Recursive Multi-Branch Function Q(m, n)

Program Overview

This Python program reads two integers m and n and computes the value of the recursive function Q(m, n) based on the following rules:

• If m = 1 or n = 1, then Q(m, n) = 1.
• If m = n, then Q(m, n) = 1 + Q(m, m - 1).
• If m > n, then Q(m, n) = Q(m - 1, n) + Q(m - 1, n - 1).
• Otherwise, Q(m, n) = Q(m, n - 1) + Q(m - 1, n).

Python Code:

def Q(m: int, n: int) -> int:
    if m == 1 or n == 1:
        return 1
    elif m == n:
        return 1 + Q(m, m - 1)
    elif m > n:
        return Q(m - 1, n) + Q(m - 1, n - 1)
    else:
        return Q(m, n - 1) + Q(m - 1, n)

# Read inputs from user
m = int(input("Enter value for m: "))
n = int(input("Enter value for n: "))

result = Q(m, n)
print(f"Q({m}, {n}) = {result}")

Sample Output (input: m = 3, n = 2):

Q(3, 2) = 5