max sub array Algorithm
binary heaps are also normally used in the heapsort sorting algorithm, which is an in-place algorithm because binary heaps can be implemented as an implicit data structure, storing keys in an array and use their relative positions within that array to represent child-parent relationships. The binary heap was introduced by J. W. J. Williams in 1964, as a data structure for heapsort.
"""
author : Mayank Kumar Jha (mk9440)
"""
from typing import List
def find_max_sub_array(A, low, high):
if low == high:
return low, high, A[low]
else:
mid = (low + high) // 2
left_low, left_high, left_sum = find_max_sub_array(A, low, mid)
right_low, right_high, right_sum = find_max_sub_array(A, mid + 1, high)
cross_left, cross_right, cross_sum = find_max_cross_sum(A, low, mid, high)
if left_sum >= right_sum and left_sum >= cross_sum:
return left_low, left_high, left_sum
elif right_sum >= left_sum and right_sum >= cross_sum:
return right_low, right_high, right_sum
else:
return cross_left, cross_right, cross_sum
def find_max_cross_sum(A, low, mid, high):
left_sum, max_left = -999999999, -1
right_sum, max_right = -999999999, -1
summ = 0
for i in range(mid, low - 1, -1):
summ += A[i]
if summ > left_sum:
left_sum = summ
max_left = i
summ = 0
for i in range(mid + 1, high + 1):
summ += A[i]
if summ > right_sum:
right_sum = summ
max_right = i
return max_left, max_right, (left_sum + right_sum)
def max_sub_array(nums: List[int]) -> int:
"""
Finds the contiguous subarray which has the largest sum and return its sum.
>>> max_sub_array([-2, 1, -3, 4, -1, 2, 1, -5, 4])
6
An empty (sub)array has sum 0.
>>> max_sub_array([])
0
If all elements are negative, the largest subarray would be the empty array,
having the sum 0.
>>> max_sub_array([-1, -2, -3])
0
>>> max_sub_array([5, -2, -3])
5
>>> max_sub_array([31, -41, 59, 26, -53, 58, 97, -93, -23, 84])
187
"""
best = 0
current = 0
for i in nums:
current += i
if current < 0:
current = 0
best = max(best, current)
return best
if __name__ == "__main__":
"""
A random simulation of this algorithm.
"""
import time
import matplotlib.pyplot as plt
from random import randint
inputs = [10, 100, 1000, 10000, 50000, 100000, 200000, 300000, 400000, 500000]
tim = []
for i in inputs:
li = [randint(1, i) for j in range(i)]
strt = time.time()
(find_max_sub_array(li, 0, len(li) - 1))
end = time.time()
tim.append(end - strt)
print("No of Inputs Time Taken")
for i in range(len(inputs)):
print(inputs[i], "\t\t", tim[i])
plt.plot(inputs, tim)
plt.xlabel("Number of Inputs")
plt.ylabel("Time taken in seconds ")
plt.show()
