Kadanes_algorithm (#1959)

* Add files via upload

* Update Kadane's_algorithm.py

* Update and rename Kadane's_algorithm.py to kadanes_algorithm.py

* Update kadanes_algorithm.py

* Update kadanes_algorithm.py

* Update kadanes_algorithm.py

* Update kadanes_algorithm.py

* Update kadanes_algorithm.py

Co-authored-by: Christian Clauss <cclauss@me.com>

maths/kadanes_algorithm.py

@@ -0,0 +1,65 @@
+"""
+Kadane's algorithm to get maximum subarray sum
+https://medium.com/@rsinghal757/kadanes-algorithm-dynamic-programming-how-and-why-does-it-work-3fd8849ed73d
+https://en.wikipedia.org/wiki/Maximum_subarray_problem
+"""
+test_data = ([-2, -8, -9], [2, 8, 9], [-1, 0, 1], [0, 0], [])
+
+
+def negative_exist(arr: list) -> int:
+    """
+    >>> negative_exist([-2,-8,-9])
+    -2
+    >>> [negative_exist(arr) for arr in test_data]
+    [-2, 0, 0, 0, 0]
+    """
+    arr = arr or [0]
+    max = arr[0]
+    for i in arr:
+        if i >= 0:
+            return 0
+        elif max <= i:
+            max = i
+    return max
+
+
+def kadanes(arr: list) -> int:
+    """
+    If negative_exist() returns 0 than this function will execute
+    else it will return the value return by negative_exist function
+
+    For example: arr = [2, 3, -9, 8, -2]
+        Initially we set value of max_sum to 0 and max_till_element to 0 than when
+        max_sum is less than max_till particular element it will assign that value to
+        max_sum and when value of max_till_sum is less than 0 it will assign 0 to i
+        and after that whole process, return the max_sum
+    So the output for above arr is 8
+
+    >>> kadanes([2, 3, -9, 8, -2])
+    8
+    >>> [kadanes(arr) for arr in test_data]
+    [-2, 19, 1, 0, 0]
+    """
+    max_sum = negative_exist(arr)
+    if max_sum < 0:
+        return max_sum
+
+    max_sum = 0
+    max_till_element = 0
+
+    for i in arr:
+        max_till_element += i
+        if max_sum <= max_till_element:
+            max_sum = max_till_element
+        if max_till_element < 0:
+            max_till_element = 0
+    return max_sum
+
+
+if __name__ == "__main__":
+    try:
+        print("Enter integer values sepatated by spaces")
+        arr = [int(x) for x in input().split()]
+        print(f"Maximum subarray sum of {arr} is {kadanes(arr)}")
+    except ValueError:
+        print("Please enter integer values.")