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seven

Prove by induction: Claim: can make n outcomes into n columns where each column has at most two outcomes

ohmygearbox

Basically for n outcomes, pick one which has less than average height and put it into a bucket with the top portion of an outcome that has greater than average height, creating a column in your solution set. This way you have n - 1 remaining columns

jesshuifeng

I still don't understand why O(1)?

atomicapple0

i think you use induction

PsychotiK

With at most two outcomes per column, once we randomly sample from the N columns which is O(1), we can then randomly sample again and check to see if it is less than or greater than the threshold between the colors if there are 2. This is also an O(1) operation.

AL_

can someone explain the induction proof again?

Evanolott

^ about the induction proof.

doberdog91

PsychotiK's explanation makes sense

jin

What is the complexity of the pre-processing? Is it like O(nlog(n))?

haotingl

induction?

notme

It is possible in general as you can use induction. The newest block you can change the width of in order to conform the height to the height of the rectangle you get from the IH.