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https://github.com/TheAlgorithms/Python.git
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287bf26bc8
* A divide and conquer method in finding the maximum difference pair * fix formatting issues * fix formatting issues * add doctest runner
48 lines
1.3 KiB
Python
48 lines
1.3 KiB
Python
from typing import List
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def max_difference(a: List[int]) -> (int, int):
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"""
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We are given an array A[1..n] of integers, n >= 1. We want to
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find a pair of indices (i, j) such that
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1 <= i <= j <= n and A[j] - A[i] is as large as possible.
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Explanation:
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https://www.geeksforgeeks.org/maximum-difference-between-two-elements/
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>>> max_difference([5, 11, 2, 1, 7, 9, 0, 7])
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(1, 9)
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"""
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# base case
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if len(a) == 1:
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return a[0], a[0]
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else:
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# split A into half.
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first = a[: len(a) // 2]
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second = a[len(a) // 2 :]
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# 2 sub problems, 1/2 of original size.
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small1, big1 = max_difference(first)
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small2, big2 = max_difference(second)
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# get min of first and max of second
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# linear time
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min_first = min(first)
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max_second = max(second)
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# 3 cases, either (small1, big1),
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# (min_first, max_second), (small2, big2)
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# constant comparisons
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if big2 - small2 > max_second - min_first and big2 - small2 > big1 - small1:
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return small2, big2
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elif big1 - small1 > max_second - min_first:
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return small1, big1
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else:
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return min_first, max_second
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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