## Sunday, November 3, 2013

### Quickselect FTW!

More than a year ago, I answered a question on Stack Overflow about the Quickselect algorithm, which takes some unsorted data and finds the k-th smallest value (that is, the value that would be in position k if you were to sort the data). The person asking the question had seen multiple technical descriptions of the algorithm, but was looking for a simplified explanation that was not expressed as computer code. I tried to illustrate the algorithm in story form, and others seemed to like my story. The surprising part to me has been that votes continue to trickle in even today, and that this deliberately silly story is now my most upvoted answer. I suppose there's a lesson in there somewhere...

You walk into a gymnasium containing 200 children. It is September 8th, so you have a burning desire to find the 98th shortest child. You know that you could line them all up from shortest to tallest, but that would take forever. “I know”, you think, “I could use QUICKSELECT!”

You walk out into the crowd, close your eyes, stick out your finger, and spin around three times. When you open your eyes, you are pointing directly at one of the children, Peter Pivot. You say, “Quickly! Everybody shorter than Peter, come stand over here. And everybody taller than Peter, go stand over there. If you're the same height as Peter, you can go into either group.”

The children shuffle around, and soon they are standing in the two groups. You count and find 120 children in the shorter group, and 79 children in the taller group. You know the 98th shortest child must be in the shorter group, so you tell Peter and the 79 taller children to sit in the bleachers.

You again close your eyes, stick out your finger, and spin around three times. When you open your eyes, you are pointing directly at Peter's sister, Paula Pivot. You say, “Quickly! Those of you who are still standing. If you're shorter than Paula, come stand over here. If you're taller than Paula, go stand over there. If you're the same height, you can go into either group.”

The children shuffle around, and soon they are standing in the two groups. You count and find 59 children in the shorter group, and 60 children in the taller group. You know the 98th shortest child must be in the taller group, so you tell Paula and the 59 shorter children to sit in the bleachers.

You again close your eyes, stick out your finger, and spin around three times. When you open your eyes, you are pointing directly at Paula's cousin, Prudence Pivot. You say, “Quickly! Those of you who are still standing. If you're shorter than Prudence, come stand over here. If you're taller than Prudence, go stand over there. If you're the same height, you can go into either group.”

The children shuffle around, and soon they are standing in the two groups. You count and find 37 children in the shorter group, and 22 children in the taller group. You know that Paula and 59 other shorter children are sitting on the bleachers. Along with the 37 shorter children still standing, you know that a total of 97 children are shorter than Prudence. Therefore, Prudence is the 98th shortest child!

Quickselect FTW!

#### 1 comment:

Stick said...

Great explanation!