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Copy file name to clipboardExpand all lines: Competitive Coding/Math/Catalan_Numbers/README.md
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The Binomial implementation has the best time complexity while the Recursive implementation has the worst time complexity<br>
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In this folder we have the Binomial and Recursive implementations of Catalan Numbers.<br><br>
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Sources : Click [here](https://www.geeksforgeeks.org/program-nth-catalan-number/) to know more about Catalan number implementations and its theory.
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Catalan Numbers have a lot of applications in Combinatorics. Some of them are listed below:
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* Cn is the number of standard Young tableaux whose diagram is a 2-by-n rectangle. In other words, it is the number of ways the numbers 1, 2, ..., 2n can be arranged in a 2-by-n rectangle so that each row and each column is increasing. As such, the formula can be derived as a special case of the hook-length formula.
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* Cn is the number of ways that the vertices of a convex 2n-gon can be paired so that the line segments joining paired vertices do not intersect. This is precisely the condition that guarantees that the paired edges can be identified (sewn together) to form a closed surface of genus zero (a topological 2-sphere).
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* Cn is the number of semiorders on n unlabeled items.
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* In chemical engineering Cn-1 is the number of possible separation sequences which can separate a mixture of n components.<br><br>
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### Sources :
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(1) Click [here](https://www.geeksforgeeks.org/program-nth-catalan-number/) to know more about Catalan number implementations and its theory.<br>
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(2) Click [here](https://en.wikipedia.org/wiki/Catalan_number) to know more about the applicatations of Catalan Numbers in Combinatorics
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