BL
U

15. Recursive Sum and Factorial

Easy

Problem Description

Given a non-negative integer NN, compute two recursive mathematical quantities:

  1. 1.The recursive sum S(N)=1+2+⋯+NS(N) = 1 + 2 + \dots + N (with S(0)=0S(0) = 0).
  2. 2.The factorial F(N)=N!=N×(N−1)×⋯×1F(N) = N! = N \times (N-1) \times \dots \times 1 (with F(0)=1F(0) = 1).

Input Format

A single line containing an integer NN (0≤N≤200 \le N \le 20).

Output Format

Print two space-separated integers: S(N)S(N) followed by F(N)F(N).

Example 1:
Input:
5
Output:
15 120
Explanation: Sum = 1 + 2 + 3 + 4 + 5 = 15. Factorial = 5! = 120.
Example 2:
Input:
0
Output:
0 1
Explanation: Base cases: sum of 0 numbers is 0, and 0! = 1.
Example 3:
Input:
3
Output:
6 6
Explanation: Sum = 1 + 2 + 3 = 6. Factorial = 3! = 6.
Constraints:
  • 0 <= N <= 20
  • Time complexity target: O(N)
  • Auxiliary space target: O(N) call stack
Follow up:How can tail-call optimization transform these recursive functions to execute in O(1) stack space?
1,180 Online