Problem - Minimum Increment to Make Array Unique

Given an array, in one move you can increment any element by $1$. Find the minimum moves to make all elements unique. For $[1,2,2]$, increment one $2$ to $3$. Answer is $1$. For $[3,2,1,2,1,7]$, answer is $6$.

Think about what happens if you sort the array first. Duplicates become adjacent. Constraint: increments are unlimited, so every array has a solution. After sorting, duplicates cluster together, making it easy to detect violations. The final array will be a consecutive or near-consecutive sequence starting from the smallest element.