Allow to Contest - Python Solution and Time Complexity Analysis

At a contest, children can participate only if they have ages between minAge and maxAge. Given the age of a child, check if they are allowed or not.

Example 1:

Input: minAge = 7, maxAge = 12, age =  7
Output: true

Example 2:

Input: minAge = 3, maxAge = 8, age = 10
Output: false

Understanding the Problem

The core challenge of this problem is to determine if a given age falls within a specified range. This is a common problem in scenarios where eligibility criteria are based on age, such as contests, sports events, or age-restricted activities.

Potential pitfalls include misunderstanding the inclusive nature of the age range or incorrectly implementing the boundary checks.

Approach

To solve this problem, we need to check if the given age is within the inclusive range defined by minAge and maxAge. There are several ways to approach this:

Naive Solution

A naive solution would involve checking if the age is less than minAge or greater than maxAge and returning False in those cases. Otherwise, return True.

Optimized Solutions

We can optimize the solution by using a single if statement with two conditions or directly returning the boolean expression.

Algorithm

Here is a step-by-step breakdown of the algorithm:

1. Check if the age is less than minAge or greater than maxAge.
2. If either condition is true, return False.
3. Otherwise, return True.

Code Implementation

Below are the implementations of the different approaches in Python:

Naive Solution

def is_allowed_to_contest(minAge, maxAge, age):
    # Check if age is less than minAge or greater than maxAge
    if age < minAge or age > maxAge:
        return False
    return True

Optimized Solution 1

def is_allowed_to_contest(minAge, maxAge, age):
    # Using a single if statement with two conditions
    return age >= minAge and age <= maxAge

Optimized Solution 2

def is_allowed_to_contest(minAge, maxAge, age):
    # Directly returning the boolean expression
    return minAge <= age <= maxAge

Complexity Analysis

All the solutions have a time complexity of O(1) because they involve a constant number of operations regardless of the input size. The space complexity is also O(1) as no additional space is required.

Edge Cases

Potential edge cases include:

• Age exactly equal to minAge or maxAge.
• Age just below minAge or just above maxAge.
• Negative ages or extremely high ages (though these may be outside the problem's realistic constraints).

Examples:

minAge = 5, maxAge = 10, age = 5  # Expected output: True
minAge = 5, maxAge = 10, age = 10 # Expected output: True
minAge = 5, maxAge = 10, age = 4  # Expected output: False
minAge = 5, maxAge = 10, age = 11 # Expected output: False

Testing

To test the solution comprehensively, consider a variety of test cases:

• Normal cases within the range.
• Boundary cases at the edges of the range.
• Cases outside the range.

Using a testing framework like unittest in Python can help automate and organize these tests.

Thinking and Problem-Solving Tips

When approaching such problems:

• Clearly understand the problem statement and constraints.
• Break down the problem into smaller, manageable parts.
• Consider edge cases and how your solution handles them.
• Practice similar problems to improve your problem-solving skills.

Conclusion

In this blog post, we discussed how to determine if a child's age falls within a specified range. We explored different approaches, analyzed their complexities, and provided Python implementations. Understanding and solving such problems is crucial for developing strong problem-solving skills.

Additional Resources

For further reading and practice:

• LeetCode - Practice coding problems.
• unittest Documentation - Learn about Python's built-in testing framework.
• GeeksforGeeks Python - Tutorials and problems on Python programming.