How should I practice Open Lockers After Toggle Passes?

Start by reading the full statement, solve the visible examples, then compare the pattern against related Tekion phone screen problems in FastPrep.

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Problem · Math

Open Lockers After Toggle Passes

Learn this problem

● Easy

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Problem statement

There are n lockers in a hallway, numbered 1 through n. Every locker starts closed.

You make exactly n passes. On pass i (1 <= i <= n), toggle every locker whose number is a multiple of i: a closed locker opens and an open locker closes.

Return how many lockers are open after the final pass.

What the interview report shared

The report asked how many of 100 initially closed lockers remain open after 100 toggle passes, and called the exercise a bulb-switcher variation.

Function

openLockers(n: int) → int

Examples

Example 1

n = 100return = 10

After 100 passes, a locker stays open only when it is toggled an odd number of times. That happens exactly for the perfect squares 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, so 10 lockers are open.

Example 2

n = 3return = 1

Pass 1 opens lockers 1, 2, 3. Pass 2 closes locker 2. Pass 3 closes locker 3. Only locker 1 remains open.

Constraints

1 <= n <= 10^6.