PPractick

The problem

A rocket-launch countdown screen shows N, N−1, ..., 1, and the exercise is to produce it recursively. This is the mirror image of the previous problem: with only n as a parameter, printing before the recursive call gives a countdown naturally, while carrying an index that counts up and printing after the recursive call produces the same countdown through backtracking. Solving both directions with both techniques makes the "work before vs after the call" idea stick, and that idea underpins preorder vs postorder traversal later.

Example: N = 5 → 5 4 3 2 1.

Function signature

void printDown(int n);                   // print n, then recurse on n - 1
void printDownByBacktracking(int i, int n); // recurse on i + 1 first, then print i (call with i = 1)

Test cases

Input n	Output	Explanation
5	5 4 3 2 1	Both versions
1	1
0	(nothing)
3	3 2 1

(Confirm: n ≥ 0; numbers separated by spaces; no loops.)

How interviewers phrase it

• "Print numbers from N down to 1 using recursion."
• "Now do it with backtracking" (using an index that counts up but printing on the way back).

Clarifying questions to ask

1. Is an extra parameter allowed?
2. Range of N?
3. Separator?

Follow-ups to expect

1. "How does the backtracking version print in reverse when i counts up?"
2. "Which of your functions is tail recursive?"
3. "How does this relate to tree traversals?"
4. "Complexity?"

Related questions

• Understand recursion by print something N times Easy
• Print name N times using recursion Easy
• Print 1 to N using Recursion Easy
• Sum of First N Numbers Easy
• Factorial of a given number Easy
• Reverse an array Easy

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