Minimum Value of Three in Python

Given 3 integers A, B and C, return the smallest number.

You are not allowed to use built-in functions such as min

Example 1:

Input: A = 7, B = 4, C = 9
Output: 4

Example 2:

Input: A = 3, B = 8, C = 3
Output: 3

Problem Definition

The problem requires us to find the smallest of three given integers A, B, and C without using built-in functions like min. The input consists of three integers, and the output should be the smallest of these integers.

Input:

Three integers A, B, and C.

Output:

The smallest integer among A, B, and C.

Constraints:

All inputs are integers.

Example:

Input: A = 7, B = 4, C = 9
Output: 4

Understanding the Problem

The core challenge is to determine the smallest of three numbers without using built-in functions. This problem is fundamental in understanding basic conditional statements and comparisons. It has applications in various fields such as sorting algorithms, decision-making processes, and more.

Potential Pitfalls:

Incorrectly comparing the numbers.
Not considering all possible cases.

Approach

To solve this problem, we can use conditional statements to compare the three numbers. We will start by comparing A with B and C, then B with A and C, and finally, if neither A nor B is the smallest, C will be the smallest by default.

Naive Solution:

The naive solution involves directly comparing the numbers using if-else statements. This approach is straightforward but not scalable for a larger number of values.

Optimized Solution:

An optimized approach involves using a variable to keep track of the minimum value found so far. This method is more scalable and can be easily extended to more than three numbers.

Algorithm

Step-by-Step Breakdown:

Initialize a variable minVal with the value of A.
Compare B with minVal. If B is smaller, update minVal to B.
Compare C with minVal. If C is smaller, update minVal to C.
Return minVal as the smallest number.

Code Implementation

def find_minimum(A, B, C):
    # Initialize minVal with A
    minVal = A
    
    # Compare B with minVal
    if B < minVal:
        minVal = B
    
    # Compare C with minVal
    if C < minVal:
        minVal = C
    
    # Return the smallest value
    return minVal

# Test cases
print(find_minimum(7, 4, 9))  # Output: 4
print(find_minimum(3, 8, 3))  # Output: 3

Complexity Analysis

The time complexity of this approach is O(1) because we are performing a constant number of comparisons regardless of the input size. The space complexity is also O(1) as we are using a fixed amount of extra space.

Edge Cases

Consider the following edge cases:

All three numbers are the same: A = 5, B = 5, C = 5. The output should be 5.
Two numbers are the same and the smallest: A = 2, B = 2, C = 3. The output should be 2.
Negative numbers: A = -1, B = -2, C = -3. The output should be -3.

Testing

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

Simple cases with distinct numbers.
Cases where two or all three numbers are the same.
Cases with negative numbers.

Thinking and Problem-Solving Tips

When approaching such problems, consider the following tips:

Break down the problem into smaller parts.
Use conditional statements effectively.
Think about edge cases and how to handle them.

Conclusion

In this blog post, we discussed how to find the minimum of three numbers without using built-in functions. We explored a naive solution and an optimized approach, provided a detailed algorithm, and analyzed the complexity. Understanding such fundamental problems is crucial for developing problem-solving skills and preparing for more complex challenges.

Additional Resources

For further reading and practice, consider the following resources: