Answered: Arithmetic progression def…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Arithmetic progression
def arithmetic_progression(items):
An arithmetic progression is a numerical sequence so that the stride between each two consecutive elements is constant throughout the sequence. For example, [4, 8, 12, 16, 20] is an arithmetic progression of length 5, starting from the value 4 with a stride of 4. Given a non-empty list items of positive integers in strictly ascending order, find and return the
longest arithmetic progression whose all values exist somewhere in that sequence. Return the answer as a tuple (start, stride, n) of the values that define the progression. To ensure unique results to facilitate automated testing, if there exist several progressions of the same length, this function should return the one with the lowest start. If several progressions of equal length emanate from the lowest start, return the progression with the smallest stride.

items	expected results
[42]	(42, 0, 1)
[2, 4, 6, 7, 8, 12, 17]	(2, 2, 4)
[1, 2, 36, 49, 50, 70, 75, 98, 104, 138, 146,148, 172, 206, 221, 240, 274, 294, 367, 440]	(2, 34, 9)
[2, 3, 7, 20, 25, 26, 28, 30, 32, 34, 36, 41, 53, 57, 73, 89, 94, 103, 105, 121, 137, 181, 186, 268, 278, 355, 370, 442, 462, 529, 554, 616, 646, 703]	(7, 87, 9)
range(1000000)	(0, 1, 1000000)

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