When it is required solve the maximum subarray problem using the divide and conquer method,
Below is the demonstration of the same −
Example
def max_crossing_sum(my_array, low, mid, high):
sum_elements = 0
sum_left_elements = -10000
for i in range(mid, low-1, -1):
sum_elements = sum_elements + my_array[i]
if (sum_elements > sum_left_elements):
sum_left_elements = sum_elements
sum_elements = 0
sum_right_elements = -1000
for i in range(mid + 1, high + 1):
sum_elements = sum_elements + my_array[i]
if (sum_elements > sum_right_elements):
sum_right_elements = sum_elements
return max(sum_left_elements + sum_right_elements, sum_left_elements, sum_right_elements)
def max_sub_array_sum(my_array, low, high):
if (low == high):
return my_array[low]
mid = (low + high) // 2
return max(max_sub_array_sum(my_array, low, mid), max_sub_array_sum(my_array, mid+1, high), max_crossing_sum(my_array, low, mid, high))
my_list = [23, 12, 45, 67, 89, 11]
list_length = len(my_list)
print("The list is :")
print(my_list)
max_sum = max_sub_array_sum(my_list, 0, list_length-1)
print("The maximum contiguous sum is ")
print(max_sum)Output
The list is : [23, 12, 45, 67, 89, 11] The maximum contiguous sum is 247
Explanation
A method named ‘max_crossing_sum’ is defined that computes the sum of elements on the left part of the list.
This is achieved using the ‘max_sub_array_sum’ that helps compute sum of every sub array.
Outside the method, a list is defined, and is displayed on the console.
The length of the list is determined.
The method to calculate the sum of sub array is called by passing this list.
The sum is displayed as output on the console