How do you solve Minimum Increment to Make Array Unique on LeetCode?

Minimum Increment to Make Array Unique (LeetCode #945) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log n) time complexity and O(1) space complexity. Key insight: Sorting the array helps in grouping duplicates together, making it easier to handle them.

What is the time complexity of Minimum Increment to Make Array Unique?

The optimal solution for Minimum Increment to Make Array Unique runs in O(n log n) time and uses O(1) space. The time complexity is O(n log n) due to the sorting step. The space complexity is O(1) because we are using a constant amount of extra space.

What is the brute force solution for Minimum Increment to Make Array Unique?

The brute force approach for Minimum Increment to Make Array Unique is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves checking every possible increment for duplicates until all elements are unique. This method is straightforward but inefficient as it may require multiple passes through the array. The optimal Optimal Solution approach improves this to O(n log n).

What algorithm or data structure is used to solve Minimum Increment to Make Array Unique?

Minimum Increment to Make Array Unique uses the following concepts: Array, Greedy, Sorting, Counting. The recommended patterns to study are: Greedy, Sorting, Array.

What are the interview tips for Minimum Increment to Make Array Unique?

Always consider edge cases, such as all numbers being the same or already unique. Explain your thought process clearly while coding; it helps the interviewer understand your approach. Practice similar problems to recognize patterns and improve your problem-solving speed.

What are common mistakes when solving Minimum Increment to Make Array Unique?

Failing to sort the array before processing, which leads to incorrect results. Not keeping track of the last unique number correctly, causing unnecessary increments.

#945

Minimum Increment to Make Array Unique

Medium

ArrayGreedySortingCountingGreedySortingArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n log n)
Space	O(1)	O(1)

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Intuition

Time O(n log n)Space O(1)

The optimal solution leverages sorting and a greedy approach to ensure each number is unique by only incrementing when necessary. This approach minimizes the number of increments by always ensuring the next number is greater than the last unique number.

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Algorithm

3 steps

1Step 1: Sort the array to group duplicates together.
2Step 2: Initialize a variable to track the last unique number.
3Step 3: Iterate through the sorted array and for each number, if it is less than or equal to the last unique number, increment it to be one more than the last unique number and update the moves count.

solution.py12 lines

1# Full working Python code
2
3def minIncrementForUnique(nums):
4    nums.sort()
5    moves = 0
6    last_unique = -1
7    for num in nums:
8        if num <= last_unique:
9            moves += (last_unique + 1 - num)
10            num = last_unique + 1
11        last_unique = num
12    return moves

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Complexity note: The time complexity is O(n log n) due to the sorting step. The space complexity is O(1) because we are using a constant amount of extra space.

1Sorting the array helps in grouping duplicates together, making it easier to handle them.
2Using a greedy approach ensures that we only increment numbers when necessary, minimizing the total moves.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.