Pigeonhole Principle
Definition
The pigeonhole principle is a mathematical principle that states if you have more pigeons than pigeonholes to put them in, at least one pigeonhole must have more than one pigeon.
Explain Like I'm 5
Imagine you have 10 cookies but only 5 plates to put them on. If you try to put each cookie on a separate plate, some plates will end up with more than one cookie because there aren't enough plates for all the cookies.
Visualization
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Digging Deeper
The pigeonhole principle is a fundamental concept in mathematics and computer science that helps in understanding the distribution of objects among containers. It essentially states that if you have n items to place into m containers where n > m, then at least one container must contain more than one item. This principle has various applications in combinatorics, graph theory, algorithms, and cryptography.
Applications
- In scheduling tasks where there are more tasks than available time slots.
- In hashing functions where collisions occur when trying to map multiple keys to the same location.
- In data compression algorithms where redundancy needs to be reduced by identifying patterns or repetitions.
- In error detection and correction codes where errors need to be detected and corrected efficiently.
- In network routing algorithms where packets need to be efficiently distributed among different paths.
Learn More
Wikipedia - Pigeonhole Principle