := moves + (need - nums[i])
 nums[i] := need
 return moves

Time: $O(n \log n)$. Space: $O(1)$ if sorting in place.

After sorting, duplicates are adjacent. Fix each one by bumping it just above its predecessor.