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95 lines
2.6 KiB
Python
95 lines
2.6 KiB
Python
"""
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author : Mayank Kumar Jha (mk9440)
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"""
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from typing import List
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def find_max_sub_array(A, low, high):
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if low == high:
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return low, high, A[low]
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else:
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mid = (low + high) // 2
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left_low, left_high, left_sum = find_max_sub_array(A, low, mid)
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right_low, right_high, right_sum = find_max_sub_array(A, mid + 1, high)
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cross_left, cross_right, cross_sum = find_max_cross_sum(A, low, mid, high)
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if left_sum >= right_sum and left_sum >= cross_sum:
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return left_low, left_high, left_sum
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elif right_sum >= left_sum and right_sum >= cross_sum:
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return right_low, right_high, right_sum
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else:
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return cross_left, cross_right, cross_sum
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def find_max_cross_sum(A, low, mid, high):
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left_sum, max_left = -999999999, -1
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right_sum, max_right = -999999999, -1
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summ = 0
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for i in range(mid, low - 1, -1):
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summ += A[i]
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if summ > left_sum:
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left_sum = summ
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max_left = i
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summ = 0
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for i in range(mid + 1, high + 1):
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summ += A[i]
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if summ > right_sum:
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right_sum = summ
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max_right = i
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return max_left, max_right, (left_sum + right_sum)
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def max_sub_array(nums: List[int]) -> int:
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"""
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Finds the contiguous subarray which has the largest sum and return its sum.
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>>> max_sub_array([-2, 1, -3, 4, -1, 2, 1, -5, 4])
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6
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An empty (sub)array has sum 0.
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>>> max_sub_array([])
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0
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If all elements are negative, the largest subarray would be the empty array,
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having the sum 0.
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>>> max_sub_array([-1, -2, -3])
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0
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>>> max_sub_array([5, -2, -3])
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5
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>>> max_sub_array([31, -41, 59, 26, -53, 58, 97, -93, -23, 84])
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187
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"""
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best = 0
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current = 0
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for i in nums:
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current += i
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if current < 0:
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current = 0
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best = max(best, current)
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return best
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if __name__ == "__main__":
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"""
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A random simulation of this algorithm.
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"""
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import time
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from random import randint
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from matplotlib import pyplot as plt
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inputs = [10, 100, 1000, 10000, 50000, 100000, 200000, 300000, 400000, 500000]
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tim = []
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for i in inputs:
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li = [randint(1, i) for j in range(i)]
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strt = time.time()
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(find_max_sub_array(li, 0, len(li) - 1))
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end = time.time()
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tim.append(end - strt)
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print("No of Inputs Time Taken")
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for i in range(len(inputs)):
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print(inputs[i], "\t\t", tim[i])
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plt.plot(inputs, tim)
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plt.xlabel("Number of Inputs")
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plt.ylabel("Time taken in seconds ")
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plt.show()
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