https://github.com/jginsburgn/drichlet-box

A function that returns the hole index for the numbered pigeon (in Pigeonhole Principle lingo).
https://github.com/jginsburgn/drichlet-box

Last synced: 16 days ago
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A function that returns the hole index for the numbered pigeon (in Pigeonhole Principle lingo).

• Host: GitHub
• URL: https://github.com/jginsburgn/drichlet-box
• Owner: jginsburgn
• License: mit
• Created: 2021-07-05T18:20:44.000Z (over 3 years ago)
• Default Branch: main
• Last Pushed: 2021-07-05T20:49:32.000Z (over 3 years ago)
• Last Synced: 2024-07-04T16:08:10.963Z (4 months ago)
• Language: JavaScript
• Size: 26.4 KB
• Stars: 1
• Watchers: 2
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
# Drichlet Box

_Context: [Pigeonhole Principle Wikipedia Article](https://en.wikipedia.org/wiki/Pigeonhole_principle)._

A function that maps the `(holesCount, pigeonsCount, pigeonIndex)` 3-tuple to the corresponding `holeIndex`, in constant time.

## Explanation

Given a wooden structure with `holesCount` pigeonholes and `pigeonsCount` pigeons, the `drichlet-box` function returns the zero-based hole index, `holeIndex`, in which a pigeon indicated by the zero-based integer `pigeonIndex` should go, so that the following holds:

1. There are at least `floor(pigeonsCount/holesCount)` pigeons in a hole (small hole).

1. There are at most `floor(pigeonsCount/holesCount)` pigeons in a hole (big hole).

1. `drichlet-box` is an [increasing function](https://mathworld.wolfram.com/IncreasingFunction.html) in regards to its `pigeonIndex` argument.

1. The big holes are the first ones. In other words, if `i` is an index of a big hole and `j` is an index of a small hole, `i < j`.