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Recursion for Coding Interviews in Python

Solution Review: Compute the Square of a Number

Explore how to compute the square of a number using iterative and recursive approaches in Python. Understand the mathematical breakdown, base cases, and recursive steps to implement recursion effectively for this problem.

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Solution #1: Iterative Method:

Python 3.5
def findSquare(testVariable) :
  return testVariable * testVariable
# Driver Code
testVariable = 5
print(findSquare(testVariable))

Explanation

The iterative solution to this problem is simple. We multiply the input variable with itself and return the result.

Solution #2: Recursive Method:

Python 3.5
def findSquare(targetNumber) :
  # Base case
  if targetNumber == 0 :
    return 0
  # Recursive case
  else :
    return findSquare(targetNumber - 1) + (2 * targetNumber) - 1
# Driver Code
targetNumber = 5
print(findSquare(targetNumber))

Explanation

Let’s break the problem down mathematically. We will compute the square of a number through direct recursion:

To implement the square operation as a recursive function, we first need to express the square operation in terms of itself:

Mathematically we know the following:

(n−1)2=n2−2n+1(n-1)^2 = n^2 - 2n + 1 ...