Lowest Unique Positive Integer Game: Ace This Common Coding Interview Question

Table of Contents#

1. What Is the Lowest Unique Positive Integer Game?
   • Game Rules Explained
   • Example Scenarios
2. Why This Question Matters in Coding Interviews
3. Step-by-Step Approach to Solve the Problem
   • Handling Edge Cases
4. Implementing the Solution in Popular Languages
   • Python
   • JavaScript
   • Java
5. Optimizing Your Solution for Efficiency
6. Common Mistakes to Avoid
7. Practice Problems to Reinforce Skills
8. Conclusion
9. References

What Is the Lowest Unique Positive Integer Game?#

Game Rules Explained#

The Lowest Unique Positive Integer Game is a classic logic game, and in coding interviews, it’s adapted into a problem where you’re given a list of positive integers (representing players’ picks) and asked to return the smallest unique integer in the list. The core rules for the interview variant are:

1. Input: A non-empty (or sometimes empty) list of positive integers.
2. Objective: Identify the smallest integer that appears exactly once in the list.
3. Edge Case: If no unique integers exist, return -1 (or a specified sentinel value like null).

Example Scenarios#

Let’s walk through a few examples to solidify your understanding:

• Example 1: Input = [3, 1, 2, 1, 3]
  Frequencies: 1 appears 2 times, 2 appears 1 time, 3 appears 2 times.
  Output: 2 (smallest unique integer).
• Example 2: Input = [5, 5, 5]
  All integers are duplicates. Output: -1.
• Example3: Input = [4]
  Single unique integer. Output:4.
• Example4: Input = [2, 3, 1, 4, 1, 2]
  Unique integers:3,4. Smallest is3. Output:3.

Why This Question Matters in Coding Interviews#

Interviewers love this problem because it evaluates multiple critical skills in one question:

1. Core Technical Skills: Tests your ability to work with data structures (hash maps, arrays) and perform frequency counting.
2. Problem-Solving Approach: Reveals whether you can break a problem into logical steps (filtering, counting, filtering again, finding minima).
3. Attention to Detail: Forces you to handle edge cases like empty inputs, all-duplicate lists, and non-positive integers (even if the problem states inputs are positive).
4. Efficiency Awareness: Challenges you to optimize your solution for time and space complexity, which is key for large input sizes.

Step-by-Step Approach to Solve the Problem#

Follow these structured steps to solve the problem consistently:

Step1: Understand Input Constraints#

First, clarify the input boundaries with the interviewer:

• Are inputs guaranteed to be positive integers? (If not, filter out non-positive values first.)
• Can the input list be empty? (If yes, return -1 or a specified value.)
• What’s the maximum possible value of an integer in the list? (This affects optimization choices.)

Step2: Count Frequency of Each Integer#

Use a frequency map (dictionary, hash map, or array) to count how many times each integer appears in the input list. This is the most efficient way to track duplicates.

Step3: Filter Unique Integers#

From the frequency map, extract all integers that have a frequency of exactly 1. These are the candidates for the lowest unique integer.

Step4: Find the Minimum Unique Integer#

If there are any unique integers, return the smallest one. If there are none, return the sentinel value (e.g., -1).

Handling Edge Cases#

Don’t forget to account for these common edge scenarios:

• Empty input list: Return -1.
• All elements are duplicates: Return -1.
• Single element: Return the element itself.
• Non-positive integers in input: Filter them out first, as the problem focuses on positive integers.

Implementing the Solution in Popular Programming Languages#

Below are clean, commented implementations of the solution in three widely used languages:

Python Implementation#

from collections import Counter
 
def lowest_unique_positive_integer(numbers: list[int]) -> int:
    # Filter out non-positive integers (defensive programming)
    positive_numbers = [num for num in numbers if num > 0]
    
    # Handle empty filtered list
    if not positive_numbers:
        return -1
    
    # Count frequency of each positive integer
    freq_counter = Counter(positive_numbers)
    
    # Collect all unique integers (frequency == 1)
    unique_integers = [num for num, count in freq_counter.items() if count == 1]
    
    # Return minimum unique integer or -1 if none exist
    return min(unique_integers) if unique_integers else -1
 
# Test cases
print(lowest_unique_positive_integer([3,1,2,1,3]))  # Output: 2
print(lowest_unique_positive_integer([5,5,5]))      # Output: -1
print(lowest_unique_positive_integer([4]))          # Output:4

JavaScript Implementation#

function lowestUniquePositiveInteger(numbers) {
    // Filter non-positive integers
    const positiveNumbers = numbers.filter(num => num > 0);
    
    if (positiveNumbers.length === 0) return -1;
    
    // Count frequency using a Map
    const freqMap = new Map();
    for (const num of positiveNumbers) {
        freqMap.set(num, (freqMap.get(num) || 0) + 1);
    }
    
    // Collect unique integers
    const uniqueIntegers = [];
    for (const [num, count] of freqMap) {
        if (count === 1) uniqueIntegers.push(num);
    }
    
    // Return minimum unique integer or -1
    return uniqueIntegers.length > 0 ? Math.min(...uniqueIntegers) : -1;
}
 
// Test cases
console.log(lowestUniquePositiveInteger([3,1,2,1,3])); // Output:2
console.log(lowestUniquePositiveInteger([5,5,5]));     // Output:-1

Java Implementation#

import java.util.*;
 
public class LowestUniquePositiveInteger {
    public static int findLowestUnique(int[] numbers) {
        // Filter positive integers
        List<Integer> positiveNumbers = new ArrayList<>();
        for (int num : numbers) {
            if (num > 0) positiveNumbers.add(num);
        }
        
        if (positiveNumbers.isEmpty()) return -1;
        
        // Count frequency using HashMap
        Map<Integer, Integer> freqMap = new HashMap<>();
        for (int num : positiveNumbers) {
            freqMap.put(num, freqMap.getOrDefault(num, 0) + 1);
        }
        
        // Collect unique integers
        List<Integer> uniqueIntegers = new ArrayList<>();
        for (Map.Entry<Integer, Integer> entry : freqMap.entrySet()) {
            if (entry.getValue() == 1) uniqueIntegers.add(entry.getKey());
        }
        
        if (uniqueIntegers.isEmpty()) return -1;
        
        // Find minimum unique integer
        int minUnique = Integer.MAX_VALUE;
        for (int num : uniqueIntegers) {
            if (num < minUnique) minUnique = num;
        }
        
        return minUnique;
    }
 
    public static void main(String[] args) {
        int[] test1 = {3,1,2,1,3};
        System.out.println(findLowestUnique(test1)); // Output:2
        int[] test2 = {5,5,5};
        System.out.println(findLowestUnique(test2)); // Output:-1
    }
}

Optimizing Your Solution for Efficiency#

Time and Space Complexity Analysis#

• Time Complexity: O(n), where n is the number of elements in the input list. We iterate through the list three times (filtering, counting, collecting unique integers), each in linear time.
• Space Complexity: O(k), where k is the number of distinct positive integers. In the worst case (all elements are unique), k = n, so space complexity is O(n).

Optimization Tips#

1. Use Arrays for Frequency Counting: If the input has a known upper limit (e.g., integers between 1 and 100), replace the hash map with an array. Array access is faster than hash map lookups, reducing overhead.
2. Early Termination: If you’re processing live inputs, you can track frequencies and unique integers in a single pass, but this won’t change the overall time complexity.
3. Avoid Unnecessary Sorting: Sorting the list first (O(n log n) time) is a common but inefficient approach. Stick to frequency counting for linear time performance.

Common Mistakes to Avoid#

1. Ignoring Non-Positive Integers: Even if the problem states inputs are positive, interviewers may test you with zero or negative values. Always filter these out.
2. Forgetting Edge Cases: Failing to handle empty lists or all-duplicate inputs will result in incorrect solutions.
3. Using Inefficient Methods: Sorting the list to find unique elements is slower than frequency counting. Opt for the O(n) approach.
4. Misinterpreting the Problem: Some variants ask for the index of the player with the lowest unique integer, not the integer itself. Read the problem statement carefully.

Practice Problems to Reinforce Your Skills#

To solidify your understanding, try these related problems:

1. LeetCode 136. Single Number: Find the only element that appears exactly once in a list.
2. LeetCode 387. First Unique Character in a String: Similar frequency-counting logic applied to strings.
3. HackerRank: Lowest Unique Number: A direct variant of this game problem.
4. CodeSignal: Lowest Unique Integer: Practice the problem with varying input constraints.

Conclusion#

The Lowest Unique Positive Integer Game is more than just a logic puzzle—it’s a window into your ability to solve real-world problems efficiently. By breaking the problem into clear steps, handling edge cases, and optimizing your solution, you’ll show interviewers that you’re a thoughtful, skilled engineer. Remember to practice this problem and its variants to build confidence, and always prioritize clarity and efficiency in your code.

References#

1. GeeksforGeeks. (n.d.). Lowest Unique Number Problem. Retrieved from https://www.geeksforgeeks.org/lowest-unique-number-problem/
2. LeetCode. (n.d.). Single Number. Retrieved from https://leetcode.com/problems/single-number/
3. McDowell, Gayle Laakmann. Cracking the Coding Interview, 6th Edition. CareerCup, 2015.
4. HackerRank. (n.d.). Lowest Unique Number. Retrieved from https://www.hackerrank.com/challenges/lowest-unique-number/problem