add : to add generate_parentheses.py under backtracking

backtracking/generate_parentheses.py

@@ -0,0 +1,63 @@
+"""
+Given 'n' pairs of parentheses,
+this program generates all combinations of parentheses.
+
+Example, n = 3 :
+[
+   "((()))",
+   "(()())",
+   "(())()",
+   "()(())",
+   "()()()"
+]
+
+This problem can be solved using the concept of "BACKTRACKING".
+
+By adding an open parenthesis to the solution and
+recursively add more till we get 'n' open parentheses.
+
+Then we start adding close parentheses until the solution is valid
+(open parenthesis is closed).
+
+If we reach a point where we can not add more parentheses to the solution,
+we backtrack to the previous step and try a different path.
+"""
+
+
+def generate_parentheses(number : int = 3):
+    """
+
+    >>> generate_parentheses(3)
+    ['((()))', '(()())', '(())()', '()(())', '()()()']
+
+    >>> generate_parentheses(3)
+    ['(())', '()()']
+
+    >>> generate_parentheses(1)
+    ['()']
+
+    >>> generate_parentheses(0)
+    ['']
+
+    """
+
+    def backtrack(x : str = "", left : int = 0, right : int = 0):
+
+        if len(x) == 2 * number:
+            result.append(x)
+            return
+        if left < number:
+            backtrack(x + "(", left + 1, right)
+        if right < left:
+            backtrack(x + ")", left, right + 1)
+
+    result = []
+    backtrack()
+    return result
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+    print(f"{generate_parentheses() = }")