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