mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-24 05:21:09 +00:00
5df8aec66c
* GitHub Action formats our code with psf/black @poyea Your review please. * fixup! Format Python code with psf/black push
94 lines
2.6 KiB
Python
94 lines
2.6 KiB
Python
"""
|
|
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()
|