CODEWITHSUNDEEP
performance
Aleph_0
Aleph_0

Reputation: 55

Is it possible to solve this, with a solution which has time complexity better than linear?

Is it possible to solve this problem with a solution which has time complexity better than linear?

N light bulbs are connected by a wire. Each bulb has a switch associated with it, however due to faulty wiring, a switch also changes the state of all the bulbs to the right of current bulb. Given an initial state of all bulbs, find the minimum number of switches you have to press to turn on all the bulbs. You can press the same switch multiple times.

Note : 0 represents the bulb is off and 1 represents the bulb is on.

Input : [0 1 0 1]

Steps:

press switch 0 : [1 0 1 0]
press switch 1 : [1 1 0 1]
press switch 2 : [1 1 1 0]
press switch 3 : [1 1 1 1]

Return : 4

Upvotes: 1

Views: 68

Answers (1)

Christopher
Christopher

Reputation: 9824

This is called a "Lights Out" riddle: http://mathworld.wolfram.com/LightsOutPuzzle.html

One speed improvement I could think off would be to paralellise the setting of all the bulbs to the right. In particular a GPU might be able to do that effectively (I am not sure as you need to change wich elements are effected with each loop).

Maybe making it a proper boolean Array and bitwise XOR-ing a pattern onto the array?

Unless the real process is a lot more complex then XOR-ing boolean values, memory speed will be the bottleneck here - not CPU time. Unless this is for purely academic purposes, the performance rant propably applies: http://ericlippert.com/2012/12/17/performance-rant/

Upvotes: 1

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