Problem: Bulb Switcher

med

30 min

Explore the Bulb Switcher problem which involves toggling bulbs through multiple rounds. Learn to analyze and implement an efficient solution using mathematical insight to determine how many bulbs stay on at the end. This lesson enhances your ability to solve pattern-based problems in code.

Statement

You are given n bulbs, all initially turned off. You perform n rounds of toggling operations:

In round $1$ , you turn on every bulb.
In round $2$ , you toggle every $2^{nd}$ bulb.
In round $3$ , you toggle every $3^{rd}$ bulb.
In general, during round i, you toggle every i-th bulb (turning it on if it is off, or turning it off if it is on).
In round n, you toggle only the last bulb.

Return the number of bulbs that remain on after all n rounds have been completed.

Constraints:

$0 \leq$ n $\leq 10^9$

Problem: Bulb Switcher

med

30 min

Statement

You are given n bulbs, all initially turned off. You perform n rounds of toggling operations:

In round $1$ , you turn on every bulb.
In round $2$ , you toggle every $2^{nd}$ bulb.
In round $3$ , you toggle every $3^{rd}$ bulb.
In general, during round i, you toggle every i-th bulb (turning it on if it is off, or turning it off if it is on).
In round n, you toggle only the last bulb.

Return the number of bulbs that remain on after all n rounds have been completed.

Constraints:

$0 \leq$ n $\leq 10^9$

Problem: Bulb Switcher

Statement

Examples

Understand the problem

Figure it out!

Try it yourself

Problem: Bulb Switcher

Statement

Examples

Understand the problem

Figure it out!

Try it yourself