Added 2 different implementations for Catalan Numbers #255
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@prateekiiest sorry closed the previous PR! Had some implementation faults in that! So just rectified my code and made the necessary changes! :) Please have a look at it :) |
| The 2 different implementations vary only in terms of time taken!<br> | ||
| Basically we can implement in 3 different ways!<br> | ||
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| (1) Recursively <br> |
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instead of numbering use *.
And write the time complexities here only like this
- Recursive -exponential
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@prateekiiest made the changes you requested :) |
| (2) Dynamic Programming <br> | ||
| (3) Binomial Coefficient <br><br> | ||
| * Recursively - Exponential time complexity<br> | ||
| * Dynamic Programming - O(n^2)<br> |
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make a tilde before and after O(n^2)
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| The 2 different programs in this folder contain the same implementation! | |||
| The Binomial implementation has the best time complexity while the Recursive implementation has the worst time complexity<br> | ||
| In this folder we have the Binomial and Recursive implementations of Catalan Numbers.<br><br> | ||
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| Sources : https://www.geeksforgeeks.org/program-nth-catalan-number/ (You can have a look at this to know more about Catalan number implementations and its theory.) |
| The Binomial implementation has the best time complexity while the Recursive implementation has the worst time complexity<br> | ||
| In this folder we have the Binomial and Recursive implementations of Catalan Numbers.<br><br> | ||
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| Sources : https://www.geeksforgeeks.org/program-nth-catalan-number/ (You can have a look at this to know more about Catalan number implementations and its theory.) |
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some examples needed where catalan number comes in like finding no. of polygon triangulation etc.
| return 1 | ||
| res = 0 #Result has been initialised to 0 | ||
| for i in range(n): | ||
| res += catalan_numbers(i) * catalan_numbers(n-i-1) #The recursive function call |
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where is the coefficient in this case?
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@prateekiiest what coefficient are you referring to?
| c = binCoeff(2*n, n) #Finding value of c by calling the binCoeff function | ||
| return c/(n + 1) #This is the final catalan number | ||
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| for i in range (5): #finds 1st 5 catalan numbers |
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just print one or two catalan numbers as example, not in a for loop
| The 2 different implementations vary only in terms of time taken!<br> | ||
| Basically we can implement in 3 different ways!<br> | ||
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| * Recursively - Exponential time complexity<br> |
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make use of tilde
like this O(n^2)
Thank you for your contribution. Please provide the details requested below.
SHORT DESCRIPTION
Added 2 different implementations of catalan numbers which vary in time complexity only!
TESTING
Just run the program and you'll get the outcome! The results of both the programs will be the same! They're just different methods to find catalan numbers