Merge pull request #258 from master-fury/master

Added Kadane Algorithm

Author: ionicc

Mathematical_Algorithms/src/Kadane_Algorithm.py

@@ -0,0 +1,36 @@
+# Kadane's Algorithm by Master-Fury
+# Worst and Average Case Time Complexity: O(n)
+
+from sys import maxsize  # importing maximum int from sys module
+
+
+def kadane_algorithm(arr: int):
+
+    len_arr = len(arr)  # Finding the len of array
+
+    max_so_far = -maxsize - 1  # Setting max value as maximum negative value
+    max_ending_here = 0
+
+    for i in range(0, len_arr):
+        max_ending_here = max_ending_here + arr[i]
+        if (max_so_far < max_ending_here):
+            max_so_far = max_ending_here
+
+        if max_ending_here < 0:
+            max_ending_here = 0
+
+    return max_so_far
+
+
+# Driver function
+sample_array = [-5, -2, 5, 9, -8, 9, 4, 7, -7, -1]
+max_cont_subarray_sum = kadane_algorithm(sample_array)
+
+print("The maximum sum of contigous sub array is - ", max_cont_subarray_sum)
+
+# DESCRIPTION
+# This algorithm is widely used to find the sum of contiguous subarray within a one-dimensional array of numbers that has the largest sum.
+# The simple idea of Kadane’s algorithm is to look for all positive contiguous segments of the array (max_ending_here is used for this).
+# And keep track of maximum sum contiguous segment among all positive segments (max_so_far is used for this).
+# Each time we get a positive-sum compare it with max_so_far and update max_so_far if it is greater than max_so_far .
+# It can be viewed both as a greedy and DP problem.