From faf2975ea7a8e7692db6c88da97fb4a9c58f3a88 Mon Sep 17 00:00:00 2001
From: Jibesh Roy <jibeshr60@gmail.com>
Date: Sun, 8 Oct 2023 09:29:12 +0530
Subject: [PATCH 01/17] Added new file Generate Parenthesis

---
 backtracking/generate_parenthesis.py | 48 ++++++++++++++++++++++++++++
 1 file changed, 48 insertions(+)
 create mode 100644 backtracking/generate_parenthesis.py

diff --git a/backtracking/generate_parenthesis.py b/backtracking/generate_parenthesis.py
new file mode 100644
index 000000000000..f321e17e20c5
--- /dev/null
+++ b/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 generateParenthesis(n):
+    open = n
+    close = n
+    ans=[]
+    op = ""
+    solve(op, open, close, ans)
+    return ans
+    
+
+print(generateParenthesis(3))
\ No newline at end of file

From 60fc3942b87b13ae67116eabb7ae1b9c6e91c15c Mon Sep 17 00:00:00 2001
From: Jibesh10101011 <114723590+Jibesh10101011@users.noreply.github.com>
Date: Sun, 8 Oct 2023 09:40:38 +0530
Subject: [PATCH 02/17] Update generate_parenthesis.py

---
 backtracking/generate_parenthesis.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/backtracking/generate_parenthesis.py b/backtracking/generate_parenthesis.py
index f321e17e20c5..64df529add63 100644
--- a/backtracking/generate_parenthesis.py
+++ b/backtracking/generate_parenthesis.py
@@ -36,7 +36,7 @@ def solve(op,open,close, ans):
         solve(op2, open, close-1, ans)
 
 
-def generateParenthesis(n):
+def generate_parenthesis(n):
     open = n
     close = n
     ans=[]
@@ -45,4 +45,4 @@ def generateParenthesis(n):
     return ans
     
 
-print(generateParenthesis(3))
\ No newline at end of file
+print(generateParenthesis(3))

From 98d7c272bec658859251b894981deb4a9b0e074e Mon Sep 17 00:00:00 2001
From: Jibesh10101011 <114723590+Jibesh10101011@users.noreply.github.com>
Date: Sun, 8 Oct 2023 09:41:12 +0530
Subject: [PATCH 03/17] Update generate_parenthesis.py

---
 backtracking/generate_parenthesis.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/backtracking/generate_parenthesis.py b/backtracking/generate_parenthesis.py
index 64df529add63..1a106c255549 100644
--- a/backtracking/generate_parenthesis.py
+++ b/backtracking/generate_parenthesis.py
@@ -45,4 +45,4 @@ def generate_parenthesis(n):
     return ans
     
 
-print(generateParenthesis(3))
+print(generate_parenthesis(3))

From b0a0f676be2046f4864de5abe266bbf51d032590 Mon Sep 17 00:00:00 2001
From: Jibesh10101011 <114723590+Jibesh10101011@users.noreply.github.com>
Date: Sun, 8 Oct 2023 09:48:34 +0530
Subject: [PATCH 04/17] Update generate_parenthesis.py

---
 backtracking/generate_parenthesis.py | 68 ++++++++++++++--------------
 1 file changed, 34 insertions(+), 34 deletions(-)

diff --git a/backtracking/generate_parenthesis.py b/backtracking/generate_parenthesis.py
index 1a106c255549..a3d0bd100679 100644
--- a/backtracking/generate_parenthesis.py
+++ b/backtracking/generate_parenthesis.py
@@ -1,48 +1,48 @@
 """
-   Given 'n' Pairs of parenthesis,
-   this program generates all combinations of parenthesis 
-   Example, n=3 :
-   [
-       "((()))",
-       "(()())",
-       "(())()",
-       "()(())",
-       "()()()"
-   ]
-   This problem is solved using Backtracking 
+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
+      ans.append(op)
+      return
     if(open == close):
-        op1 = op
-        op1+=('(')
-        solve(op1, open-1, close, ans)
+      op1 = op
+      op1+=('(')
+      solve(op1, open-1, close, ans)
     elif(open == 0):
-        op1 = op
-        op1+=(')')
-        solve(op1, open, close-1, ans)
+      op1 = op
+      op1+=(')')
+      solve(op1, open, close-1, ans)
     elif(close == 0):
-        op1 = op
-        op1+=('(')
-        solve(op1, open-1, close, ans)
+      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)
+      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
+   open = n
+   close = n
+   ans=[]
+   op = ""
+   solve(op, open, close, ans)
+   return ans
     
 
 print(generate_parenthesis(3))

From a69d5eb81e7b914c5c967149c5e7b656cd723ccc Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Sun, 8 Oct 2023 04:26:44 +0000
Subject: [PATCH 05/17] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 backtracking/generate_parenthesis.py | 64 ++++++++++++++--------------
 1 file changed, 33 insertions(+), 31 deletions(-)

diff --git a/backtracking/generate_parenthesis.py b/backtracking/generate_parenthesis.py
index a3d0bd100679..b5cf1542e6ed 100644
--- a/backtracking/generate_parenthesis.py
+++ b/backtracking/generate_parenthesis.py
@@ -1,6 +1,6 @@
 """
 Given 'n' Pairs of parenthesis,
-this program generates all combinations of parenthesis 
+this program generates all combinations of parenthesis
 Example, n=3 :
 [
     "((()))",
@@ -9,40 +9,42 @@
     "()(())",
     "()()()"
 ]
-This problem is solved using Backtracking 
+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)
+
+
+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)
+        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
-    
+    open = n
+    close = n
+    ans = []
+    op = ""
+    solve(op, open, close, ans)
+    return ans
+
 
 print(generate_parenthesis(3))

From 5ecc4611c13c81abf86c26c4658f8192fbfb5509 Mon Sep 17 00:00:00 2001
From: Jibesh10101011 <114723590+Jibesh10101011@users.noreply.github.com>
Date: Sun, 8 Oct 2023 10:22:50 +0530
Subject: [PATCH 06/17] Update generate_parenthesis.py

---
 backtracking/generate_parenthesis.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/backtracking/generate_parenthesis.py b/backtracking/generate_parenthesis.py
index b5cf1542e6ed..b8275d4fbeda 100644
--- a/backtracking/generate_parenthesis.py
+++ b/backtracking/generate_parenthesis.py
@@ -13,7 +13,7 @@
 """
 
 
-def solve(op, open, close, ans):
+def solve(op, open, close, ans) -> int :
     if open == 0 and close == 0:
         ans.append(op)
         return
@@ -38,7 +38,7 @@ def solve(op, open, close, ans):
         solve(op2, open, close - 1, ans)
 
 
-def generate_parenthesis(n):
+def generate_parenthesis(n) -> list[str] :
     open = n
     close = n
     ans = []

From 45eea59cfe5fe6204707ab9fa71b856475b2fc77 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Sun, 8 Oct 2023 04:53:23 +0000
Subject: [PATCH 07/17] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 backtracking/generate_parenthesis.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/backtracking/generate_parenthesis.py b/backtracking/generate_parenthesis.py
index b8275d4fbeda..36510faf1f18 100644
--- a/backtracking/generate_parenthesis.py
+++ b/backtracking/generate_parenthesis.py
@@ -13,7 +13,7 @@
 """
 
 
-def solve(op, open, close, ans) -> int :
+def solve(op, open, close, ans) -> int:
     if open == 0 and close == 0:
         ans.append(op)
         return
@@ -38,7 +38,7 @@ def solve(op, open, close, ans) -> int :
         solve(op2, open, close - 1, ans)
 
 
-def generate_parenthesis(n) -> list[str] :
+def generate_parenthesis(n) -> list[str]:
     open = n
     close = n
     ans = []

From 76a64a008a9d873609e8bfae4bdb0af16c8f79ba Mon Sep 17 00:00:00 2001
From: Jibesh10101011 <114723590+Jibesh10101011@users.noreply.github.com>
Date: Sun, 8 Oct 2023 11:34:03 +0530
Subject: [PATCH 08/17] Update generate_parenthesis.py

---
 backtracking/generate_parenthesis.py | 87 ++++++++++++++--------------
 1 file changed, 44 insertions(+), 43 deletions(-)

diff --git a/backtracking/generate_parenthesis.py b/backtracking/generate_parenthesis.py
index 36510faf1f18..fd03ea64aff9 100644
--- a/backtracking/generate_parenthesis.py
+++ b/backtracking/generate_parenthesis.py
@@ -1,50 +1,51 @@
 """
-Given 'n' Pairs of parenthesis,
-this program generates all combinations of parenthesis
-Example, n=3 :
-[
-    "((()))",
-    "(()())",
-    "(())()",
-    "()(())",
-    "()()()"
-]
-This problem is solved using Backtracking
+Given, 'n' pairs of parenthesis,
+this program will generate all combinations of valid parenthesis 
 """
-
-
-def solve(op, open, close, ans) -> int:
-    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)
+def solve(op : str,open : int ,close : int , ans : list[str]) -> int :
+    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 = op
-        op2 = op
-        op1 += "("
-        op2 += ")"
-        solve(op1, open - 1, close, ans)
-        solve(op2, open, close - 1, ans)
+      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] :
+   """
+   >>> 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)
+   return ans
+    
+if __name__ == "__main__":
+    import doctest
 
-def generate_parenthesis(n) -> list[str]:
-    open = n
-    close = n
-    ans = []
-    op = ""
-    solve(op, open, close, ans)
-    return ans
+    doctest.testmod()
 
 
-print(generate_parenthesis(3))

From d6dd070c6a6f6dfb5afd92f4fbab33b804e7a8f5 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Sun, 8 Oct 2023 06:04:32 +0000
Subject: [PATCH 09/17] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 backtracking/generate_parenthesis.py | 83 ++++++++++++++--------------
 1 file changed, 42 insertions(+), 41 deletions(-)

diff --git a/backtracking/generate_parenthesis.py b/backtracking/generate_parenthesis.py
index fd03ea64aff9..93378052d5cd 100644
--- a/backtracking/generate_parenthesis.py
+++ b/backtracking/generate_parenthesis.py
@@ -1,51 +1,52 @@
 """
 Given, 'n' pairs of parenthesis,
-this program will generate all combinations of valid parenthesis 
+this program will generate all combinations of valid parenthesis
 """
-def solve(op : str,open : int ,close : int , ans : list[str]) -> int :
-    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)
+
+
+def solve(op: str, open: int, close: int, ans: list[str]) -> int:
+    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)
+        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]:
+    """
+    >>> 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)
+    return ans
 
 
-def generate_parenthesis(n : int) -> list[str] :
-   """
-   >>> 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)
-   return ans
-    
 if __name__ == "__main__":
     import doctest
 
     doctest.testmod()
-
-

From a3efa4f9a13af1b03b564e73cc52709f0541a8d8 Mon Sep 17 00:00:00 2001
From: Jibesh10101011 <114723590+Jibesh10101011@users.noreply.github.com>
Date: Sun, 8 Oct 2023 12:05:24 +0530
Subject: [PATCH 10/17] Update generate_parenthesis.py

---
 backtracking/generate_parenthesis.py | 85 +++++++++++++---------------
 1 file changed, 40 insertions(+), 45 deletions(-)

diff --git a/backtracking/generate_parenthesis.py b/backtracking/generate_parenthesis.py
index 93378052d5cd..ca4abcfc448b 100644
--- a/backtracking/generate_parenthesis.py
+++ b/backtracking/generate_parenthesis.py
@@ -1,52 +1,47 @@
-"""
-Given, 'n' pairs of parenthesis,
-this program will generate all combinations of valid parenthesis
-"""
-
-
-def solve(op: str, open: int, close: int, ans: list[str]) -> int:
-    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)
+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]:
-    """
-    >>> 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)
-    return ans
+      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()
+

From 4aaeba721fadd42f51c1a2c42f5b19b1748796d0 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Sun, 8 Oct 2023 06:35:53 +0000
Subject: [PATCH 11/17] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 backtracking/generate_parenthesis.py | 80 ++++++++++++++--------------
 1 file changed, 40 insertions(+), 40 deletions(-)

diff --git a/backtracking/generate_parenthesis.py b/backtracking/generate_parenthesis.py
index ca4abcfc448b..4983ea4835cd 100644
--- a/backtracking/generate_parenthesis.py
+++ b/backtracking/generate_parenthesis.py
@@ -1,47 +1,47 @@
-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)
+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)
+        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
 
 
-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()
-

From e0c1e185145fafca986a9f26dab1cd4c737bbf1a Mon Sep 17 00:00:00 2001
From: Jibesh10101011 <114723590+Jibesh10101011@users.noreply.github.com>
Date: Sun, 8 Oct 2023 12:08:30 +0530
Subject: [PATCH 12/17] Update generate_parenthesis.py

---
 backtracking/generate_parenthesis.py | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/backtracking/generate_parenthesis.py b/backtracking/generate_parenthesis.py
index 4983ea4835cd..0707dbc2250c 100644
--- a/backtracking/generate_parenthesis.py
+++ b/backtracking/generate_parenthesis.py
@@ -43,5 +43,4 @@ def generate_parenthesis(n: int) -> list[str]:  # n = no. of pairs of parenthesi
 
 if __name__ == "__main__":
     import doctest
-
-    doctest.testmod()
+doctest.testmod()

From 43cb929d06fb10af395ccd4552dc4dad92297373 Mon Sep 17 00:00:00 2001
From: Jibesh10101011 <114723590+Jibesh10101011@users.noreply.github.com>
Date: Sun, 8 Oct 2023 12:24:51 +0530
Subject: [PATCH 13/17] Update generate_parenthesis.py

---
 backtracking/generate_parenthesis.py | 6 ++----
 1 file changed, 2 insertions(+), 4 deletions(-)

diff --git a/backtracking/generate_parenthesis.py b/backtracking/generate_parenthesis.py
index 0707dbc2250c..5919260b3e3a 100644
--- a/backtracking/generate_parenthesis.py
+++ b/backtracking/generate_parenthesis.py
@@ -1,3 +1,4 @@
+import doctest
 def solve(op: str, open: int, close: int, ans: list[str]) -> None:
     if open == 0 and close == 0:
         ans.append(op)
@@ -39,8 +40,5 @@ def generate_parenthesis(n: int) -> list[str]:  # n = no. of pairs of parenthesi
     solve(op, open, close, ans)
     if n > 0:
         return ans
-
-
-if __name__ == "__main__":
-    import doctest
+        
 doctest.testmod()

From 5cacd540808734a9bfb1945ed5f99091c7ed3417 Mon Sep 17 00:00:00 2001
From: Jibesh10101011 <114723590+Jibesh10101011@users.noreply.github.com>
Date: Sun, 8 Oct 2023 12:25:00 +0530
Subject: [PATCH 14/17] Update generate_parenthesis.py

---
 backtracking/generate_parenthesis.py | 1 +
 1 file changed, 1 insertion(+)

diff --git a/backtracking/generate_parenthesis.py b/backtracking/generate_parenthesis.py
index 5919260b3e3a..bc7007f31031 100644
--- a/backtracking/generate_parenthesis.py
+++ b/backtracking/generate_parenthesis.py
@@ -1,4 +1,5 @@
 import doctest
+
 def solve(op: str, open: int, close: int, ans: list[str]) -> None:
     if open == 0 and close == 0:
         ans.append(op)

From 1fa5f0506c93b2a4a30932e5f7850e66a8e12d82 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Sun, 8 Oct 2023 06:55:50 +0000
Subject: [PATCH 15/17] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 backtracking/generate_parenthesis.py | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/backtracking/generate_parenthesis.py b/backtracking/generate_parenthesis.py
index bc7007f31031..86e93bb04f62 100644
--- a/backtracking/generate_parenthesis.py
+++ b/backtracking/generate_parenthesis.py
@@ -1,5 +1,6 @@
 import doctest
 
+
 def solve(op: str, open: int, close: int, ans: list[str]) -> None:
     if open == 0 and close == 0:
         ans.append(op)
@@ -41,5 +42,6 @@ def generate_parenthesis(n: int) -> list[str]:  # n = no. of pairs of parenthesi
     solve(op, open, close, ans)
     if n > 0:
         return ans
-        
+
+
 doctest.testmod()

From 78d25036b73e9c0e991b3d77ba37c37f3bacbc21 Mon Sep 17 00:00:00 2001
From: Jibesh10101011 <114723590+Jibesh10101011@users.noreply.github.com>
Date: Sun, 8 Oct 2023 14:39:55 +0530
Subject: [PATCH 16/17] Update generate_parenthesis.py

---
 backtracking/generate_parenthesis.py | 4 ----
 1 file changed, 4 deletions(-)

diff --git a/backtracking/generate_parenthesis.py b/backtracking/generate_parenthesis.py
index 86e93bb04f62..71d310ac27ee 100644
--- a/backtracking/generate_parenthesis.py
+++ b/backtracking/generate_parenthesis.py
@@ -1,6 +1,5 @@
 import doctest
 
-
 def solve(op: str, open: int, close: int, ans: list[str]) -> None:
     if open == 0 and close == 0:
         ans.append(op)
@@ -32,8 +31,6 @@ def generate_parenthesis(n: int) -> list[str]:  # n = no. of pairs of parenthesi
     ['((()))', '(()())', '(())()', '()(())', '()()()']
     >>> generate_parenthesis(4)
     ['(((())))', '((()()))', '((())())', '((()))()', '(()(()))', '(()()())', '(()())()', '(())(())', '(())()()', '()((()))', '()(()())', '()(())()', '()()(())', '()()()()']
-    >>> generate_parenthesis(5)
-    ['((((()))))', '(((()())))', '(((())()))', '(((()))())', '(((())))()', '((()(())))', '((()()()))', '((()())())', '((()()))()', '((())(()))', '((())()())', '((())())()', '((()))(())', '((()))()()', '(()((())))', '(()(()()))', '(()(())())', '(()(()))()', '(()()(()))', '(()()()())', '(()()())()', '(()())(())', '(()())()()', '(())((()))', '(())(()())', '(())(())()', '(())()(())', '(())()()()', '()(((())))', '()((()()))', '()((())())', '()((()))()', '()(()(()))', '()(()()())', '()(()())()', '()(())(())', '()(())()()', '()()((()))', '()()(()())', '()()(())()', '()()()(())', '()()()()()']
     """
     open: int = n
     close: int = n
@@ -43,5 +40,4 @@ def generate_parenthesis(n: int) -> list[str]:  # n = no. of pairs of parenthesi
     if n > 0:
         return ans
 
-
 doctest.testmod()

From e5e0efa4858d1ce9768e45769086a0d6ed222383 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Sun, 8 Oct 2023 09:10:29 +0000
Subject: [PATCH 17/17] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 backtracking/generate_parenthesis.py | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/backtracking/generate_parenthesis.py b/backtracking/generate_parenthesis.py
index 71d310ac27ee..be6971569312 100644
--- a/backtracking/generate_parenthesis.py
+++ b/backtracking/generate_parenthesis.py
@@ -1,5 +1,6 @@
 import doctest
 
+
 def solve(op: str, open: int, close: int, ans: list[str]) -> None:
     if open == 0 and close == 0:
         ans.append(op)
@@ -40,4 +41,5 @@ def generate_parenthesis(n: int) -> list[str]:  # n = no. of pairs of parenthesi
     if n > 0:
         return ans
 
+
 doctest.testmod()