From 3ac47ce2149a56c3b9f99776613b47ec2867c864 Mon Sep 17 00:00:00 2001
From: git-britta-michel <55396916+git-britta-michel@users.noreply.github.com>
Date: Fri, 4 Oct 2019 21:23:14 +0530
Subject: [PATCH] get max sum of sub arrays

---
 max_subarray.py | 56 +++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 56 insertions(+)
 create mode 100644 max_subarray.py

diff --git a/max_subarray.py b/max_subarray.py
new file mode 100644
index 0000000..a075f57
--- /dev/null
+++ b/max_subarray.py
@@ -0,0 +1,56 @@
+def max_sum_from_start(array):
+    """ This function finds the maximum contiguous sum of array from 0 index
+    Parameters : 
+    array (list[int]) : given array
+    
+    Returns : 
+    max_sum (int) : maximum contiguous sum of array from 0 index
+    """
+    array_sum = 0
+    max_sum = float("-inf")
+    for num in array:
+        array_sum += num
+        if array_sum > max_sum:
+            max_sum = array_sum
+    return max_sum
+
+
+def max_cross_array_sum(array, left, mid, right):
+    """ This function finds the maximum contiguous sum of left and right arrays
+    Parameters : 
+    array, left, mid, right (list[int], int, int, int) 
+    
+    Returns : 
+    (int) :  maximum of sum of contiguous sum of left and right arrays
+    """
+
+    max_sum_of_left = max_sum_from_start(array[left:mid+1][::-1])
+    max_sum_of_right = max_sum_from_start(array[mid+1: right+1])
+    return max_sum_of_left + max_sum_of_right
+
+
+def max_subarray_sum(array, left, right):
+    """ Maximum contiguous sub-array sum, using divide and conquer method
+    Parameters : 
+    array, left, right (list[int], int, int) : 
+    given array, current left index and current right index
+    
+    Returns : 
+    int :  maximum of sum of contiguous sub-array
+    """
+
+    # base case: array has only one element
+    if left == right:
+        return array[right]
+    
+    # Recursion
+    mid = (left + right) // 2
+    left_half_sum = max_subarray_sum(array, left, mid)
+    right_half_sum = max_subarray_sum(array, mid + 1, right)
+    cross_sum = max_cross_array_sum(array, left, mid, right)
+    return max(left_half_sum, right_half_sum, cross_sum)
+
+
+array = [-2, -5, 6, -2, -3, 1, 5, -6]
+array_length = len(array)
+print("Maximum sum of contiguous subarray:", max_subarray_sum(array, 0, array_length - 1))