From b0bc67231484bdfbde5be58b3c957a22ab46648a Mon Sep 17 00:00:00 2001
From: hollowcrust <72879387+hollowcrust@users.noreply.github.com>
Date: Sat, 7 Oct 2023 21:42:28 +0800
Subject: [PATCH 1/6] Add new algorithm

Finding kth root of a number up to a given decimal places without using ** or pow()
---
 maths/finding_kth_root.py | 73 +++++++++++++++++++++++++++++++++++++++
 1 file changed, 73 insertions(+)
 create mode 100644 maths/finding_kth_root.py

diff --git a/maths/finding_kth_root.py b/maths/finding_kth_root.py
new file mode 100644
index 000000000000..a8143f1c6af4
--- /dev/null
+++ b/maths/finding_kth_root.py
@@ -0,0 +1,73 @@
+"""
+Finding the real root of a given degree of a given number, rounding to the nearest given number of decimal places without using **
+
+Input:
+    - number: 3
+    - deg: 2
+    - decimal_place: 5
+Output:
+    - 1.73205
+"""
+
+def finding_kth_root(number: float, deg: int, decimal_place: int) -> float:
+    """
+    Implementing binary search to find the kth root of a number
+    Negative numbers are treated the same way as positive numbers, with the minus sign added at the end
+    
+    >>> finding_kth_root(3, 2, 5)
+    1.73205
+    >>> finding_kth_root(122.683, 10, 7)
+    1.6176272
+    >>> finding_kth_root(5, 1, 3)
+    5.0
+    >>> finding_kth_root(0, 2, 2)
+    0.0
+    >>> finding_kth_root(125.7, 2, 0)
+    11.0
+    >>> finding_kth_root(-123, 5, 3)
+    -2.618
+    >>> finding_kth_root(-123, 4, 3)
+    Traceback (most recent call last):
+        ...
+    ValueError: Cannot calculate real root of an even degree of a negative number.
+    >>> finding_kth_root(123, -1, 3)
+    Traceback (most recent call last):
+        ...
+    ValueError: Degree of the root must be at least 1.
+    
+    """
+    if deg < 1:
+        raise ValueError("Degree of the root must be at least 1.")   
+
+    if deg % 2 == 0 and number < 0:
+        raise ValueError("Cannot calculate real root of an even degree of a negative number.")
+    
+    hi, lo = number, 0
+    if number < 0:
+        hi = -number
+        
+    error = 1
+    for i in range(decimal_place+1):
+        error /= 10
+
+    while(hi - lo >= error):    #Precision is not reached, continue looping
+        mid = (hi + lo) / 2
+        product = 1
+        for i in range(deg):    
+            product *= mid
+
+        if product > abs(number):   #Overestimation, higher bound decreases to mid
+            hi = mid
+            
+        else:   #Underestimation, lower bound increases to mid
+            lo = mid
+        
+    if number < 0:
+        return -round(lo, decimal_place)
+    
+    return round(lo, decimal_place)
+
+if __name__ == "__main__":
+    import doctest
+    
+    doctest.testmod()

From 897f8e5966a3563261b83f863860c1e84434a575 Mon Sep 17 00:00:00 2001
From: hollowcrust <72879387+hollowcrust@users.noreply.github.com>
Date: Sat, 7 Oct 2023 21:46:55 +0800
Subject: [PATCH 2/6] Change all int assignment to float

---
 maths/finding_kth_root.py | 14 ++++++++------
 1 file changed, 8 insertions(+), 6 deletions(-)

diff --git a/maths/finding_kth_root.py b/maths/finding_kth_root.py
index a8143f1c6af4..469ee5368b51 100644
--- a/maths/finding_kth_root.py
+++ b/maths/finding_kth_root.py
@@ -1,5 +1,6 @@
 """
-Finding the real root of a given degree of a given number, rounding to the nearest given number of decimal places without using **
+Finding the real root of a given degree of a given number
+rounding to the nearest given number of decimal places without using ** or pow()
 
 Input:
     - number: 3
@@ -11,8 +12,9 @@
 
 def finding_kth_root(number: float, deg: int, decimal_place: int) -> float:
     """
-    Implementing binary search to find the kth root of a number
-    Negative numbers are treated the same way as positive numbers, with the minus sign added at the end
+    Implementing binary search to find the kth root of a number.
+    Negative numbers are treated the same way as positive numbers, 
+    with the minus sign added at the end.
     
     >>> finding_kth_root(3, 2, 5)
     1.73205
@@ -42,17 +44,17 @@ def finding_kth_root(number: float, deg: int, decimal_place: int) -> float:
     if deg % 2 == 0 and number < 0:
         raise ValueError("Cannot calculate real root of an even degree of a negative number.")
     
-    hi, lo = number, 0
+    hi, lo = number, 0.0
     if number < 0:
         hi = -number
         
-    error = 1
+    error = 1.0
     for i in range(decimal_place+1):
         error /= 10
 
     while(hi - lo >= error):    #Precision is not reached, continue looping
         mid = (hi + lo) / 2
-        product = 1
+        product = 1.0
         for i in range(deg):    
             product *= mid
 

From 30daa416490ef75b897bf8e543f579c553deab16 Mon Sep 17 00:00:00 2001
From: hollowcrust <72879387+hollowcrust@users.noreply.github.com>
Date: Sat, 7 Oct 2023 21:52:25 +0800
Subject: [PATCH 3/6] Update finding_kth_root.py

---
 maths/finding_kth_root.py | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/maths/finding_kth_root.py b/maths/finding_kth_root.py
index 469ee5368b51..a6ec6e8c20df 100644
--- a/maths/finding_kth_root.py
+++ b/maths/finding_kth_root.py
@@ -2,6 +2,8 @@
 Finding the real root of a given degree of a given number
 rounding to the nearest given number of decimal places without using ** or pow()
 
+[Problem link] https://www.geeksforgeeks.org/calculating-n-th-real-root-using-binary-search/
+
 Input:
     - number: 3
     - deg: 2

From becf43dedf9923b26801d5990e8165c083fd95b2 Mon Sep 17 00:00:00 2001
From: hollowcrust <72879387+hollowcrust@users.noreply.github.com>
Date: Sat, 7 Oct 2023 21:52:37 +0800
Subject: [PATCH 4/6] Update finding_kth_root.py

---
 maths/finding_kth_root.py | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/maths/finding_kth_root.py b/maths/finding_kth_root.py
index a6ec6e8c20df..ef3dffa14267 100644
--- a/maths/finding_kth_root.py
+++ b/maths/finding_kth_root.py
@@ -2,7 +2,8 @@
 Finding the real root of a given degree of a given number
 rounding to the nearest given number of decimal places without using ** or pow()
 
-[Problem link] https://www.geeksforgeeks.org/calculating-n-th-real-root-using-binary-search/
+[Problem link] 
+https://www.geeksforgeeks.org/calculating-n-th-real-root-using-binary-search/
 
 Input:
     - number: 3

From fa8121ff3b21873fbd06e75f32d8e36d3f448cf2 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Sat, 7 Oct 2023 13:54:31 +0000
Subject: [PATCH 5/6] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 maths/finding_kth_root.py | 38 +++++++++++++++++++++-----------------
 1 file changed, 21 insertions(+), 17 deletions(-)

diff --git a/maths/finding_kth_root.py b/maths/finding_kth_root.py
index ef3dffa14267..dabd07cb79eb 100644
--- a/maths/finding_kth_root.py
+++ b/maths/finding_kth_root.py
@@ -2,7 +2,7 @@
 Finding the real root of a given degree of a given number
 rounding to the nearest given number of decimal places without using ** or pow()
 
-[Problem link] 
+[Problem link]
 https://www.geeksforgeeks.org/calculating-n-th-real-root-using-binary-search/
 
 Input:
@@ -13,12 +13,13 @@
     - 1.73205
 """
 
+
 def finding_kth_root(number: float, deg: int, decimal_place: int) -> float:
     """
     Implementing binary search to find the kth root of a number.
-    Negative numbers are treated the same way as positive numbers, 
+    Negative numbers are treated the same way as positive numbers,
     with the minus sign added at the end.
-    
+
     >>> finding_kth_root(3, 2, 5)
     1.73205
     >>> finding_kth_root(122.683, 10, 7)
@@ -39,40 +40,43 @@ def finding_kth_root(number: float, deg: int, decimal_place: int) -> float:
     Traceback (most recent call last):
         ...
     ValueError: Degree of the root must be at least 1.
-    
+
     """
     if deg < 1:
-        raise ValueError("Degree of the root must be at least 1.")   
+        raise ValueError("Degree of the root must be at least 1.")
 
     if deg % 2 == 0 and number < 0:
-        raise ValueError("Cannot calculate real root of an even degree of a negative number.")
-    
+        raise ValueError(
+            "Cannot calculate real root of an even degree of a negative number."
+        )
+
     hi, lo = number, 0.0
     if number < 0:
         hi = -number
-        
+
     error = 1.0
-    for i in range(decimal_place+1):
+    for i in range(decimal_place + 1):
         error /= 10
 
-    while(hi - lo >= error):    #Precision is not reached, continue looping
+    while hi - lo >= error:  # Precision is not reached, continue looping
         mid = (hi + lo) / 2
         product = 1.0
-        for i in range(deg):    
+        for i in range(deg):
             product *= mid
 
-        if product > abs(number):   #Overestimation, higher bound decreases to mid
+        if product > abs(number):  # Overestimation, higher bound decreases to mid
             hi = mid
-            
-        else:   #Underestimation, lower bound increases to mid
+
+        else:  # Underestimation, lower bound increases to mid
             lo = mid
-        
+
     if number < 0:
         return -round(lo, decimal_place)
-    
+
     return round(lo, decimal_place)
 
+
 if __name__ == "__main__":
     import doctest
-    
+
     doctest.testmod()

From 753512e8babf9baba7f94184c93f4dce0f0bfce9 Mon Sep 17 00:00:00 2001
From: hollowcrust <72879387+hollowcrust@users.noreply.github.com>
Date: Sat, 7 Oct 2023 21:58:44 +0800
Subject: [PATCH 6/6] Change i to _i

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

diff --git a/maths/finding_kth_root.py b/maths/finding_kth_root.py
index dabd07cb79eb..31ed25a2bf1f 100644
--- a/maths/finding_kth_root.py
+++ b/maths/finding_kth_root.py
@@ -55,13 +55,13 @@ def finding_kth_root(number: float, deg: int, decimal_place: int) -> float:
         hi = -number
 
     error = 1.0
-    for i in range(decimal_place + 1):
+    for _i in range(decimal_place + 1):
         error /= 10
 
     while hi - lo >= error:  # Precision is not reached, continue looping
         mid = (hi + lo) / 2
         product = 1.0
-        for i in range(deg):
+        for _i in range(deg):
             product *= mid
 
         if product > abs(number):  # Overestimation, higher bound decreases to mid