Answer
Program 1: Output is
15
program 2: Output: is
7
6
5
4
3
2
1
Work Step by Step
Program 1:
Base case: n == 1
Recursive calls: f(n - 1)
Explanation: The function f recursively adds the previous numbers to the current number until the base case of n == 1 is reached. In this case, the function is called with f(5), which leads to the following recursive calls:
f(5) = 5 + f(4)
f(4) = 4 + f(3)
f(3) = 3 + f(2)
f(2) = 2 + f(1)
f(1) = 1
The final result is the sum of all these numbers, which is 15.
Program 2 :
Base case: n <= 0
Recursive calls: f(n // 10)
Explanation: The function f recursively prints the last digit of a number and then calls itself with the remaining digits until there are no more digits left. In this case, the function is called with f(1234567), which leads to the following recursive calls:
f(1234567) prints 7 and calls f(123456)
f(123456) prints 6 and calls f(12345)
f(12345) prints 5 and calls f(1234)
f(1234) prints 4 and calls f(123)
f(123) prints 3 and calls f(12)
f(12) prints 2 and calls f(1)
f(1) prints 1 and then returns.
The digits are printed in reverse order, which is the expected behavior when working with integers.
