Added 2 different implementations for Catalan Numbers

Author: rahulkumaran

Competitive Coding/Math/Catalan_Numbers/catalan_binomial.py

@@ -0,0 +1,15 @@
+def binCoeff(n, k):#Finds the binomial coefficient
+ if (k > n - k):#As binCoeff(n,k)=binCoeff(n,n-k)
+ k = n - k
+ res = 1#Initialising Result 
+ for i in range(k):
+ res = res * (n - i)
+ res = res / (i + 1)
+ return res#The binomial coefficient is returned
+
+def catalan(n):#Function that finds catalan numbers
+ c = binCoeff(2*n, n)#Finding value of c by calling the binCoeff function
+ return c/(n + 1)#This is the final catalan number
+ 
+for i in range (5):#finds 1st 5 catalan numbers
+ print (catalan(i))#Prints the Catalan numbers

Competitive Coding/Math/Catalan_Numbers/catalan_recursive.py

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+def catalan_numbers(n):
+ if n <=1 :#The result will be 1, if the function takes an argument that's equal to or less than 1
+ 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
+ return res
+
+for i in range(5):#Implements the algo and finds the first 5 catalan numbers
+ print catalan_numbers(i)