write algorithm maximum_subarray_sum in algorithm.py

Author: yuvraj-rathod-1202

pydatastructs/linear_data_structures/__init__.py

@@ -47,6 +47,7 @@
     jump_search,
     selection_sort,
     insertion_sort,
-    intro_sort
+    intro_sort,
+    maximum_subarray_sum,
 )
 __all__.extend(algorithms.__all__)

pydatastructs/linear_data_structures/_backend/cpp/_algorithms.cp312-win_amd64.pyd

@@ -30,7 +30,8 @@
     'jump_search',
     'selection_sort',
     'insertion_sort',
-    'intro_sort'
+    'intro_sort',
+    'maximum_subarray_sum',
 ]
 
 def _merge(array, sl, el, sr, er, end, comp):
@@ -1850,3 +1851,70 @@ def partition(array, lower, upper):
         intro_sort(array, start=p+1, end=upper,  maxdepth=maxdepth-1, ins_threshold=ins_threshold)
 
         return array
+
+
+def maximum_subarray_sum(array, **kwargs):
+    """
+    Finds the maximum subarray sum of the given array.
+
+    Parameters
+    ==========
+
+    array: OneDimensionalArray
+        The array for which the maximum subarray sum
+        has to be found.
+    start: int
+        The starting index of the portion
+        which is to be considered.
+        Optional, by default 0
+    end: int
+        The ending index of the portion which
+        is to be considered.
+        Optional, by default the index
+        of the last position filled.
+    comp: lambda/function
+        The comparator which is to be used
+        for performing comparisons.
+        Optional, by default, less than or
+        equal to is used for comparing two
+        values.
+    backend: pydatastructs.Backend
+        The backend to be used.
+        Optional, by default, the best available
+        backend is used.
+
+    Returns
+    =======
+
+    output: int
+        The maximum subarray sum.
+
+    Examples
+    ========
+
+    >>> from pydatastructs import OneDimensionalArray as ODA, maximum_subarray_sum
+    >>> arr = ODA(int, [-2, 1, -3, 4, -1, 2, 1, -5, 4])
+    >>> maximum_subarray_sum(arr)
+    6
+    >>> arr = ODA(int, [1, 2, 3, 4, 5])
+    >>> maximum_subarray_sum(arr)
+    15
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Maximum_subarray_problem
+    """
+    raise_if_backend_is_not_python(
+        maximum_subarray_sum, kwargs.get('backend', Backend.PYTHON))
+    start = kwargs.get('start', 0)
+    end = kwargs.get('end', len(array) - 1)
+    comp = kwargs.get('comp', lambda u, v: u <= v)
+
+    max_sum = array[start]
+    max_ending_here = array[start]
+    for i in range(start + 1, end + 1):
+        max_ending_here = max(array[i], max_ending_here + array[i])
+        max_sum = max(max_sum, max_ending_here)
+
+    return max_sum