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Commitbbad761

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Luke-Polsonkeon
authored andcommitted
Add recursive binomial coefficient (keon#598)
* added recursive binomial coefficient algorithm* updated readme link* changed return to raise exceptioninstead of returning a string when inputs are invalid, function now raises a ValueError exception
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‎README.md

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@@ -217,7 +217,8 @@ If you want to uninstall algorithms, it is as simple as:
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-[sqrt_precision_factor](algorithms/maths/sqrt_precision_factor.py)
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-[summing_digits](algorithms/maths/summing_digits.py)
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-[hailstone](algorithms/maths/hailstone.py)
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- [find_order](algorithms/maths/find_order_simple.py)
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-[recursive_binomial_coefficient](algorithms/maths/recursive_binomial_coefficient.py)
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-[find_order](algorithms/maths/find_order_simple.py)
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- [find_primitive_root](algorithms/maths/find_primitive_root_simple.py)
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-[matrix](algorithms/matrix)
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-[sudoku_validator](algorithms/matrix/sudoku_validator.py)
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defrecursive_binomial_coefficient(n,k):
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"""Calculates the binomial coefficient, C(n,k), with n>=k using recursion
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Time complexity is O(k), so can calculate fairly quickly for large values of k.
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>>> recursive_binomial_coefficient(5,0)
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1
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>>> recursive_binomial_coefficient(8,2)
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28
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>>> recursive_binomial_coefficient(500,300)
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5054949849935535817667719165973249533761635252733275327088189563256013971725761702359997954491403585396607971745777019273390505201262259748208640
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"""
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ifk>n:
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raiseValueError('Invalid Inputs, ensure that n >= k')
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#function is only defined for n>=k
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ifk==0orn==k:
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#C(n,0) = C(n,n) = 1, so this is our base case.
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return1
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ifk>n/2:
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#C(n,k) = C(n,n-k), so if n/2 is sufficiently small, we can reduce the problem size.
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returnrecursive_binomial_coefficient(n,n-k)
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else:
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#else, we know C(n,k) = (n/k)C(n-1,k-1), so we can use this to reduce our problem size.
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returnint((n/k)*recursive_binomial_coefficient(n-1,k-1))
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