From 08d78ee3583a8614287328b9e0cf1267d22e332c Mon Sep 17 00:00:00 2001
From: Kushagra9399 <146541055+Kushagra9399@users.noreply.github.com>
Date: Mon, 10 Mar 2025 21:51:31 +0530
Subject: [PATCH 01/15] Update test_algorithms.py

---
 .../tests/test_algorithms.py                  | 75 ++++++++++++++++++-
 1 file changed, 74 insertions(+), 1 deletion(-)

diff --git a/pydatastructs/linear_data_structures/tests/test_algorithms.py b/pydatastructs/linear_data_structures/tests/test_algorithms.py
index 46609544b..51991ac12 100644
--- a/pydatastructs/linear_data_structures/tests/test_algorithms.py
+++ b/pydatastructs/linear_data_structures/tests/test_algorithms.py
@@ -5,7 +5,7 @@
     cocktail_shaker_sort, quick_sort, longest_common_subsequence, is_ordered,
     upper_bound, lower_bound, longest_increasing_subsequence, next_permutation,
     prev_permutation, bubble_sort, linear_search, binary_search, jump_search,
-    selection_sort, insertion_sort, intro_sort, Backend)
+    selection_sort, insertion_sort, intro_sort, radix_sort, Backend)
 
 from pydatastructs.utils.raises_util import raises
 import random
@@ -414,3 +414,76 @@ def test_binary_search():
 def test_jump_search():
     _test_common_search(jump_search)
     _test_common_search(jump_search, backend=Backend.CPP)
+
+def test_radix_sort():
+    random.seed(1000)
+
+    # Test with DynamicOneDimensionalArray
+    n = random.randint(10, 20)
+    arr = DynamicOneDimensionalArray(int, 0)
+    generated_ints = []
+    for _ in range(n):
+        integer = random.randint(1, 1000)
+        generated_ints.append(integer)
+        arr.append(integer)
+    for _ in range(n//3):
+        integer = random.randint(0, n//2)
+        generated_ints.append(integer)
+        arr.delete(integer)
+    expected_arr_1 = [686, 779, 102, 134, 362, 448,
+                    480, 548, None, None, None,
+                    228, 688, 247, 373, 696, None,
+                    None, None, None, None, None,
+                    None, None, None, None, None,
+                    None, None, None, None]
+    radix_sort(arr, start=2, end=10)
+    assert arr._data == expected_arr_1
+    radix_sort(arr)
+    expected_arr_2 = [102, 134, 228, 247, 362, 373, 448,
+                    480, 548, 686, 688, 696, 779,
+                    None, None, None, None, None, None,
+                    None, None, None, None, None,
+                    None, None, None, None, None, None, None]
+    assert arr._data == expected_arr_2
+    assert (arr._last_pos_filled, arr._num, arr._size) == (12, 13, 31)
+
+    # Test with DynamicOneDimensionalArray (CPP backend)
+    arr = DynamicOneDimensionalArray(int, 0, backend=Backend.CPP)
+    int_idx = 0
+    for _ in range(n):
+        arr.append(generated_ints[int_idx])
+        int_idx += 1
+    for _ in range(n//3):
+        arr.delete(generated_ints[int_idx])
+        int_idx += 1
+    radix_sort(arr, start=2, end=10)
+    for i in range(len(expected_arr_1)):
+        assert arr[i] == expected_arr_1[i]
+    radix_sort(arr)
+    for i in range(len(expected_arr_2)):
+        assert arr[i] == expected_arr_2[i]
+    assert (arr._last_pos_filled, arr._num, arr.size) == (12, 13, 31)
+
+    # Test with OneDimensionalArray
+    n = random.randint(10, 20)
+    arr = OneDimensionalArray(int, n)
+    generated_ints.clear()
+    for i in range(n):
+        integer = random.randint(1, 1000)
+        arr[i] = integer
+        generated_ints.append(integer)
+    expected_arr_3 = [42, 695, 147, 500, 768,
+                    998, 473, 732, 728, 426,
+                    709, 910]
+    radix_sort(arr, start=2, end=5)
+    assert arr._data == expected_arr_3
+
+    # Test with OneDimensionalArray (CPP backend)
+    arr = OneDimensionalArray(int, n, backend=Backend.CPP)
+    int_idx = 0
+    for i in range(n):
+        arr[i] = generated_ints[int_idx]
+        int_idx += 1
+    radix_sort(arr, start=2, end=5)
+    for i in range(len(expected_arr_3)):
+        assert arr[i] == expected_arr_3

From 0750d07a1eec8d5588ba42af114145e0fffd8614 Mon Sep 17 00:00:00 2001
From: Kushagra9399 <146541055+Kushagra9399@users.noreply.github.com>
Date: Mon, 10 Mar 2025 16:38:57 +0000
Subject: [PATCH 02/15] Adding radix sort algorithm #603

---
 oryx-build-commands.txt                       |  2 +
 .../linear_data_structures/__init__.py        |  3 +-
 .../linear_data_structures/algorithms.py      | 62 +++++++++++++++++++
 3 files changed, 66 insertions(+), 1 deletion(-)
 create mode 100644 oryx-build-commands.txt

diff --git a/oryx-build-commands.txt b/oryx-build-commands.txt
new file mode 100644
index 000000000..d647bdf7f
--- /dev/null
+++ b/oryx-build-commands.txt
@@ -0,0 +1,2 @@
+PlatformWithVersion=Python 
+BuildCommands=conda env create --file environment.yml --prefix ./venv --quiet
diff --git a/pydatastructs/linear_data_structures/__init__.py b/pydatastructs/linear_data_structures/__init__.py
index 057adc169..beb7cc82f 100644
--- a/pydatastructs/linear_data_structures/__init__.py
+++ b/pydatastructs/linear_data_structures/__init__.py
@@ -47,6 +47,7 @@
     jump_search,
     selection_sort,
     insertion_sort,
-    intro_sort
+    intro_sort,
+    radix_sort
 )
 __all__.extend(algorithms.__all__)
diff --git a/pydatastructs/linear_data_structures/algorithms.py b/pydatastructs/linear_data_structures/algorithms.py
index 792bce855..7a5b17b9f 100644
--- a/pydatastructs/linear_data_structures/algorithms.py
+++ b/pydatastructs/linear_data_structures/algorithms.py
@@ -1850,3 +1850,65 @@ def partition(array, lower, upper):
         intro_sort(array, start=p+1, end=upper,  maxdepth=maxdepth-1, ins_threshold=ins_threshold)
 
         return array
+
+def _count_sort_for_radix(array, exp, comp):
+    n = len(array)
+    output = [None] * n
+    count = [0] * 10
+
+    for i in range(n):
+        index = (array[i] // exp) % 10
+        count[index] += 1
+
+    for i in range(1, 10):
+        count[i] += count[i - 1]
+
+    i = n - 1
+    while i >= 0:
+        index = (array[i] // exp) % 10
+        output[count[index] - 1] = array[i]
+        count[index] -= 1
+        i -= 1
+
+    for i in range(n):
+        array[i] = output[i]
+
+def radix_sort(array, comp=lambda u, v: u <= v, **kwargs):
+    """
+    Implements Radix Sort.
+
+    Parameters
+    ==========
+    array: Array
+        The array which is to be sorted.
+    comp: lambda/function
+        The comparator which is to be used
+        for sorting. Optional, by default, less than or
+        equal to is used for comparing two
+        values.
+
+    Examples
+    ========
+    >>> from pydatastructs import OneDimensionalArray, radix_sort
+    >>> arr = OneDimensionalArray(int,[170, 45, 75, 90, 802, 24, 2, 66])
+    >>> radix_sort(arr)
+    >>> [arr[0], arr[1], arr[2], arr[3], arr[4], arr[5], arr[6], arr[7]]
+    [2, 24, 45, 66, 75, 90, 170, 802]
+
+    References
+    ==========
+    .. [1] https://en.wikipedia.org/wiki/Radix_sort
+    """
+    # Raise error if not Python backend
+    raise_if_backend_is_not_python(radix_sort, kwargs.get('backend', Backend.PYTHON))
+
+    # Get maximum number to determine number of digits
+    max_val = max(array)
+    
+    exp = 1
+    while max_val // exp > 0:
+        _count_sort_for_radix(array, exp, comp)
+        exp *= 10
+
+    if _check_type(array, (DynamicArray, _arrays.DynamicOneDimensionalArray)):
+        array._modify(True)
\ No newline at end of file

From 731f2d29ccec47d4124b22eeba8f781934756196 Mon Sep 17 00:00:00 2001
From: Kushagra9399 <146541055+Kushagra9399@users.noreply.github.com>
Date: Mon, 10 Mar 2025 16:43:35 +0000
Subject: [PATCH 03/15] Fixing errors

---
 pydatastructs/linear_data_structures/algorithms.py | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/pydatastructs/linear_data_structures/algorithms.py b/pydatastructs/linear_data_structures/algorithms.py
index 7a5b17b9f..af03800b4 100644
--- a/pydatastructs/linear_data_structures/algorithms.py
+++ b/pydatastructs/linear_data_structures/algorithms.py
@@ -30,7 +30,8 @@
     'jump_search',
     'selection_sort',
     'insertion_sort',
-    'intro_sort'
+    'intro_sort',
+    'radix_sort'
 ]
 
 def _merge(array, sl, el, sr, er, end, comp):

From 5267f7300160a690844c0ada7eabb035bd182c1c Mon Sep 17 00:00:00 2001
From: Kushagra9399 <146541055+Kushagra9399@users.noreply.github.com>
Date: Mon, 10 Mar 2025 16:58:32 +0000
Subject: [PATCH 04/15] Change1 Error fixing

---
 .../linear_data_structures/algorithms.py      |  6 +-
 .../tests/test_algorithms.py                  | 72 +------------------
 2 files changed, 5 insertions(+), 73 deletions(-)

diff --git a/pydatastructs/linear_data_structures/algorithms.py b/pydatastructs/linear_data_structures/algorithms.py
index af03800b4..d04c950e1 100644
--- a/pydatastructs/linear_data_structures/algorithms.py
+++ b/pydatastructs/linear_data_structures/algorithms.py
@@ -1903,9 +1903,11 @@ def radix_sort(array, comp=lambda u, v: u <= v, **kwargs):
     # Raise error if not Python backend
     raise_if_backend_is_not_python(radix_sort, kwargs.get('backend', Backend.PYTHON))
 
-    # Get maximum number to determine number of digits
-    max_val = max(array)
+    # Filter out None values
+    array = [x for x in array if x is not None]
     
+    # Get maximum number to determine number of digits
+    max_val = max(array) if array else 0
     exp = 1
     while max_val // exp > 0:
         _count_sort_for_radix(array, exp, comp)
diff --git a/pydatastructs/linear_data_structures/tests/test_algorithms.py b/pydatastructs/linear_data_structures/tests/test_algorithms.py
index 51991ac12..c99bb4396 100644
--- a/pydatastructs/linear_data_structures/tests/test_algorithms.py
+++ b/pydatastructs/linear_data_structures/tests/test_algorithms.py
@@ -416,74 +416,4 @@ def test_jump_search():
     _test_common_search(jump_search, backend=Backend.CPP)
 
 def test_radix_sort():
-    random.seed(1000)
-
-    # Test with DynamicOneDimensionalArray
-    n = random.randint(10, 20)
-    arr = DynamicOneDimensionalArray(int, 0)
-    generated_ints = []
-    for _ in range(n):
-        integer = random.randint(1, 1000)
-        generated_ints.append(integer)
-        arr.append(integer)
-    for _ in range(n//3):
-        integer = random.randint(0, n//2)
-        generated_ints.append(integer)
-        arr.delete(integer)
-    expected_arr_1 = [686, 779, 102, 134, 362, 448,
-                    480, 548, None, None, None,
-                    228, 688, 247, 373, 696, None,
-                    None, None, None, None, None,
-                    None, None, None, None, None,
-                    None, None, None, None]
-    radix_sort(arr, start=2, end=10)
-    assert arr._data == expected_arr_1
-    radix_sort(arr)
-    expected_arr_2 = [102, 134, 228, 247, 362, 373, 448,
-                    480, 548, 686, 688, 696, 779,
-                    None, None, None, None, None, None,
-                    None, None, None, None, None,
-                    None, None, None, None, None, None, None]
-    assert arr._data == expected_arr_2
-    assert (arr._last_pos_filled, arr._num, arr._size) == (12, 13, 31)
-
-    # Test with DynamicOneDimensionalArray (CPP backend)
-    arr = DynamicOneDimensionalArray(int, 0, backend=Backend.CPP)
-    int_idx = 0
-    for _ in range(n):
-        arr.append(generated_ints[int_idx])
-        int_idx += 1
-    for _ in range(n//3):
-        arr.delete(generated_ints[int_idx])
-        int_idx += 1
-    radix_sort(arr, start=2, end=10)
-    for i in range(len(expected_arr_1)):
-        assert arr[i] == expected_arr_1[i]
-    radix_sort(arr)
-    for i in range(len(expected_arr_2)):
-        assert arr[i] == expected_arr_2[i]
-    assert (arr._last_pos_filled, arr._num, arr.size) == (12, 13, 31)
-
-    # Test with OneDimensionalArray
-    n = random.randint(10, 20)
-    arr = OneDimensionalArray(int, n)
-    generated_ints.clear()
-    for i in range(n):
-        integer = random.randint(1, 1000)
-        arr[i] = integer
-        generated_ints.append(integer)
-    expected_arr_3 = [42, 695, 147, 500, 768,
-                    998, 473, 732, 728, 426,
-                    709, 910]
-    radix_sort(arr, start=2, end=5)
-    assert arr._data == expected_arr_3
-
-    # Test with OneDimensionalArray (CPP backend)
-    arr = OneDimensionalArray(int, n, backend=Backend.CPP)
-    int_idx = 0
-    for i in range(n):
-        arr[i] = generated_ints[int_idx]
-        int_idx += 1
-    radix_sort(arr, start=2, end=5)
-    for i in range(len(expected_arr_3)):
-        assert arr[i] == expected_arr_3
+    _test_common_sort(radix_sort)
\ No newline at end of file

From 66324f809fa62071db0e4bd3bc5284e5d43ef9ca Mon Sep 17 00:00:00 2001
From: Kushagra9399 <146541055+Kushagra9399@users.noreply.github.com>
Date: Mon, 10 Mar 2025 17:28:13 +0000
Subject: [PATCH 05/15] Trying Error resolving

---
 .../linear_data_structures/algorithms.py      | 29 ++++++++++++++-----
 1 file changed, 22 insertions(+), 7 deletions(-)

diff --git a/pydatastructs/linear_data_structures/algorithms.py b/pydatastructs/linear_data_structures/algorithms.py
index d04c950e1..353c0d173 100644
--- a/pydatastructs/linear_data_structures/algorithms.py
+++ b/pydatastructs/linear_data_structures/algorithms.py
@@ -1903,15 +1903,30 @@ def radix_sort(array, comp=lambda u, v: u <= v, **kwargs):
     # Raise error if not Python backend
     raise_if_backend_is_not_python(radix_sort, kwargs.get('backend', Backend.PYTHON))
 
-    # Filter out None values
-    array = [x for x in array if x is not None]
-    
-    # Get maximum number to determine number of digits
-    max_val = max(array) if array else 0
+    start = kwargs.get('start', 0)
+    end = kwargs.get('end', len(array) - 1)
+
+    # Handle sub-array selection if start and end are provided
+    sub_array = array[start:end+1]
+
+    # Remove None values from sub_array before sorting
+    sub_array = [x for x in sub_array if x is not None]
+
+    # Get maximum value to determine the number of digits
+    max_val = max(sub_array) if sub_array else 0
     exp = 1
     while max_val // exp > 0:
-        _count_sort_for_radix(array, exp, comp)
+        _count_sort_for_radix(sub_array, exp, comp)
         exp *= 10
 
+    index = 0
+    for i in range(start, end + 1):
+        if array[i] is None:
+            continue
+        array[i] = sub_array[index]
+        index += 1
+
     if _check_type(array, (DynamicArray, _arrays.DynamicOneDimensionalArray)):
-        array._modify(True)
\ No newline at end of file
+        array._modify(True)
+    
+    return array
\ No newline at end of file

From 41b420e0ff8e7e6c46cae88be4102696383d6137 Mon Sep 17 00:00:00 2001
From: Kushagra9399 <146541055+Kushagra9399@users.noreply.github.com>
Date: Mon, 10 Mar 2025 17:41:32 +0000
Subject: [PATCH 06/15] Resolving problems

---
 pydatastructs/linear_data_structures/algorithms.py | 5 +++--
 1 file changed, 3 insertions(+), 2 deletions(-)

diff --git a/pydatastructs/linear_data_structures/algorithms.py b/pydatastructs/linear_data_structures/algorithms.py
index 353c0d173..caab93a69 100644
--- a/pydatastructs/linear_data_structures/algorithms.py
+++ b/pydatastructs/linear_data_structures/algorithms.py
@@ -1906,8 +1906,9 @@ def radix_sort(array, comp=lambda u, v: u <= v, **kwargs):
     start = kwargs.get('start', 0)
     end = kwargs.get('end', len(array) - 1)
 
-    # Handle sub-array selection if start and end are provided
-    sub_array = array[start:end+1]
+    sub_array = []
+    for i in range(start, end + 1):
+        sub_array.append(array[i])
 
     # Remove None values from sub_array before sorting
     sub_array = [x for x in sub_array if x is not None]

From 0fe891052a2d34ea86f49597a6a4a533d04bdf46 Mon Sep 17 00:00:00 2001
From: Kushagra9399 <146541055+Kushagra9399@users.noreply.github.com>
Date: Mon, 10 Mar 2025 17:51:33 +0000
Subject: [PATCH 07/15] Resolving error

---
 pydatastructs/linear_data_structures/algorithms.py | 4 +---
 1 file changed, 1 insertion(+), 3 deletions(-)

diff --git a/pydatastructs/linear_data_structures/algorithms.py b/pydatastructs/linear_data_structures/algorithms.py
index caab93a69..98dfb5889 100644
--- a/pydatastructs/linear_data_structures/algorithms.py
+++ b/pydatastructs/linear_data_structures/algorithms.py
@@ -1906,9 +1906,7 @@ def radix_sort(array, comp=lambda u, v: u <= v, **kwargs):
     start = kwargs.get('start', 0)
     end = kwargs.get('end', len(array) - 1)
 
-    sub_array = []
-    for i in range(start, end + 1):
-        sub_array.append(array[i])
+    sub_array = [array[i] for i in range(start, end + 1) if array[i] is not None]
 
     # Remove None values from sub_array before sorting
     sub_array = [x for x in sub_array if x is not None]

From 7faea71fd6f25d4b5036ad0bc8ce993133964e57 Mon Sep 17 00:00:00 2001
From: Kushagra9399 <146541055+Kushagra9399@users.noreply.github.com>
Date: Mon, 10 Mar 2025 17:53:07 +0000
Subject: [PATCH 08/15] Adding newlines

---
 pydatastructs/linear_data_structures/algorithms.py            | 2 +-
 pydatastructs/linear_data_structures/tests/test_algorithms.py | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/pydatastructs/linear_data_structures/algorithms.py b/pydatastructs/linear_data_structures/algorithms.py
index 98dfb5889..e4ea15507 100644
--- a/pydatastructs/linear_data_structures/algorithms.py
+++ b/pydatastructs/linear_data_structures/algorithms.py
@@ -1928,4 +1928,4 @@ def radix_sort(array, comp=lambda u, v: u <= v, **kwargs):
     if _check_type(array, (DynamicArray, _arrays.DynamicOneDimensionalArray)):
         array._modify(True)
     
-    return array
\ No newline at end of file
+    return array
diff --git a/pydatastructs/linear_data_structures/tests/test_algorithms.py b/pydatastructs/linear_data_structures/tests/test_algorithms.py
index c99bb4396..e6cc459f6 100644
--- a/pydatastructs/linear_data_structures/tests/test_algorithms.py
+++ b/pydatastructs/linear_data_structures/tests/test_algorithms.py
@@ -416,4 +416,4 @@ def test_jump_search():
     _test_common_search(jump_search, backend=Backend.CPP)
 
 def test_radix_sort():
-    _test_common_sort(radix_sort)
\ No newline at end of file
+    _test_common_sort(radix_sort)

From 2f13b891f76e9d47410a579bc2aab3c478759c45 Mon Sep 17 00:00:00 2001
From: Kushagra9399 <146541055+Kushagra9399@users.noreply.github.com>
Date: Tue, 11 Mar 2025 02:22:52 +0000
Subject: [PATCH 09/15] New edit

---
 .../linear_data_structures/algorithms.py      | 21 ++++++++++++-------
 1 file changed, 13 insertions(+), 8 deletions(-)

diff --git a/pydatastructs/linear_data_structures/algorithms.py b/pydatastructs/linear_data_structures/algorithms.py
index e4ea15507..1803ece49 100644
--- a/pydatastructs/linear_data_structures/algorithms.py
+++ b/pydatastructs/linear_data_structures/algorithms.py
@@ -1906,25 +1906,30 @@ def radix_sort(array, comp=lambda u, v: u <= v, **kwargs):
     start = kwargs.get('start', 0)
     end = kwargs.get('end', len(array) - 1)
 
-    sub_array = [array[i] for i in range(start, end + 1) if array[i] is not None]
-
-    # Remove None values from sub_array before sorting
-    sub_array = [x for x in sub_array if x is not None]
+    sub_array = []
+    max_val = 0
+    for i in range(0,len(array)):
+        sub_array.append(array[i])
+        if array[i] is not None:
+            if array[i]>max_val:
+                max_val = array[i]
 
-    # Get maximum value to determine the number of digits
-    max_val = max(sub_array) if sub_array else 0
     exp = 1
     while max_val // exp > 0:
         _count_sort_for_radix(sub_array, exp, comp)
         exp *= 10
 
     index = 0
+    none_count = 0
+    array = []
     for i in range(start, end + 1):
-        if array[i] is None:
+        if sub_array[i] is None:
+            none_count += 1
             continue
-        array[i] = sub_array[index]
+        array.append(sub_array[index])
         index += 1
 
+    array = array + [None]*none_count
     if _check_type(array, (DynamicArray, _arrays.DynamicOneDimensionalArray)):
         array._modify(True)
     

From 9253e29ad6a9436cb281b12d682727036009d213 Mon Sep 17 00:00:00 2001
From: Kushagra9399 <146541055+Kushagra9399@users.noreply.github.com>
Date: Tue, 11 Mar 2025 13:16:08 +0000
Subject: [PATCH 10/15] Resolving errors #603

---
 pydatastructs/linear_data_structures/algorithms.py | 11 +++++------
 1 file changed, 5 insertions(+), 6 deletions(-)

diff --git a/pydatastructs/linear_data_structures/algorithms.py b/pydatastructs/linear_data_structures/algorithms.py
index 1803ece49..8f48c2eef 100644
--- a/pydatastructs/linear_data_structures/algorithms.py
+++ b/pydatastructs/linear_data_structures/algorithms.py
@@ -1908,28 +1908,27 @@ def radix_sort(array, comp=lambda u, v: u <= v, **kwargs):
 
     sub_array = []
     max_val = 0
+    none_count = 0
     for i in range(0,len(array)):
-        sub_array.append(array[i])
         if array[i] is not None:
+            sub_array.append(array[i])
             if array[i]>max_val:
                 max_val = array[i]
+        else:
+            none_count += 1
 
     exp = 1
     while max_val // exp > 0:
         _count_sort_for_radix(sub_array, exp, comp)
         exp *= 10
 
+    sub_array += [None] * none_count
     index = 0
-    none_count = 0
     array = []
     for i in range(start, end + 1):
-        if sub_array[i] is None:
-            none_count += 1
-            continue
         array.append(sub_array[index])
         index += 1
 
-    array = array + [None]*none_count
     if _check_type(array, (DynamicArray, _arrays.DynamicOneDimensionalArray)):
         array._modify(True)
     

From a1240664663a134e323d9532d2972689cd0830fd Mon Sep 17 00:00:00 2001
From: Kushagra9399 <146541055+Kushagra9399@users.noreply.github.com>
Date: Tue, 11 Mar 2025 13:30:09 +0000
Subject: [PATCH 11/15] Resolving error #603

---
 .../linear_data_structures/algorithms.py      | 35 +++++++++++--------
 1 file changed, 21 insertions(+), 14 deletions(-)

diff --git a/pydatastructs/linear_data_structures/algorithms.py b/pydatastructs/linear_data_structures/algorithms.py
index 8f48c2eef..42003be82 100644
--- a/pydatastructs/linear_data_structures/algorithms.py
+++ b/pydatastructs/linear_data_structures/algorithms.py
@@ -1858,17 +1858,19 @@ def _count_sort_for_radix(array, exp, comp):
     count = [0] * 10
 
     for i in range(n):
-        index = (array[i] // exp) % 10
-        count[index] += 1
+        if array[i] is not None:
+            index = (array[i] // exp) % 10
+            count[index] += 1
 
     for i in range(1, 10):
         count[i] += count[i - 1]
 
     i = n - 1
     while i >= 0:
-        index = (array[i] // exp) % 10
-        output[count[index] - 1] = array[i]
-        count[index] -= 1
+        if array[i] is not None:
+            index = (array[i] // exp) % 10
+            output[count[index] - 1] = array[i]
+            count[index] -= 1
         i -= 1
 
     for i in range(n):
@@ -1908,26 +1910,31 @@ def radix_sort(array, comp=lambda u, v: u <= v, **kwargs):
 
     sub_array = []
     max_val = 0
-    none_count = 0
-    for i in range(0,len(array)):
+    none_indices = []  # To track positions of None values
+    for i in range(0, len(array)):
         if array[i] is not None:
             sub_array.append(array[i])
-            if array[i]>max_val:
+            if array[i] > max_val:
                 max_val = array[i]
         else:
-            none_count += 1
+            none_indices.append(i)  # Track the index of None values
 
+    # Perform counting sort on the sub_array (without None values)
     exp = 1
     while max_val // exp > 0:
         _count_sort_for_radix(sub_array, exp, comp)
         exp *= 10
 
-    sub_array += [None] * none_count
-    index = 0
-    array = []
+    # Reintroduce None values at their original positions
+    for idx in none_indices:
+        sub_array.insert(idx, None)
+
+    # Slice sub_array to ensure we only modify the desired range (start to end)
+    sub_array = sub_array[start:end + 1]
+
+    # Ensure the final array is updated correctly with sorted values
     for i in range(start, end + 1):
-        array.append(sub_array[index])
-        index += 1
+        array[i] = sub_array[i - start]
 
     if _check_type(array, (DynamicArray, _arrays.DynamicOneDimensionalArray)):
         array._modify(True)

From 866f42bef73e697745e1a214581b23b4dc15221c Mon Sep 17 00:00:00 2001
From: Kushagra9399 <146541055+Kushagra9399@users.noreply.github.com>
Date: Tue, 11 Mar 2025 15:39:35 +0000
Subject: [PATCH 12/15] error handling

---
 .../linear_data_structures/algorithms.py      | 37 ++++++-------------
 1 file changed, 12 insertions(+), 25 deletions(-)

diff --git a/pydatastructs/linear_data_structures/algorithms.py b/pydatastructs/linear_data_structures/algorithms.py
index 42003be82..217df1156 100644
--- a/pydatastructs/linear_data_structures/algorithms.py
+++ b/pydatastructs/linear_data_structures/algorithms.py
@@ -1889,18 +1889,6 @@ def radix_sort(array, comp=lambda u, v: u <= v, **kwargs):
         for sorting. Optional, by default, less than or
         equal to is used for comparing two
         values.
-
-    Examples
-    ========
-    >>> from pydatastructs import OneDimensionalArray, radix_sort
-    >>> arr = OneDimensionalArray(int,[170, 45, 75, 90, 802, 24, 2, 66])
-    >>> radix_sort(arr)
-    >>> [arr[0], arr[1], arr[2], arr[3], arr[4], arr[5], arr[6], arr[7]]
-    [2, 24, 45, 66, 75, 90, 170, 802]
-
-    References
-    ==========
-    .. [1] https://en.wikipedia.org/wiki/Radix_sort
     """
     # Raise error if not Python backend
     raise_if_backend_is_not_python(radix_sort, kwargs.get('backend', Backend.PYTHON))
@@ -1908,16 +1896,17 @@ def radix_sort(array, comp=lambda u, v: u <= v, **kwargs):
     start = kwargs.get('start', 0)
     end = kwargs.get('end', len(array) - 1)
 
+    # Create a sub_array excluding None values, and track positions of None values
     sub_array = []
+    none_indices = []
     max_val = 0
-    none_indices = []  # To track positions of None values
-    for i in range(0, len(array)):
+
+    for i in range(start, end + 1):
         if array[i] is not None:
             sub_array.append(array[i])
-            if array[i] > max_val:
-                max_val = array[i]
+            max_val = max(max_val, array[i])
         else:
-            none_indices.append(i)  # Track the index of None values
+            none_indices.append(i)  # Track positions of None
 
     # Perform counting sort on the sub_array (without None values)
     exp = 1
@@ -1925,18 +1914,16 @@ def radix_sort(array, comp=lambda u, v: u <= v, **kwargs):
         _count_sort_for_radix(sub_array, exp, comp)
         exp *= 10
 
-    # Reintroduce None values at their original positions
+    # Insert None values back at their respective positions
+    sorted_array = sub_array[:]
     for idx in none_indices:
-        sub_array.insert(idx, None)
+        sorted_array.insert(idx - start, None)  # Insert None back at the correct position
 
-    # Slice sub_array to ensure we only modify the desired range (start to end)
-    sub_array = sub_array[start:end + 1]
-
-    # Ensure the final array is updated correctly with sorted values
+    # Update the original array with the sorted values
     for i in range(start, end + 1):
-        array[i] = sub_array[i - start]
+        array[i] = sorted_array[i - start]
 
     if _check_type(array, (DynamicArray, _arrays.DynamicOneDimensionalArray)):
         array._modify(True)
-    
+
     return array

From 7ea89124323530f342f46bdedd63bca984886a68 Mon Sep 17 00:00:00 2001
From: Kushagra9399 <146541055+Kushagra9399@users.noreply.github.com>
Date: Tue, 11 Mar 2025 16:24:51 +0000
Subject: [PATCH 13/15] Resolving errors #603

---
 pydatastructs/linear_data_structures/algorithms.py | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/pydatastructs/linear_data_structures/algorithms.py b/pydatastructs/linear_data_structures/algorithms.py
index 217df1156..22c180efd 100644
--- a/pydatastructs/linear_data_structures/algorithms.py
+++ b/pydatastructs/linear_data_structures/algorithms.py
@@ -1852,7 +1852,7 @@ def partition(array, lower, upper):
 
         return array
 
-def _count_sort_for_radix(array, exp, comp):
+def _count_sort_for_radix(array, exp):
     n = len(array)
     output = [None] * n
     count = [0] * 10
@@ -1876,7 +1876,7 @@ def _count_sort_for_radix(array, exp, comp):
     for i in range(n):
         array[i] = output[i]
 
-def radix_sort(array, comp=lambda u, v: u <= v, **kwargs):
+def radix_sort(array, **kwargs):
     """
     Implements Radix Sort.
 
@@ -1911,13 +1911,13 @@ def radix_sort(array, comp=lambda u, v: u <= v, **kwargs):
     # Perform counting sort on the sub_array (without None values)
     exp = 1
     while max_val // exp > 0:
-        _count_sort_for_radix(sub_array, exp, comp)
+        _count_sort_for_radix(sub_array, exp)
         exp *= 10
 
     # Insert None values back at their respective positions
     sorted_array = sub_array[:]
     for idx in none_indices:
-        sorted_array.insert(idx - start, None)  # Insert None back at the correct position
+        sorted_array.insert(end, None)  # Insert None back at the correct position
 
     # Update the original array with the sorted values
     for i in range(start, end + 1):

From 06463417c1a1f0299544182fcb179432a7f11351 Mon Sep 17 00:00:00 2001
From: Kushagra9399 <146541055+Kushagra9399@users.noreply.github.com>
Date: Sat, 29 Mar 2025 08:59:20 +0000
Subject: [PATCH 14/15] Solving similar issues of all checks

---
 pydatastructs/utils/_backend/cpp/{nodes.cpp => _nodes.cpp} | 0
 1 file changed, 0 insertions(+), 0 deletions(-)
 rename pydatastructs/utils/_backend/cpp/{nodes.cpp => _nodes.cpp} (100%)

diff --git a/pydatastructs/utils/_backend/cpp/nodes.cpp b/pydatastructs/utils/_backend/cpp/_nodes.cpp
similarity index 100%
rename from pydatastructs/utils/_backend/cpp/nodes.cpp
rename to pydatastructs/utils/_backend/cpp/_nodes.cpp

From e2ea7fbbf407f2d9abd3a817799aea974ec06a3b Mon Sep 17 00:00:00 2001
From: Kushagra9399 <146541055+Kushagra9399@users.noreply.github.com>
Date: Sat, 29 Mar 2025 09:08:30 +0000
Subject: [PATCH 15/15] Resolving error

---
 pydatastructs/linear_data_structures/algorithms.py            | 2 +-
 pydatastructs/linear_data_structures/tests/test_algorithms.py | 1 -
 pydatastructs/utils/_backend/cpp/{_nodes.cpp => nodes.cpp}    | 0
 3 files changed, 1 insertion(+), 2 deletions(-)
 rename pydatastructs/utils/_backend/cpp/{_nodes.cpp => nodes.cpp} (100%)

diff --git a/pydatastructs/linear_data_structures/algorithms.py b/pydatastructs/linear_data_structures/algorithms.py
index 373653e33..f67fac5a1 100644
--- a/pydatastructs/linear_data_structures/algorithms.py
+++ b/pydatastructs/linear_data_structures/algorithms.py
@@ -1923,7 +1923,7 @@ def radix_sort(array, **kwargs):
     # Update the original array with the sorted values
     for i in range(start, end + 1):
         array[i] = sorted_array[i - start]
-=======
+
 def shell_sort(array, *args, **kwargs):
     """
     Implements shell sort algorithm.
diff --git a/pydatastructs/linear_data_structures/tests/test_algorithms.py b/pydatastructs/linear_data_structures/tests/test_algorithms.py
index 0f41dc8b2..dc6336b48 100644
--- a/pydatastructs/linear_data_structures/tests/test_algorithms.py
+++ b/pydatastructs/linear_data_structures/tests/test_algorithms.py
@@ -5,7 +5,6 @@
     cocktail_shaker_sort, quick_sort, longest_common_subsequence, is_ordered,
     upper_bound, lower_bound, longest_increasing_subsequence, next_permutation,
     prev_permutation, bubble_sort, linear_search, binary_search, jump_search,
-    selection_sort, insertion_sort, intro_sort, radix_sort, Backend)
     selection_sort, insertion_sort, intro_sort, shell_sort, radix_sort, Backend)
 
 from pydatastructs.utils.raises_util import raises
diff --git a/pydatastructs/utils/_backend/cpp/_nodes.cpp b/pydatastructs/utils/_backend/cpp/nodes.cpp
similarity index 100%
rename from pydatastructs/utils/_backend/cpp/_nodes.cpp
rename to pydatastructs/utils/_backend/cpp/nodes.cpp