Create nth_catalan_numbers.py

Author: abhisheks008

Dynamic Programming/Nth Catalan Numbers/nth_catalan_numbers.py

@@ -0,0 +1,74 @@
+# Problem Name: Nth Catalan Numbers
+# Approach: Dynamic Programming
+
+# -----------------------------------------------------------------------------------
+
+# Problem Statement: Catalan numbers are defined as a mathematical sequence 
+#                    that consists of positive integers, which can be used to 
+#                    find the number of possibilities of various combinations. 
+#                    Find out the catalan numbers in between the range from 0 to N.
+
+
+# -----------------------------------------------------------------------------------
+
+# Constraints:
+# n -> Integer taken as the range of the Catalan Numbers.
+# catalan[] -> Array of Catalan Numbers from 0 to n.
+
+# -----------------------------------------------------------------------------------
+
+# A dynamic programming based function to find nth
+# Catalan number
+ 
+def catalan(n):
+    if (n == 0 or n == 1):
+        return 1
+ 
+    # Table to store results of subproblems
+    catalan = [0]*(n+1)
+ 
+    # Initialize first two values in table
+    catalan[0] = 1
+    catalan[1] = 1
+ 
+    # Fill entries in catalan[]
+    # using recursive formula
+    for i in range(2, n + 1):
+        for j in range(i):
+            catalan[i] += catalan[j] * catalan[i-j-1]
+ 
+    # Return last entry
+    return catalan[n]
+ 
+ 
+# Driver Code
+print ("-- Nth Catalan Numbers using Dynamic Programming --")
+print ()
+print ("Enter the upper range : ")
+k = int(input())
+print ()
+print ("Printing Nth Catalan Numbers from 0 to {0}...".format(k))
+print ()
+print ("Here you go!")
+for i in range(k):
+	  print(catalan(i), end=" ")
+    
+    
+# -----------------------------------------------------------------------------------
+
+# Output:
+# -- Nth Catalan Numbers using Dynamic Programming --
+
+# Enter the upper range : 
+# 12
+
+# Printing Nth Catalan Numbers from 0 to 12...
+
+# Here you go!
+# 1 1 2 5 14 42 132 429 1430 4862 16796 58786 
+
+# -----------------------------------------------------------------------------------
+
+# Code Contributed by, Abhishek Sharma, 2022
+
+# -----------------------------------------------------------------------------------