#3396

Easy

auto_awesomeArray scanning plus hash lookup

LeetCode Problem Workspace

Minimum Number of Operations to Make Elements in Array Distinct

Find the minimum number of operations to make all elements of an array distinct.

Problem Statement

You are given an integer array nums. Your task is to ensure that all elements in the array are distinct. You can perform the following operation any number of times: select a duplicate element and change it to a value that is not already in the array. An empty array is considered to have distinct elements. Return the minimum number of operations required to make the elements in the array distinct.

Example 1: For nums = [1,2,3,4,2,3,3,5,7], two changes are needed to remove duplicates, so the output is 2. In contrast, for nums = [6,7,8,9], no changes are necessary as the array already contains distinct elements, thus the answer is 0.

Examples

Example 1

Input: nums = [1,2,3,4,2,3,3,5,7]

Output: 2

Therefore, the answer is 2.

Example 2

Input: nums = [4,5,6,4,4]

Output: 2

Therefore, the answer is 2.

Example 3

Input: nums = [6,7,8,9]

Output: 0

The array already contains distinct elements. Therefore, the answer is 0.

Constraints

1 <= nums.length <= 100
1 <= nums[i] <= 100

Solution Approach

Iterate and Count Frequencies

Start by iterating through the array while maintaining a hash table to store the frequency of each element. This allows you to quickly identify duplicates during the scan.

Resolve Duplicates Efficiently

For each duplicate element, change it to a number that is not already in the array. This ensures that you are minimizing the number of operations by always addressing duplicates immediately.

Optimize with Constraints in Mind

Since the array size is relatively small (up to 100 elements), a brute force solution using hash lookups works efficiently. You can resolve duplicates in linear time, which is optimal for this problem.

Complexity Analysis

Metric	Value
Time	O(n)
Space	O(n)

The time complexity is O(n) because you only iterate through the array once, while the space complexity is O(n) due to the hash table used to track frequencies.

What Interviewers Usually Probe

Can the candidate recognize that the problem is best solved with an array scan and hash table approach?
Does the candidate consider efficient ways to handle duplicates using the constraints?
Is the candidate aware of the potential to optimize this solution even further?

Common Pitfalls or Variants

Common pitfalls

Not utilizing a hash table to track element frequencies and relying on brute force solutions which are less efficient.
Changing an element to a duplicate number, causing more operations than necessary.
Ignoring the constraints and trying complex solutions when a simple approach suffices due to the small array size.

Follow-up variants

Handling arrays with larger sizes while maintaining efficient operations.
Considering edge cases like empty arrays or arrays with only one element.
Exploring other methods of tracking duplicates besides hash tables, like sorting or using counters.

FAQ

What is the optimal approach for solving the Minimum Number of Operations to Make Elements in Array Distinct problem?

The optimal solution uses array scanning combined with hash lookups to identify duplicates and perform the minimum number of operations to make the array distinct.

How do hash tables help in solving the problem?

Hash tables help efficiently track the frequency of each element in the array, making it easy to identify duplicates and replace them with minimal effort.

Can I use sorting instead of a hash table for this problem?

Sorting the array could work, but it would have a higher time complexity of O(n log n). Using a hash table is more efficient with a time complexity of O(n).

What if the array contains a very large number of duplicate elements?

Even in cases with many duplicates, the solution still works efficiently due to the hash table allowing for quick lookups and ensuring each operation is minimal.

What should I focus on when solving the Minimum Number of Operations to Make Elements in Array Distinct problem?

Focus on recognizing the pattern of array scanning and hash lookups to efficiently handle duplicates while considering the problem's constraints.

terminal

Solution

Solution 1: Hash Table + Reverse Traversal

We can traverse the array $\textit{nums}$ in reverse order and use a hash table $\textit{s}$ to record the elements that have already been traversed. When we encounter an element $\textit{nums}[i]$, if $\textit{nums}[i]$ is already in the hash table $\textit{s}$, it means we need to remove all elements from $\textit{nums}[0..i]$. The number of operations required is $\left\lfloor \frac{i}{3} \right\rfloor + 1$. Otherwise, we add $\textit{nums}[i]$ to the hash table $\textit{s}$ and continue to the next element.

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class Solution:
    def minimumOperations(self, nums: List[int]) -> int:
        s = set()
        for i in range(len(nums) - 1, -1, -1):
            if nums[i] in s:
                return i // 3 + 1
            s.add(nums[i])
        return 0

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