DSA interview question

While Loops: Collatz Steps and Digit Count

Easy · Algorithms · Topics: language basics

The problem

A maths club is exploring the Collatz sequence. Start from any positive integer n. If it's even, halve it; if it's odd, replace it with 3n + 1. Repeat until you reach 1. Nobody has proved that every starting number reaches 1, and nobody can predict in advance how many steps it will take, which makes this the perfect use of a while loop, where you loop until a condition changes rather than a fixed number of times. The club also wants a helper that counts the digits of a number, where the number 0 must count as having one digit. That's a natural fit for a do-while loop, which always runs its body at least once.

Example: 6 → 3 → 10 → 5 → 16 → 8 → 4 → 2 → 1 takes 8 steps.

Function signature

long long collatzSteps(long long n);  // steps to reach 1; -1 if n < 1
int countDigits(long long n);         // number of decimal digits; countDigits(0) == 1

Test cases

Input	Output	Explanation
`collatzSteps(1)`	`0`	Already at 1; the loop body never runs
`collatzSteps(2)`	`1`	2 → 1
`collatzSteps(6)`	`8`	6 → 3 → 10 → 5 → 16 → 8 → 4 → 2 → 1
`collatzSteps(7)`	`16`	Climbs as high as 52 before falling
`collatzSteps(27)`	`111`	Peaks at 9232, famous for how long it takes
`collatzSteps(0)`	`-1`	Invalid; 0 would loop forever
`countDigits(0)`	`1`	do-while runs once even when n is 0
`countDigits(12345)`	`5`
`countDigits(-4096)`	`4`	The sign is not a digit

(Confirm: n fits in a long long; intermediate Collatz values (3n + 1) can exceed the int range for large starting values.)

How interviewers phrase it

"Count the number of digits in a number." / "Reverse a number." / "Keep dividing N by 2 until it becomes 1. How many steps?"
"Given N, how many steps to reach 1 if you halve even numbers and do 3N + 1 for odd numbers?"
Theory: "When would you use a while loop instead of a for loop? What's special about do-while?"

Clarifying questions to ask

What should happen for 0 or negative input? (Collatz on 0 never reaches 1.)
How large can N be? (3N + 1 can overflow an int.)
For digit counting, does the minus sign count, and how many digits does 0 have?
Should I return the count, or also the sequence itself?

Follow-ups to expect

"When do you pick while over for?"
"What's the difference between while and do-while?"
"How do you make sure a while loop terminates?"
"Why long long for Collatz?"
"Can you count digits without a loop?"

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