How do you write a function to find the k-th missing positive integer?

How do you write a function to find the k-th missing positive integer?

How do you write a function to find the k-th missing positive integer?

Approach

When faced with the interview question, "How do you write a function to find the k-th missing positive integer?", it’s essential to adopt a structured approach for crafting a compelling response. Here’s a framework to guide your answer:

  1. Understand the Problem: Clarify the requirements and constraints of the question.

  2. Outline the Solution: Discuss the logic behind the solution, including the algorithm you would use.

  3. Implement the Code: Provide a clear and concise code snippet.

  4. Test the Function: Explain how you would verify that your function works correctly.

  5. Optimize: Discuss potential optimizations for performance.

Key Points

  • Clarity: Ensure you understand what the k-th missing positive integer means within the context of the provided input.

  • Algorithm Choice: Choose an appropriate algorithm (e.g., binary search, iteration) based on the input size and constraints.

  • Code Quality: Write clean, readable code with comments to enhance understanding.

  • Edge Cases: Consider edge cases such as when the array is empty or when k is larger than the number of missing integers.

Standard Response

To tackle the problem of finding the k-th missing positive integer, here is a systematic approach:

Step 1: Understand the Problem

Given an array of positive integers sorted in increasing order, our goal is to determine which positive integer is missing at the k-th position.

  • Input: arr = [2, 3, 4, 7, 11], k = 5

  • Output: 9 (The missing positive integers are 1, 5, 6, 8, and 9)

  • Example:

Step 2: Outline the Solution

  • Identify Missing Integers:

  • Start from 1 and check each integer sequentially to see if it is in the array.

  • Count the missing integers until we reach k.

  • Efficient Search:

  • Use a pointer to traverse through the array instead of checking each integer against the entire array, which improves efficiency.

Step 3: Implement the Code

Here’s a Python function that implements the above logic:

def findKthPositive(arr, k):
 missing_count = 0
 current = 1
 index = 0

 while missing_count < k:
 if index < len(arr) and arr[index] == current:
 index += 1
 else:
 missing_count += 1
 if missing_count == k:
 return current
 current += 1

 return current # This line may never be reached but is good for completeness

Step 4: Test the Function

To ensure our function works as expected, we can run a few test cases:

print(findKthPositive([2, 3, 4, 7, 11], 5)) # Output: 9
print(findKthPositive([1, 2, 3, 4], 2)) # Output: 6
print(findKthPositive([], 1)) # Output: 1

Step 5: Optimize

For larger inputs, we can optimize our function further by using binary search if the array is large and k is significantly smaller than the length of the array. This will reduce the time complexity.

Tips & Variations

Common Mistakes to Avoid

  • Ignoring Edge Cases: Always consider scenarios such as empty arrays or large k values.

  • Inefficient Solutions: Avoid nested loops that lead to O(n^2) complexity for large inputs.

Alternative Ways to Answer

  • Use Binary Search: If the array is large, discuss the possibility of using binary search to find the position of the first missing positive integer efficiently.

  • Mathematical Approach: Consider a mathematical formula to derive the k-th missing integer based on the properties of series.

Role-Specific Variations

  • Technical Positions: Focus on the efficiency of the algorithm (time and space complexity).

  • Managerial Roles: Emphasize the ability to guide team members through problem-solving processes and understanding algorithm design.

  • Creative Roles: Discuss how you can visualize the problem or explain it using real-world analogies.

Follow-Up Questions

  • How would you handle a large array of integers?

  • Can you explain the time complexity of your solution?

  • What would you do if the input array contained duplicates?

  • How would you adapt your function to return all missing integers up to the k-th one?

By following this structured approach, you can confidently articulate your thought process and coding ability during the interview, showcasing your problem-solving skills effectively

Question Details

Difficulty
Medium
Medium
Type
Coding
Coding
Companies
Meta
Netflix
Meta
Netflix
Tags
Programming
Problem-Solving
Algorithmic Thinking
Programming
Problem-Solving
Algorithmic Thinking
Roles
Software Engineer
Data Scientist
Computer Programmer
Software Engineer
Data Scientist
Computer Programmer

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