945. Minimum Increment to Make Array Unique
Description
You are given an integer array nums
. In one move, you can pick an index i
where 0 <= i < nums.length
and increment nums[i]
by 1
.
Return the minimum number of moves to make every value in nums
unique.
The test cases are generated so that the answer fits in a 32-bit integer.
Example 1:
Input: nums = [1,2,2] Output: 1 Explanation: After 1 move, the array could be [1, 2, 3].
Example 2:
Input: nums = [3,2,1,2,1,7] Output: 6 Explanation: After 6 moves, the array could be [3, 4, 1, 2, 5, 7]. It can be shown that it is impossible for the array to have all unique values with 5 or less moves.
Constraints:
1 <= nums.length <= 105
0 <= nums[i] <= 105
Solutions
Solution 1: Sorting + Greedy
First, we sort the array $\textit{nums}$, and use a variable $\textit{y}$ to record the current maximum value, initially $\textit{y} = -1$.
Then, we iterate through the array $\textit{nums}$. For each element $x$, we update $y$ to $\max(y + 1, x)$, and accumulate the operation count $y - x$ into the result.
After completing the iteration, we return the result.
The time complexity is $O(n \log n)$, and the space complexity is $O(\log n)$. Here, $n$ is the length of the array $\textit{nums}$.
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Solution 2: Counting + Greedy
According to the problem description, the maximum value of the result array $m = \max(\textit{nums}) + \textit{len}(\textit{nums})$. We can use a counting array $\textit{cnt}$ to record the occurrence count of each element.
Then, we iterate from $0$ to $m - 1$. For each element $i$, if its occurrence count $\textit{cnt}[i]$ is greater than $1$, then we add $\textit{cnt}[i] - 1$ elements to $i + 1$, and accumulate the operation count into the result.
After completing the iteration, we return the result.
The time complexity is $O(m)$, and the space complexity is $O(m)$. Here, $m$ is the length of the array $\textit{nums}$ plus the maximum value in the array.
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