From 451d4e14e290c596ee7c38f342fd7725fae3c459 Mon Sep 17 00:00:00 2001
From: ANANT JAIN <139585700+anant-jain01@users.noreply.github.com>
Date: Sat, 12 Oct 2024 00:06:23 +0530
Subject: [PATCH 01/24] Create adaptive_merge_sort.py

---
 sorts/adaptive_merge_sort.py | 51 ++++++++++++++++++++++++++++++++++++
 1 file changed, 51 insertions(+)
 create mode 100644 sorts/adaptive_merge_sort.py

diff --git a/sorts/adaptive_merge_sort.py b/sorts/adaptive_merge_sort.py
new file mode 100644
index 000000000000..a3a7f4dc22af
--- /dev/null
+++ b/sorts/adaptive_merge_sort.py
@@ -0,0 +1,51 @@
+def adaptive_merge_sort(sequence: list) -> list:
+    """
+    Sorts a list using the Adaptive Merge Sort algorithm.
+    """
+    if len(sequence) < 2:
+        return sequence
+
+    aux = sequence[:]
+    print(f"Initial sequence: {sequence}")
+    adaptive_merge_sort_helper(sequence, aux, 0, len(sequence) - 1)
+    print(f"Sorted sequence: {sequence}")
+    return sequence
+
+
+def adaptive_merge_sort_helper(array: list, aux: list, low: int, high: int):
+    if high <= low:
+        return
+
+    mid = (low + high) // 2
+    print(f"Sorting: array[{low}:{mid + 1}] and array[{mid + 1}:{high + 1}]")
+
+    adaptive_merge_sort_helper(aux, array, low, mid)
+    adaptive_merge_sort_helper(aux, array, mid + 1, high)
+
+    if array[mid] <= array[mid + 1]:
+        print(f"Skipping merge as array[{mid}] <= array[{mid + 1}]")
+        array[low:high + 1] = aux[low:high + 1]
+        return
+
+    merge(array, aux, low, mid, high)
+
+
+def merge(array: list, aux: list, low: int, mid: int, high: int):
+    print(f"Merging: array[{low}:{mid + 1}] and array[{mid + 1}:{high + 1}]")
+    i, j = low, mid + 1
+
+    for k in range(low, high + 1):
+        if i > mid:
+            aux[k] = array[j]
+            j += 1
+        elif j > high:
+            aux[k] = array[i]
+            i += 1
+        elif array[j] < array[i]:
+            aux[k] = array[j]
+            j += 1
+        else:
+            aux[k] = array[i]
+            i += 1
+
+    print(f"After merge: {aux[low:high + 1]}")

From 97aa418474cf5e1fa7762f2f77726e223c2865f2 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Fri, 11 Oct 2024 18:37:04 +0000
Subject: [PATCH 02/24] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 sorts/adaptive_merge_sort.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/sorts/adaptive_merge_sort.py b/sorts/adaptive_merge_sort.py
index a3a7f4dc22af..6c44baf8072e 100644
--- a/sorts/adaptive_merge_sort.py
+++ b/sorts/adaptive_merge_sort.py
@@ -24,7 +24,7 @@ def adaptive_merge_sort_helper(array: list, aux: list, low: int, high: int):
 
     if array[mid] <= array[mid + 1]:
         print(f"Skipping merge as array[{mid}] <= array[{mid + 1}]")
-        array[low:high + 1] = aux[low:high + 1]
+        array[low : high + 1] = aux[low : high + 1]
         return
 
     merge(array, aux, low, mid, high)

From 8d5ecd68830a8c0514cff86e1d96deef54689ef9 Mon Sep 17 00:00:00 2001
From: ANANT JAIN <139585700+anant-jain01@users.noreply.github.com>
Date: Thu, 17 Oct 2024 00:57:11 +0530
Subject: [PATCH 03/24] Update adaptive_merge_sort.py

---
 sorts/adaptive_merge_sort.py | 42 +++++++++++++++++++++++++++---------
 1 file changed, 32 insertions(+), 10 deletions(-)

diff --git a/sorts/adaptive_merge_sort.py b/sorts/adaptive_merge_sort.py
index 6c44baf8072e..07cb459e43f4 100644
--- a/sorts/adaptive_merge_sort.py
+++ b/sorts/adaptive_merge_sort.py
@@ -1,39 +1,62 @@
 def adaptive_merge_sort(sequence: list) -> list:
     """
     Sorts a list using the Adaptive Merge Sort algorithm.
+    
+    >>> adaptive_merge_sort([4, 3, 1, 2])
+    Initial sequence: [4, 3, 1, 2]
+    Sorting: array[0:2] and array[2:4]
+    Sorting: array[0:1] and array[1:2]
+    Sorting: array[2:3] and array[3:4]
+    Skipping merge as array[0] <= array[1]
+    Skipping merge as array[2] <= array[3]
+    Merging: array[0:2] and array[2:4]
+    After merge: [1, 2, 3, 4]
+    Sorted sequence: [1, 2, 3, 4]
+    [1, 2, 3, 4]
     """
     if len(sequence) < 2:
         return sequence
-
     aux = sequence[:]
     print(f"Initial sequence: {sequence}")
     adaptive_merge_sort_helper(sequence, aux, 0, len(sequence) - 1)
     print(f"Sorted sequence: {sequence}")
     return sequence
 
-
-def adaptive_merge_sort_helper(array: list, aux: list, low: int, high: int):
+def adaptive_merge_sort_helper(array: list, aux: list, low: int, high: int) -> None:
+    """
+    Helper function for Adaptive Merge Sort algorithm.
+    
+    >>> adaptive_merge_sort_helper([4, 3, 1, 2], [4, 3, 1, 2], 0, 3)
+    Sorting: array[0:2] and array[2:4]
+    Sorting: array[0:1] and array[1:2]
+    Sorting: array[2:3] and array[3:4]
+    Skipping merge as array[0] <= array[1]
+    Skipping merge as array[2] <= array[3]
+    Merging: array[0:2] and array[2:4]
+    After merge: [1, 2, 3, 4]
+    """
     if high <= low:
         return
-
     mid = (low + high) // 2
     print(f"Sorting: array[{low}:{mid + 1}] and array[{mid + 1}:{high + 1}]")
-
     adaptive_merge_sort_helper(aux, array, low, mid)
     adaptive_merge_sort_helper(aux, array, mid + 1, high)
-
     if array[mid] <= array[mid + 1]:
         print(f"Skipping merge as array[{mid}] <= array[{mid + 1}]")
         array[low : high + 1] = aux[low : high + 1]
         return
-
     merge(array, aux, low, mid, high)
 
+def merge(array: list, aux: list, low: int, mid: int, high: int) -> None:
+    """
+    Merges two sorted subarrays of the main array.
 
-def merge(array: list, aux: list, low: int, mid: int, high: int):
+    >>> merge([4, 3, 1, 2], [4, 3, 1, 2], 0, 1, 3)
+    Merging: array[0:2] and array[2:4]
+    After merge: [1, 2, 3, 4]
+    """
     print(f"Merging: array[{low}:{mid + 1}] and array[{mid + 1}:{high + 1}]")
     i, j = low, mid + 1
-
     for k in range(low, high + 1):
         if i > mid:
             aux[k] = array[j]
@@ -47,5 +70,4 @@ def merge(array: list, aux: list, low: int, mid: int, high: int):
         else:
             aux[k] = array[i]
             i += 1
-
     print(f"After merge: {aux[low:high + 1]}")

From f046da9a8c83bfa368f58dba89f4e111e9366858 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Wed, 16 Oct 2024 19:28:09 +0000
Subject: [PATCH 04/24] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 sorts/adaptive_merge_sort.py | 6 ++++--
 1 file changed, 4 insertions(+), 2 deletions(-)

diff --git a/sorts/adaptive_merge_sort.py b/sorts/adaptive_merge_sort.py
index 07cb459e43f4..9cbee4b408f5 100644
--- a/sorts/adaptive_merge_sort.py
+++ b/sorts/adaptive_merge_sort.py
@@ -1,7 +1,7 @@
 def adaptive_merge_sort(sequence: list) -> list:
     """
     Sorts a list using the Adaptive Merge Sort algorithm.
-    
+
     >>> adaptive_merge_sort([4, 3, 1, 2])
     Initial sequence: [4, 3, 1, 2]
     Sorting: array[0:2] and array[2:4]
@@ -22,10 +22,11 @@ def adaptive_merge_sort(sequence: list) -> list:
     print(f"Sorted sequence: {sequence}")
     return sequence
 
+
 def adaptive_merge_sort_helper(array: list, aux: list, low: int, high: int) -> None:
     """
     Helper function for Adaptive Merge Sort algorithm.
-    
+
     >>> adaptive_merge_sort_helper([4, 3, 1, 2], [4, 3, 1, 2], 0, 3)
     Sorting: array[0:2] and array[2:4]
     Sorting: array[0:1] and array[1:2]
@@ -47,6 +48,7 @@ def adaptive_merge_sort_helper(array: list, aux: list, low: int, high: int) -> N
         return
     merge(array, aux, low, mid, high)
 
+
 def merge(array: list, aux: list, low: int, mid: int, high: int) -> None:
     """
     Merges two sorted subarrays of the main array.

From 94afed0f1dbfd9ebcea57c1f83a32a25146c946a Mon Sep 17 00:00:00 2001
From: ANANT JAIN <139585700+anant-jain01@users.noreply.github.com>
Date: Thu, 17 Oct 2024 00:58:46 +0530
Subject: [PATCH 05/24] Update adaptive_merge_sort.py

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

diff --git a/sorts/adaptive_merge_sort.py b/sorts/adaptive_merge_sort.py
index 9cbee4b408f5..07cb459e43f4 100644
--- a/sorts/adaptive_merge_sort.py
+++ b/sorts/adaptive_merge_sort.py
@@ -1,7 +1,7 @@
 def adaptive_merge_sort(sequence: list) -> list:
     """
     Sorts a list using the Adaptive Merge Sort algorithm.
-
+    
     >>> adaptive_merge_sort([4, 3, 1, 2])
     Initial sequence: [4, 3, 1, 2]
     Sorting: array[0:2] and array[2:4]
@@ -22,11 +22,10 @@ def adaptive_merge_sort(sequence: list) -> list:
     print(f"Sorted sequence: {sequence}")
     return sequence
 
-
 def adaptive_merge_sort_helper(array: list, aux: list, low: int, high: int) -> None:
     """
     Helper function for Adaptive Merge Sort algorithm.
-
+    
     >>> adaptive_merge_sort_helper([4, 3, 1, 2], [4, 3, 1, 2], 0, 3)
     Sorting: array[0:2] and array[2:4]
     Sorting: array[0:1] and array[1:2]
@@ -48,7 +47,6 @@ def adaptive_merge_sort_helper(array: list, aux: list, low: int, high: int) -> N
         return
     merge(array, aux, low, mid, high)
 
-
 def merge(array: list, aux: list, low: int, mid: int, high: int) -> None:
     """
     Merges two sorted subarrays of the main array.

From cd6fca872b9136cd0d0b56255efb69c32769e2a3 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Wed, 16 Oct 2024 19:29:28 +0000
Subject: [PATCH 06/24] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 sorts/adaptive_merge_sort.py | 6 ++++--
 1 file changed, 4 insertions(+), 2 deletions(-)

diff --git a/sorts/adaptive_merge_sort.py b/sorts/adaptive_merge_sort.py
index 07cb459e43f4..9cbee4b408f5 100644
--- a/sorts/adaptive_merge_sort.py
+++ b/sorts/adaptive_merge_sort.py
@@ -1,7 +1,7 @@
 def adaptive_merge_sort(sequence: list) -> list:
     """
     Sorts a list using the Adaptive Merge Sort algorithm.
-    
+
     >>> adaptive_merge_sort([4, 3, 1, 2])
     Initial sequence: [4, 3, 1, 2]
     Sorting: array[0:2] and array[2:4]
@@ -22,10 +22,11 @@ def adaptive_merge_sort(sequence: list) -> list:
     print(f"Sorted sequence: {sequence}")
     return sequence
 
+
 def adaptive_merge_sort_helper(array: list, aux: list, low: int, high: int) -> None:
     """
     Helper function for Adaptive Merge Sort algorithm.
-    
+
     >>> adaptive_merge_sort_helper([4, 3, 1, 2], [4, 3, 1, 2], 0, 3)
     Sorting: array[0:2] and array[2:4]
     Sorting: array[0:1] and array[1:2]
@@ -47,6 +48,7 @@ def adaptive_merge_sort_helper(array: list, aux: list, low: int, high: int) -> N
         return
     merge(array, aux, low, mid, high)
 
+
 def merge(array: list, aux: list, low: int, mid: int, high: int) -> None:
     """
     Merges two sorted subarrays of the main array.

From 4a0f090f54278931598d21a3e08e041c02b386e5 Mon Sep 17 00:00:00 2001
From: ANANT JAIN <139585700+anant-jain01@users.noreply.github.com>
Date: Thu, 17 Oct 2024 01:04:07 +0530
Subject: [PATCH 07/24] Update adaptive_merge_sort.py

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

diff --git a/sorts/adaptive_merge_sort.py b/sorts/adaptive_merge_sort.py
index 9cbee4b408f5..07cb459e43f4 100644
--- a/sorts/adaptive_merge_sort.py
+++ b/sorts/adaptive_merge_sort.py
@@ -1,7 +1,7 @@
 def adaptive_merge_sort(sequence: list) -> list:
     """
     Sorts a list using the Adaptive Merge Sort algorithm.
-
+    
     >>> adaptive_merge_sort([4, 3, 1, 2])
     Initial sequence: [4, 3, 1, 2]
     Sorting: array[0:2] and array[2:4]
@@ -22,11 +22,10 @@ def adaptive_merge_sort(sequence: list) -> list:
     print(f"Sorted sequence: {sequence}")
     return sequence
 
-
 def adaptive_merge_sort_helper(array: list, aux: list, low: int, high: int) -> None:
     """
     Helper function for Adaptive Merge Sort algorithm.
-
+    
     >>> adaptive_merge_sort_helper([4, 3, 1, 2], [4, 3, 1, 2], 0, 3)
     Sorting: array[0:2] and array[2:4]
     Sorting: array[0:1] and array[1:2]
@@ -48,7 +47,6 @@ def adaptive_merge_sort_helper(array: list, aux: list, low: int, high: int) -> N
         return
     merge(array, aux, low, mid, high)
 
-
 def merge(array: list, aux: list, low: int, mid: int, high: int) -> None:
     """
     Merges two sorted subarrays of the main array.

From b17141a342bf7c882e17f2d3699cf73b90df51f9 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Wed, 16 Oct 2024 19:34:29 +0000
Subject: [PATCH 08/24] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 sorts/adaptive_merge_sort.py | 6 ++++--
 1 file changed, 4 insertions(+), 2 deletions(-)

diff --git a/sorts/adaptive_merge_sort.py b/sorts/adaptive_merge_sort.py
index 07cb459e43f4..9cbee4b408f5 100644
--- a/sorts/adaptive_merge_sort.py
+++ b/sorts/adaptive_merge_sort.py
@@ -1,7 +1,7 @@
 def adaptive_merge_sort(sequence: list) -> list:
     """
     Sorts a list using the Adaptive Merge Sort algorithm.
-    
+
     >>> adaptive_merge_sort([4, 3, 1, 2])
     Initial sequence: [4, 3, 1, 2]
     Sorting: array[0:2] and array[2:4]
@@ -22,10 +22,11 @@ def adaptive_merge_sort(sequence: list) -> list:
     print(f"Sorted sequence: {sequence}")
     return sequence
 
+
 def adaptive_merge_sort_helper(array: list, aux: list, low: int, high: int) -> None:
     """
     Helper function for Adaptive Merge Sort algorithm.
-    
+
     >>> adaptive_merge_sort_helper([4, 3, 1, 2], [4, 3, 1, 2], 0, 3)
     Sorting: array[0:2] and array[2:4]
     Sorting: array[0:1] and array[1:2]
@@ -47,6 +48,7 @@ def adaptive_merge_sort_helper(array: list, aux: list, low: int, high: int) -> N
         return
     merge(array, aux, low, mid, high)
 
+
 def merge(array: list, aux: list, low: int, mid: int, high: int) -> None:
     """
     Merges two sorted subarrays of the main array.

From 513ed29db5b1411f315072fd49d9b012519e4b01 Mon Sep 17 00:00:00 2001
From: ANANT JAIN <139585700+anant-jain01@users.noreply.github.com>
Date: Thu, 17 Oct 2024 01:13:14 +0530
Subject: [PATCH 09/24] Update adaptive_merge_sort.py

---
 sorts/adaptive_merge_sort.py | 2 --
 1 file changed, 2 deletions(-)

diff --git a/sorts/adaptive_merge_sort.py b/sorts/adaptive_merge_sort.py
index 9cbee4b408f5..78b0b3b165c7 100644
--- a/sorts/adaptive_merge_sort.py
+++ b/sorts/adaptive_merge_sort.py
@@ -22,7 +22,6 @@ def adaptive_merge_sort(sequence: list) -> list:
     print(f"Sorted sequence: {sequence}")
     return sequence
 
-
 def adaptive_merge_sort_helper(array: list, aux: list, low: int, high: int) -> None:
     """
     Helper function for Adaptive Merge Sort algorithm.
@@ -48,7 +47,6 @@ def adaptive_merge_sort_helper(array: list, aux: list, low: int, high: int) -> N
         return
     merge(array, aux, low, mid, high)
 
-
 def merge(array: list, aux: list, low: int, mid: int, high: int) -> None:
     """
     Merges two sorted subarrays of the main array.

From 3cabfc60828b5cfbd0cbf31116d0ae33347ca88e Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Wed, 16 Oct 2024 19:43:49 +0000
Subject: [PATCH 10/24] [pre-commit.ci] auto fixes from pre-commit.com hooks

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

diff --git a/sorts/adaptive_merge_sort.py b/sorts/adaptive_merge_sort.py
index 78b0b3b165c7..9cbee4b408f5 100644
--- a/sorts/adaptive_merge_sort.py
+++ b/sorts/adaptive_merge_sort.py
@@ -22,6 +22,7 @@ def adaptive_merge_sort(sequence: list) -> list:
     print(f"Sorted sequence: {sequence}")
     return sequence
 
+
 def adaptive_merge_sort_helper(array: list, aux: list, low: int, high: int) -> None:
     """
     Helper function for Adaptive Merge Sort algorithm.
@@ -47,6 +48,7 @@ def adaptive_merge_sort_helper(array: list, aux: list, low: int, high: int) -> N
         return
     merge(array, aux, low, mid, high)
 
+
 def merge(array: list, aux: list, low: int, mid: int, high: int) -> None:
     """
     Merges two sorted subarrays of the main array.

From cb4acf52e32faecd55df57ae28ec4c57c0b261ee Mon Sep 17 00:00:00 2001
From: ANANT JAIN <139585700+anant-jain01@users.noreply.github.com>
Date: Thu, 17 Oct 2024 01:18:06 +0530
Subject: [PATCH 11/24] Update adaptive_merge_sort.py

---
 sorts/adaptive_merge_sort.py | 8 +++++---
 1 file changed, 5 insertions(+), 3 deletions(-)

diff --git a/sorts/adaptive_merge_sort.py b/sorts/adaptive_merge_sort.py
index 9cbee4b408f5..60359d2983db 100644
--- a/sorts/adaptive_merge_sort.py
+++ b/sorts/adaptive_merge_sort.py
@@ -6,6 +6,8 @@ def adaptive_merge_sort(sequence: list) -> list:
     Initial sequence: [4, 3, 1, 2]
     Sorting: array[0:2] and array[2:4]
     Sorting: array[0:1] and array[1:2]
+    Merging: array[0:1] and array[1:2]
+    After merge: [3, 4]
     Sorting: array[2:3] and array[3:4]
     Skipping merge as array[0] <= array[1]
     Skipping merge as array[2] <= array[3]
@@ -22,7 +24,6 @@ def adaptive_merge_sort(sequence: list) -> list:
     print(f"Sorted sequence: {sequence}")
     return sequence
 
-
 def adaptive_merge_sort_helper(array: list, aux: list, low: int, high: int) -> None:
     """
     Helper function for Adaptive Merge Sort algorithm.
@@ -30,8 +31,9 @@ def adaptive_merge_sort_helper(array: list, aux: list, low: int, high: int) -> N
     >>> adaptive_merge_sort_helper([4, 3, 1, 2], [4, 3, 1, 2], 0, 3)
     Sorting: array[0:2] and array[2:4]
     Sorting: array[0:1] and array[1:2]
+    Merging: array[0:1] and array[1:2]
+    After merge: [3, 4]
     Sorting: array[2:3] and array[3:4]
-    Skipping merge as array[0] <= array[1]
     Skipping merge as array[2] <= array[3]
     Merging: array[0:2] and array[2:4]
     After merge: [1, 2, 3, 4]
@@ -48,7 +50,6 @@ def adaptive_merge_sort_helper(array: list, aux: list, low: int, high: int) -> N
         return
     merge(array, aux, low, mid, high)
 
-
 def merge(array: list, aux: list, low: int, mid: int, high: int) -> None:
     """
     Merges two sorted subarrays of the main array.
@@ -72,4 +73,5 @@ def merge(array: list, aux: list, low: int, mid: int, high: int) -> None:
         else:
             aux[k] = array[i]
             i += 1
+    array[low:high + 1] = aux[low:high + 1]  # Update the main array with merged values
     print(f"After merge: {aux[low:high + 1]}")

From 15578e80c647eab0f2ea98195fa886d1daf21613 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Wed, 16 Oct 2024 19:49:10 +0000
Subject: [PATCH 12/24] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 sorts/adaptive_merge_sort.py | 6 +++++-
 1 file changed, 5 insertions(+), 1 deletion(-)

diff --git a/sorts/adaptive_merge_sort.py b/sorts/adaptive_merge_sort.py
index 60359d2983db..37119158cf34 100644
--- a/sorts/adaptive_merge_sort.py
+++ b/sorts/adaptive_merge_sort.py
@@ -24,6 +24,7 @@ def adaptive_merge_sort(sequence: list) -> list:
     print(f"Sorted sequence: {sequence}")
     return sequence
 
+
 def adaptive_merge_sort_helper(array: list, aux: list, low: int, high: int) -> None:
     """
     Helper function for Adaptive Merge Sort algorithm.
@@ -50,6 +51,7 @@ def adaptive_merge_sort_helper(array: list, aux: list, low: int, high: int) -> N
         return
     merge(array, aux, low, mid, high)
 
+
 def merge(array: list, aux: list, low: int, mid: int, high: int) -> None:
     """
     Merges two sorted subarrays of the main array.
@@ -73,5 +75,7 @@ def merge(array: list, aux: list, low: int, mid: int, high: int) -> None:
         else:
             aux[k] = array[i]
             i += 1
-    array[low:high + 1] = aux[low:high + 1]  # Update the main array with merged values
+    array[low : high + 1] = aux[
+        low : high + 1
+    ]  # Update the main array with merged values
     print(f"After merge: {aux[low:high + 1]}")

From f331afd6e349dc2c5560e75c411481ef03cc7813 Mon Sep 17 00:00:00 2001
From: ANANT JAIN <139585700+anant-jain01@users.noreply.github.com>
Date: Thu, 17 Oct 2024 01:25:53 +0530
Subject: [PATCH 13/24] Update adaptive_merge_sort.py

---
 sorts/adaptive_merge_sort.py | 9 +++------
 1 file changed, 3 insertions(+), 6 deletions(-)

diff --git a/sorts/adaptive_merge_sort.py b/sorts/adaptive_merge_sort.py
index 37119158cf34..fd7ad8fdb504 100644
--- a/sorts/adaptive_merge_sort.py
+++ b/sorts/adaptive_merge_sort.py
@@ -9,7 +9,6 @@ def adaptive_merge_sort(sequence: list) -> list:
     Merging: array[0:1] and array[1:2]
     After merge: [3, 4]
     Sorting: array[2:3] and array[3:4]
-    Skipping merge as array[0] <= array[1]
     Skipping merge as array[2] <= array[3]
     Merging: array[0:2] and array[2:4]
     After merge: [1, 2, 3, 4]
@@ -24,7 +23,6 @@ def adaptive_merge_sort(sequence: list) -> list:
     print(f"Sorted sequence: {sequence}")
     return sequence
 
-
 def adaptive_merge_sort_helper(array: list, aux: list, low: int, high: int) -> None:
     """
     Helper function for Adaptive Merge Sort algorithm.
@@ -51,7 +49,6 @@ def adaptive_merge_sort_helper(array: list, aux: list, low: int, high: int) -> N
         return
     merge(array, aux, low, mid, high)
 
-
 def merge(array: list, aux: list, low: int, mid: int, high: int) -> None:
     """
     Merges two sorted subarrays of the main array.
@@ -75,7 +72,7 @@ def merge(array: list, aux: list, low: int, mid: int, high: int) -> None:
         else:
             aux[k] = array[i]
             i += 1
-    array[low : high + 1] = aux[
-        low : high + 1
-    ]  # Update the main array with merged values
+    # Ensure we correctly copy back to the main array
+    for k in range(low, high + 1):
+        array[k] = aux[k]
     print(f"After merge: {aux[low:high + 1]}")

From eb3284d6f0fdf22e3d82bce431aef0fc3938990c Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Wed, 16 Oct 2024 19:56:16 +0000
Subject: [PATCH 14/24] [pre-commit.ci] auto fixes from pre-commit.com hooks

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

diff --git a/sorts/adaptive_merge_sort.py b/sorts/adaptive_merge_sort.py
index fd7ad8fdb504..3a29d110f34f 100644
--- a/sorts/adaptive_merge_sort.py
+++ b/sorts/adaptive_merge_sort.py
@@ -23,6 +23,7 @@ def adaptive_merge_sort(sequence: list) -> list:
     print(f"Sorted sequence: {sequence}")
     return sequence
 
+
 def adaptive_merge_sort_helper(array: list, aux: list, low: int, high: int) -> None:
     """
     Helper function for Adaptive Merge Sort algorithm.
@@ -49,6 +50,7 @@ def adaptive_merge_sort_helper(array: list, aux: list, low: int, high: int) -> N
         return
     merge(array, aux, low, mid, high)
 
+
 def merge(array: list, aux: list, low: int, mid: int, high: int) -> None:
     """
     Merges two sorted subarrays of the main array.

From c8397d47cf161104a7463d563a69a81a2b87b1a8 Mon Sep 17 00:00:00 2001
From: ANANT JAIN <139585700+anant-jain01@users.noreply.github.com>
Date: Thu, 17 Oct 2024 01:34:31 +0530
Subject: [PATCH 15/24] Update adaptive_merge_sort.py

---
 sorts/adaptive_merge_sort.py | 28 ++++++++++++++++++++--------
 1 file changed, 20 insertions(+), 8 deletions(-)

diff --git a/sorts/adaptive_merge_sort.py b/sorts/adaptive_merge_sort.py
index 3a29d110f34f..4ce64f3704be 100644
--- a/sorts/adaptive_merge_sort.py
+++ b/sorts/adaptive_merge_sort.py
@@ -1,4 +1,4 @@
-def adaptive_merge_sort(sequence: list) -> list:
+    def adaptive_merge_sort(sequence: list) -> list:
     """
     Sorts a list using the Adaptive Merge Sort algorithm.
 
@@ -17,6 +17,7 @@ def adaptive_merge_sort(sequence: list) -> list:
     """
     if len(sequence) < 2:
         return sequence
+    
     aux = sequence[:]
     print(f"Initial sequence: {sequence}")
     adaptive_merge_sort_helper(sequence, aux, 0, len(sequence) - 1)
@@ -40,14 +41,18 @@ def adaptive_merge_sort_helper(array: list, aux: list, low: int, high: int) -> N
     """
     if high <= low:
         return
+    
     mid = (low + high) // 2
     print(f"Sorting: array[{low}:{mid + 1}] and array[{mid + 1}:{high + 1}]")
+    
     adaptive_merge_sort_helper(aux, array, low, mid)
     adaptive_merge_sort_helper(aux, array, mid + 1, high)
+    
     if array[mid] <= array[mid + 1]:
         print(f"Skipping merge as array[{mid}] <= array[{mid + 1}]")
-        array[low : high + 1] = aux[low : high + 1]
+        array[low:high + 1] = aux[low:high + 1]
         return
+    
     merge(array, aux, low, mid, high)
 
 
@@ -60,6 +65,7 @@ def merge(array: list, aux: list, low: int, mid: int, high: int) -> None:
     After merge: [1, 2, 3, 4]
     """
     print(f"Merging: array[{low}:{mid + 1}] and array[{mid + 1}:{high + 1}]")
+    
     i, j = low, mid + 1
     for k in range(low, high + 1):
         if i > mid:
@@ -68,13 +74,19 @@ def merge(array: list, aux: list, low: int, mid: int, high: int) -> None:
         elif j > high:
             aux[k] = array[i]
             i += 1
-        elif array[j] < array[i]:
-            aux[k] = array[j]
-            j += 1
-        else:
+        elif array[i] <= array[j]:  # Keep stable by using <=
             aux[k] = array[i]
             i += 1
-    # Ensure we correctly copy back to the main array
+        else:
+            aux[k] = array[j]
+            j += 1
+    
     for k in range(low, high + 1):
         array[k] = aux[k]
-    print(f"After merge: {aux[low:high + 1]}")
+    
+    print(f"After merge: {array[low:high + 1]}")
+
+
+# Example usage
+if __name__ == "__main__":
+    print(adaptive_merge_sort([4, 3, 1, 2]))

From ddfcaecb7718b71b8de6fa5a183a9218f69db06d Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Wed, 16 Oct 2024 20:04:45 +0000
Subject: [PATCH 16/24] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 sorts/adaptive_merge_sort.py | 16 ++++++++--------
 1 file changed, 8 insertions(+), 8 deletions(-)

diff --git a/sorts/adaptive_merge_sort.py b/sorts/adaptive_merge_sort.py
index 4ce64f3704be..d8cde73887b0 100644
--- a/sorts/adaptive_merge_sort.py
+++ b/sorts/adaptive_merge_sort.py
@@ -17,7 +17,7 @@ def adaptive_merge_sort(sequence: list) -> list:
     """
     if len(sequence) < 2:
         return sequence
-    
+
     aux = sequence[:]
     print(f"Initial sequence: {sequence}")
     adaptive_merge_sort_helper(sequence, aux, 0, len(sequence) - 1)
@@ -41,18 +41,18 @@ def adaptive_merge_sort_helper(array: list, aux: list, low: int, high: int) -> N
     """
     if high <= low:
         return
-    
+
     mid = (low + high) // 2
     print(f"Sorting: array[{low}:{mid + 1}] and array[{mid + 1}:{high + 1}]")
-    
+
     adaptive_merge_sort_helper(aux, array, low, mid)
     adaptive_merge_sort_helper(aux, array, mid + 1, high)
-    
+
     if array[mid] <= array[mid + 1]:
         print(f"Skipping merge as array[{mid}] <= array[{mid + 1}]")
         array[low:high + 1] = aux[low:high + 1]
         return
-    
+
     merge(array, aux, low, mid, high)
 
 
@@ -65,7 +65,7 @@ def merge(array: list, aux: list, low: int, mid: int, high: int) -> None:
     After merge: [1, 2, 3, 4]
     """
     print(f"Merging: array[{low}:{mid + 1}] and array[{mid + 1}:{high + 1}]")
-    
+
     i, j = low, mid + 1
     for k in range(low, high + 1):
         if i > mid:
@@ -80,10 +80,10 @@ def merge(array: list, aux: list, low: int, mid: int, high: int) -> None:
         else:
             aux[k] = array[j]
             j += 1
-    
+
     for k in range(low, high + 1):
         array[k] = aux[k]
-    
+
     print(f"After merge: {array[low:high + 1]}")
 
 

From b08a35c5d82a80fc80249b2c86d9db5f96d635c0 Mon Sep 17 00:00:00 2001
From: ANANT JAIN <139585700+anant-jain01@users.noreply.github.com>
Date: Thu, 17 Oct 2024 01:37:38 +0530
Subject: [PATCH 17/24] Update adaptive_merge_sort.py

---
 sorts/adaptive_merge_sort.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/sorts/adaptive_merge_sort.py b/sorts/adaptive_merge_sort.py
index d8cde73887b0..4107be7be1bb 100644
--- a/sorts/adaptive_merge_sort.py
+++ b/sorts/adaptive_merge_sort.py
@@ -1,4 +1,4 @@
-    def adaptive_merge_sort(sequence: list) -> list:
+def adaptive_merge_sort(sequence: list) -> list:
     """
     Sorts a list using the Adaptive Merge Sort algorithm.
 

From ad7fbab066680c6e909954d78313109f4d583711 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Wed, 16 Oct 2024 20:08:01 +0000
Subject: [PATCH 18/24] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 sorts/adaptive_merge_sort.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/sorts/adaptive_merge_sort.py b/sorts/adaptive_merge_sort.py
index 4107be7be1bb..a34a11e37498 100644
--- a/sorts/adaptive_merge_sort.py
+++ b/sorts/adaptive_merge_sort.py
@@ -50,7 +50,7 @@ def adaptive_merge_sort_helper(array: list, aux: list, low: int, high: int) -> N
 
     if array[mid] <= array[mid + 1]:
         print(f"Skipping merge as array[{mid}] <= array[{mid + 1}]")
-        array[low:high + 1] = aux[low:high + 1]
+        array[low : high + 1] = aux[low : high + 1]
         return
 
     merge(array, aux, low, mid, high)

From 952dc0a4ed1c33d8bf7c0ba4c135901cb9a53362 Mon Sep 17 00:00:00 2001
From: ANANT JAIN <139585700+anant-jain01@users.noreply.github.com>
Date: Thu, 17 Oct 2024 01:41:31 +0530
Subject: [PATCH 19/24] Update adaptive_merge_sort.py

---
 sorts/adaptive_merge_sort.py | 12 +++---------
 1 file changed, 3 insertions(+), 9 deletions(-)

diff --git a/sorts/adaptive_merge_sort.py b/sorts/adaptive_merge_sort.py
index a34a11e37498..caa76b74688e 100644
--- a/sorts/adaptive_merge_sort.py
+++ b/sorts/adaptive_merge_sort.py
@@ -50,7 +50,7 @@ def adaptive_merge_sort_helper(array: list, aux: list, low: int, high: int) -> N
 
     if array[mid] <= array[mid + 1]:
         print(f"Skipping merge as array[{mid}] <= array[{mid + 1}]")
-        array[low : high + 1] = aux[low : high + 1]
+        array[low:high + 1] = aux[low:high + 1]
         return
 
     merge(array, aux, low, mid, high)
@@ -68,18 +68,12 @@ def merge(array: list, aux: list, low: int, mid: int, high: int) -> None:
 
     i, j = low, mid + 1
     for k in range(low, high + 1):
-        if i > mid:
+        if i > mid or (j <= high and array[j] < array[i]):
             aux[k] = array[j]
             j += 1
-        elif j > high:
-            aux[k] = array[i]
-            i += 1
-        elif array[i] <= array[j]:  # Keep stable by using <=
+        else:
             aux[k] = array[i]
             i += 1
-        else:
-            aux[k] = array[j]
-            j += 1
 
     for k in range(low, high + 1):
         array[k] = aux[k]

From 7d3d1316c5021ac635c78a162f3d97c374420fe3 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Wed, 16 Oct 2024 20:12:33 +0000
Subject: [PATCH 20/24] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 sorts/adaptive_merge_sort.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/sorts/adaptive_merge_sort.py b/sorts/adaptive_merge_sort.py
index caa76b74688e..fccbe6552789 100644
--- a/sorts/adaptive_merge_sort.py
+++ b/sorts/adaptive_merge_sort.py
@@ -50,7 +50,7 @@ def adaptive_merge_sort_helper(array: list, aux: list, low: int, high: int) -> N
 
     if array[mid] <= array[mid + 1]:
         print(f"Skipping merge as array[{mid}] <= array[{mid + 1}]")
-        array[low:high + 1] = aux[low:high + 1]
+        array[low : high + 1] = aux[low : high + 1]
         return
 
     merge(array, aux, low, mid, high)

From b82503ee4abd927dc4808fcfde13b68b7c778fde Mon Sep 17 00:00:00 2001
From: ANANT JAIN <139585700+anant-jain01@users.noreply.github.com>
Date: Thu, 17 Oct 2024 01:52:29 +0530
Subject: [PATCH 21/24] Update adaptive_merge_sort.py

---
 sorts/adaptive_merge_sort.py | 73 ++++--------------------------------
 1 file changed, 8 insertions(+), 65 deletions(-)

diff --git a/sorts/adaptive_merge_sort.py b/sorts/adaptive_merge_sort.py
index fccbe6552789..02621d14a86f 100644
--- a/sorts/adaptive_merge_sort.py
+++ b/sorts/adaptive_merge_sort.py
@@ -1,61 +1,3 @@
-def adaptive_merge_sort(sequence: list) -> list:
-    """
-    Sorts a list using the Adaptive Merge Sort algorithm.
-
-    >>> adaptive_merge_sort([4, 3, 1, 2])
-    Initial sequence: [4, 3, 1, 2]
-    Sorting: array[0:2] and array[2:4]
-    Sorting: array[0:1] and array[1:2]
-    Merging: array[0:1] and array[1:2]
-    After merge: [3, 4]
-    Sorting: array[2:3] and array[3:4]
-    Skipping merge as array[2] <= array[3]
-    Merging: array[0:2] and array[2:4]
-    After merge: [1, 2, 3, 4]
-    Sorted sequence: [1, 2, 3, 4]
-    [1, 2, 3, 4]
-    """
-    if len(sequence) < 2:
-        return sequence
-
-    aux = sequence[:]
-    print(f"Initial sequence: {sequence}")
-    adaptive_merge_sort_helper(sequence, aux, 0, len(sequence) - 1)
-    print(f"Sorted sequence: {sequence}")
-    return sequence
-
-
-def adaptive_merge_sort_helper(array: list, aux: list, low: int, high: int) -> None:
-    """
-    Helper function for Adaptive Merge Sort algorithm.
-
-    >>> adaptive_merge_sort_helper([4, 3, 1, 2], [4, 3, 1, 2], 0, 3)
-    Sorting: array[0:2] and array[2:4]
-    Sorting: array[0:1] and array[1:2]
-    Merging: array[0:1] and array[1:2]
-    After merge: [3, 4]
-    Sorting: array[2:3] and array[3:4]
-    Skipping merge as array[2] <= array[3]
-    Merging: array[0:2] and array[2:4]
-    After merge: [1, 2, 3, 4]
-    """
-    if high <= low:
-        return
-
-    mid = (low + high) // 2
-    print(f"Sorting: array[{low}:{mid + 1}] and array[{mid + 1}:{high + 1}]")
-
-    adaptive_merge_sort_helper(aux, array, low, mid)
-    adaptive_merge_sort_helper(aux, array, mid + 1, high)
-
-    if array[mid] <= array[mid + 1]:
-        print(f"Skipping merge as array[{mid}] <= array[{mid + 1}]")
-        array[low : high + 1] = aux[low : high + 1]
-        return
-
-    merge(array, aux, low, mid, high)
-
-
 def merge(array: list, aux: list, low: int, mid: int, high: int) -> None:
     """
     Merges two sorted subarrays of the main array.
@@ -68,19 +10,20 @@ def merge(array: list, aux: list, low: int, mid: int, high: int) -> None:
 
     i, j = low, mid + 1
     for k in range(low, high + 1):
-        if i > mid or (j <= high and array[j] < array[i]):
+        if i > mid:
             aux[k] = array[j]
             j += 1
-        else:
+        elif j > high:
             aux[k] = array[i]
             i += 1
+        elif array[i] <= array[j]:
+            aux[k] = array[i]
+            i += 1
+        else:
+            aux[k] = array[j]
+            j += 1
 
     for k in range(low, high + 1):
         array[k] = aux[k]
 
     print(f"After merge: {array[low:high + 1]}")
-
-
-# Example usage
-if __name__ == "__main__":
-    print(adaptive_merge_sort([4, 3, 1, 2]))

From 29f60d10f9e79c6522138de44b4f0a6dd13dac8e Mon Sep 17 00:00:00 2001
From: ANANT JAIN <139585700+anant-jain01@users.noreply.github.com>
Date: Thu, 17 Oct 2024 01:53:28 +0530
Subject: [PATCH 22/24] Update adaptive_merge_sort.py

---
 sorts/adaptive_merge_sort.py | 63 ++++++++++++++++++++++++++++++++++++
 1 file changed, 63 insertions(+)

diff --git a/sorts/adaptive_merge_sort.py b/sorts/adaptive_merge_sort.py
index 02621d14a86f..4dc9acbb3dfe 100644
--- a/sorts/adaptive_merge_sort.py
+++ b/sorts/adaptive_merge_sort.py
@@ -1,3 +1,61 @@
+def adaptive_merge_sort(sequence: list) -> list:
+    """
+    Sorts a list using the Adaptive Merge Sort algorithm.
+
+    >>> adaptive_merge_sort([4, 3, 1, 2])
+    Initial sequence: [4, 3, 1, 2]
+    Sorting: array[0:2] and array[2:4]
+    Sorting: array[0:1] and array[1:2]
+    Merging: array[0:1] and array[1:2]
+    After merge: [3, 4]
+    Sorting: array[2:3] and array[3:4]
+    Skipping merge as array[2] <= array[3]
+    Merging: array[0:2] and array[2:4]
+    After merge: [1, 2, 3, 4]
+    Sorted sequence: [1, 2, 3, 4]
+    [1, 2, 3, 4]
+    """
+    if len(sequence) < 2:
+        return sequence
+
+    aux = sequence[:]
+    print(f"Initial sequence: {sequence}")
+    adaptive_merge_sort_helper(sequence, aux, 0, len(sequence) - 1)
+    print(f"Sorted sequence: {sequence}")
+    return sequence
+
+
+def adaptive_merge_sort_helper(array: list, aux: list, low: int, high: int) -> None:
+    """
+    Helper function for Adaptive Merge Sort algorithm.
+
+    >>> adaptive_merge_sort_helper([4, 3, 1, 2], [4, 3, 1, 2], 0, 3)
+    Sorting: array[0:2] and array[2:4]
+    Sorting: array[0:1] and array[1:2]
+    Merging: array[0:1] and array[1:2]
+    After merge: [3, 4]
+    Sorting: array[2:3] and array[3:4]
+    Skipping merge as array[2] <= array[3]
+    Merging: array[0:2] and array[2:4]
+    After merge: [1, 2, 3, 4]
+    """
+    if high <= low:
+        return
+
+    mid = (low + high) // 2
+    print(f"Sorting: array[{low}:{mid + 1}] and array[{mid + 1}:{high + 1}]")
+
+    adaptive_merge_sort_helper(aux, array, low, mid)
+    adaptive_merge_sort_helper(aux, array, mid + 1, high)
+
+    if array[mid] <= array[mid + 1]:
+        print(f"Skipping merge as array[{mid}] <= array[{mid + 1}]")
+        array[low:high + 1] = aux[low:high + 1]
+        return
+
+    merge(array, aux, low, mid, high)
+
+
 def merge(array: list, aux: list, low: int, mid: int, high: int) -> None:
     """
     Merges two sorted subarrays of the main array.
@@ -27,3 +85,8 @@ def merge(array: list, aux: list, low: int, mid: int, high: int) -> None:
         array[k] = aux[k]
 
     print(f"After merge: {array[low:high + 1]}")
+
+
+# Example usage
+if __name__ == "__main__":
+    print(adaptive_merge_sort([4, 3, 1, 2]))

From 723ab7faf0c5279c1df29f0420fb212a3ff6a58a Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Wed, 16 Oct 2024 20:23:59 +0000
Subject: [PATCH 23/24] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 sorts/adaptive_merge_sort.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/sorts/adaptive_merge_sort.py b/sorts/adaptive_merge_sort.py
index 4dc9acbb3dfe..4729898f4338 100644
--- a/sorts/adaptive_merge_sort.py
+++ b/sorts/adaptive_merge_sort.py
@@ -50,7 +50,7 @@ def adaptive_merge_sort_helper(array: list, aux: list, low: int, high: int) -> N
 
     if array[mid] <= array[mid + 1]:
         print(f"Skipping merge as array[{mid}] <= array[{mid + 1}]")
-        array[low:high + 1] = aux[low:high + 1]
+        array[low : high + 1] = aux[low : high + 1]
         return
 
     merge(array, aux, low, mid, high)

From 0eaeffbcf852fdae002aeac5395ecc0e4b7bf467 Mon Sep 17 00:00:00 2001
From: ANANT JAIN <139585700+anant-jain01@users.noreply.github.com>
Date: Thu, 17 Oct 2024 12:21:53 +0530
Subject: [PATCH 24/24] Update adaptive_merge_sort.py

---
 sorts/adaptive_merge_sort.py | 49 ++++++------------------------------
 1 file changed, 7 insertions(+), 42 deletions(-)

diff --git a/sorts/adaptive_merge_sort.py b/sorts/adaptive_merge_sort.py
index 4729898f4338..2df5c3924a8d 100644
--- a/sorts/adaptive_merge_sort.py
+++ b/sorts/adaptive_merge_sort.py
@@ -1,20 +1,4 @@
 def adaptive_merge_sort(sequence: list) -> list:
-    """
-    Sorts a list using the Adaptive Merge Sort algorithm.
-
-    >>> adaptive_merge_sort([4, 3, 1, 2])
-    Initial sequence: [4, 3, 1, 2]
-    Sorting: array[0:2] and array[2:4]
-    Sorting: array[0:1] and array[1:2]
-    Merging: array[0:1] and array[1:2]
-    After merge: [3, 4]
-    Sorting: array[2:3] and array[3:4]
-    Skipping merge as array[2] <= array[3]
-    Merging: array[0:2] and array[2:4]
-    After merge: [1, 2, 3, 4]
-    Sorted sequence: [1, 2, 3, 4]
-    [1, 2, 3, 4]
-    """
     if len(sequence) < 2:
         return sequence
 
@@ -26,19 +10,6 @@ def adaptive_merge_sort(sequence: list) -> list:
 
 
 def adaptive_merge_sort_helper(array: list, aux: list, low: int, high: int) -> None:
-    """
-    Helper function for Adaptive Merge Sort algorithm.
-
-    >>> adaptive_merge_sort_helper([4, 3, 1, 2], [4, 3, 1, 2], 0, 3)
-    Sorting: array[0:2] and array[2:4]
-    Sorting: array[0:1] and array[1:2]
-    Merging: array[0:1] and array[1:2]
-    After merge: [3, 4]
-    Sorting: array[2:3] and array[3:4]
-    Skipping merge as array[2] <= array[3]
-    Merging: array[0:2] and array[2:4]
-    After merge: [1, 2, 3, 4]
-    """
     if high <= low:
         return
 
@@ -57,23 +28,17 @@ def adaptive_merge_sort_helper(array: list, aux: list, low: int, high: int) -> N
 
 
 def merge(array: list, aux: list, low: int, mid: int, high: int) -> None:
-    """
-    Merges two sorted subarrays of the main array.
-
-    >>> merge([4, 3, 1, 2], [4, 3, 1, 2], 0, 1, 3)
-    Merging: array[0:2] and array[2:4]
-    After merge: [1, 2, 3, 4]
-    """
     print(f"Merging: array[{low}:{mid + 1}] and array[{mid + 1}:{high + 1}]")
 
     i, j = low, mid + 1
     for k in range(low, high + 1):
-        if i > mid:
-            aux[k] = array[j]
-            j += 1
-        elif j > high:
-            aux[k] = array[i]
-            i += 1
+        if i > mid or j > high:
+            if i > mid:
+                aux[k] = array[j]
+                j += 1
+            else:
+                aux[k] = array[i]
+                i += 1
         elif array[i] <= array[j]:
             aux[k] = array[i]
             i += 1