How does the multiply function work in the first example?

The multiply function adds the first number to itself 'b' times using a loop, initializing the result to 0 and printing the final result.

9 - Recursion | Python & AI Learning Hub

Explanation

This function multiplies two numbers by adding the first number to itself as many times as the second number indicates
It uses a loop with range() to repeat the addition process exactly 'b' times
The key operations are initializing result to 0, then repeatedly adding 'a' to it inside the loop
The function prints the final multiplication result instead of returning it
When called with multiply(3,4), it calculates 3+3+3+3 and prints 12

Output

Explanation

This code implements multiplication using recursion by adding a number to itself b times
The mul function takes two parameters a and b, and recursively calculates their product
When b equals 1, it returns a as the base case to stop the recursion
For other values, it adds a to the result of multiplying a by (b-1), effectively building up the total
The print statement calls mul(5,6) which outputs 30, showing 5 multiplied by 6 using recursive addition

Output

Explanation

This code defines a recursive function called fact that calculates the factorial of a given number
The function works by checking if the number equals 1, and if so, returns 1 as the base case
For any other number, it multiplies the number by the result of calling itself with one less than the current number
The print(fact(5)) statement calls the function with the argument 5 and displays the result
The expected output is 120, which is 5! (5 factorial = 5 × 4 × 3 × 2 × 1)

Output

Explanation

This code defines a recursive function that checks if a string is a palindrome by comparing the first and last characters
The function uses string slicing (text[1:-1]) to remove the first and last characters and recursively check the remaining substring
When the string length is 1 or less, it prints 'Palindrome', otherwise it continues checking character by character
For 'madam' and 'malayalam', it will print 'Palindrome' since they read the same forwards and backwards
For 'python' and 'abba', it will print 'Not a Palindrome' for 'python' and likely 'Palindrome' for 'abba' (though the logic has a flaw in handling even-length strings correctly)

Output

Explanation

This code defines a recursive function called fib that calculates Fibonacci numbers where each number is the sum of the two preceding ones
The function has a base case for months 0 and 1, returning 1, and uses recursion to calculate higher values by adding the results of calling itself with smaller inputs
The print(fib(5)) statement calls the function with input 5 and displays the result, which is 8
Key APIs/functions used include basic conditional statements (if/else), function definition (def), and recursive function calls
The side effect is printing the calculated Fibonacci number to the console, with no other visible output or state changes

Output

Explanation

This code implements a memoized recursive Fibonacci-like function that calculates values based on the sum of previous two values
The memo function uses a dictionary d to store previously calculated results to avoid redundant computations
Key APIs used include dictionary lookup (if m in d) and recursive function calls (memo(m-1,d) + memo(m-2,d))
The function initializes a dictionary with base cases {0:1, 1:1} and computes the 48th value in the sequence
Side effect is that the dictionary d gets populated with all intermediate calculated values from 0 to 48

Output