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73 changes: 13 additions & 60 deletions dynamic_programming/max_sub_array.py
Original file line number Diff line number Diff line change
@@ -1,43 +1,10 @@
"""
author : Mayank Kumar Jha (mk9440)
author(after editing) : Snehanjali G V S
"""
from __future__ import annotations


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.
Expand All @@ -57,37 +24,23 @@ def max_sub_array(nums: list[int]) -> int:
5
>>> max_sub_array([31, -41, 59, 26, -53, 58, 97, -93, -23, 84])
187
>>> max_sub_array([10, 100, 1000, 10000, 50000, 100000, 200000, 300000, 400000, 500000])
1561110
"""
best = 0
current = 0
for i in nums:
current += i
current = max(current, 0)
best = max(best, current)
return best
sol = [0] * (len(a) + 1)
for i in range(1, len(sol)):
sol[i] = max(sol[i - 1] + a[i - 1], a[i - 1])

answer = sol[0]
for i in range(1, len(sol)):
if answer < sol[i]:
answer = sol[i]
return answer


if __name__ == "__main__":
"""
A random simulation of this algorithm.
"""
import time
from random import randint

from matplotlib import pyplot as plt

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()
print(max_sub_array(inputs))