Added generate parenthesis algorithm

backtracking/generate_parenthesis.py

@@ -0,0 +1,48 @@
+"""
+Given 'n' Pairs of parenthesis,
+this program generates all combinations of parenthesis 
+Example, n=3 :
+[
+    "((()))",
+    "(()())",
+    "(())()",
+    "()(())",
+    "()()()"
+]
+This problem is solved using Backtracking 
+"""
+def solve(op,open,close, ans):
+    if(open == 0 and close == 0):
+      ans.append(op)
+      return
+    if(open == close):
+      op1 = op
+      op1+=('(')
+      solve(op1, open-1, close, ans)
+    elif(open == 0):
+      op1 = op
+      op1+=(')')
+      solve(op1, open, close-1, ans)
+    elif(close == 0):
+      op1 = op
+      op1+=('(')
+      solve(op1, open-1, close, ans)
+    else:
+      op1 = op
+      op2 = op
+      op1+=('(')
+      op2+=(')')
+      solve(op1, open-1, close, ans)
+      solve(op2, open, close-1, ans)
+
+
+def generate_parenthesis(n):
+   open = n
+   close = n
+   ans=[]
+   op = ""
+   solve(op, open, close, ans)
+   return ans
+
+
+print(generate_parenthesis(3))