Return Negative in Python with O(1) Time Complexity

Create a function that takes a number as an argument and returns negative of that number. Return negative numbers without any change.

Examples:

negative(4) ➞ -4

negative(15) ➞ -15

negative(-4) ➞ -4

negative(0) ➞ 0

Understanding the Problem

The core challenge of this problem is to ensure that any given number is returned as its negative counterpart. If the number is already negative, it should be returned as is. This problem is straightforward but can be tricky if not approached correctly. It is commonly used in scenarios where normalization of data is required, such as in mathematical computations or data preprocessing.

Approach

To solve this problem, we need to check the sign of the number:

• If the number is positive, we return its negative.
• If the number is already negative or zero, we return it as is.

Let's start with a naive solution and then optimize it.

Naive Solution

A naive approach would involve using an if-else statement to check the sign of the number:

def negative(n):
    if n > 0:
        return -n
    else:
        return n

While this solution works, it can be simplified further.

Optimized Solution

We can use the min function to achieve the same result in a more concise manner:

def negative(n):
    return -abs(n)

This approach leverages the abs function to get the absolute value of the number and then negates it, ensuring the result is always negative.

Algorithm

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

1. Take the absolute value of the input number using abs(n).
2. Negate the result to ensure it is negative.
3. Return the negated value.

Code Implementation

Below is the Python code for the optimized solution:

def negative(n):
    # Get the absolute value of n and negate it
    return -abs(n)

# Test cases
print(negative(4))   # ➞ -4
print(negative(15))  # ➞ -15
print(negative(-4))  # ➞ -4
print(negative(0))   # ➞ 0

Complexity Analysis

The time complexity of the optimized solution is O(1) because it involves 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:

• Zero: negative(0) ➞ 0
• Negative numbers: negative(-5) ➞ -5
• Large positive and negative numbers

These edge cases are handled effectively by the algorithm.

Testing

To test the solution comprehensively, consider the following test cases:

• Positive numbers: negative(10) ➞ -10
• Negative numbers: negative(-10) ➞ -10
• Zero: negative(0) ➞ 0
• Large numbers: negative(1000000) ➞ -1000000

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

Thinking and Problem-Solving Tips

When approaching such problems, consider the following tips:

• Understand the problem requirements and constraints thoroughly.
• Start with a simple solution and then look for optimizations.
• Test your solution with a variety of inputs, including edge cases.
• Practice similar problems to improve your problem-solving skills.

Conclusion

In this blog post, we discussed how to solve the problem of returning the negative of a given number. We explored a naive solution and an optimized solution, analyzed their complexities, and discussed edge cases and testing strategies. Understanding and solving such problems is crucial for developing strong problem-solving skills in programming.

Additional Resources

For further reading and practice, consider the following resources:

• Python abs() function documentation
• LeetCode - Practice coding problems
• HackerRank - Coding challenges and tutorials