Added generate parenthesis algorithm

backtracking/generate_parenthesis.py

@@ -0,0 +1,46 @@
+def solve(op: str, open: int, close: int, ans: list[str]) -> None:
+    if open == 0 and close == 0:
+        ans.append(op)
+        return
+    if open == close:
+        op1: str = op
+        op1 += "("
+        solve(op1, open - 1, close, ans)
+    elif open == 0:
+        op1: str = op
+        op1 += ")"
+        solve(op1, open, close - 1, ans)
+    elif close == 0:
+        op1: str = op
+        op1 += "("
+        solve(op1, open - 1, close, ans)
+    else:
+        op1: str = op
+        op2: str = op
+        op1 += "("
+        op2 += ")"
+        solve(op1, open - 1, close, ans)
+        solve(op2, open, close - 1, ans)
+
+
+def generate_parenthesis(n: int) -> list[str]:  # n = no. of pairs of parenthesis > 0
+    """
+    >>> generate_parenthesis(3)
+    ['((()))', '(()())', '(())()', '()(())', '()()()']
+    >>> generate_parenthesis(4)
+    ['(((())))', '((()()))', '((())())', '((()))()', '(()(()))', '(()()())', '(()())()', '(())(())', '(())()()', '()((()))', '()(()())', '()(())()', '()()(())', '()()()()']
+    >>> generate_parenthesis(5)
+    ['((((()))))', '(((()())))', '(((())()))', '(((()))())', '(((())))()', '((()(())))', '((()()()))', '((()())())', '((()()))()', '((())(()))', '((())()())', '((())())()', '((()))(())', '((()))()()', '(()((())))', '(()(()()))', '(()(())())', '(()(()))()', '(()()(()))', '(()()()())', '(()()())()', '(()())(())', '(()())()()', '(())((()))', '(())(()())', '(())(())()', '(())()(())', '(())()()()', '()(((())))', '()((()()))', '()((())())', '()((()))()', '()(()(()))', '()(()()())', '()(()())()', '()(())(())', '()(())()()', '()()((()))', '()()(()())', '()()(())()', '()()()(())', '()()()()()']
+    """
+    open: int = n
+    close: int = n
+    ans: list[str] = []
+    op: str = ""
+    solve(op, open, close, ans)
+    if n > 0:
+        return ans
+
+
+if __name__ == "__main__":
+    import doctest
+doctest.testmod()