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Michael O'Brien

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Introduction

Collatz numbers follow the sequence until x(n) is 1....

    odd numbers are multiplied by 3 and increased by 1

    even numbers are divided by 2

or (with shifting)

    x(n) = initial

    if x(n) even then x(n + 1) = x(n) >> 1 else x(n + 1) = x(n) << 1 + x(n) + 1



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jenkins

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Requirements

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R#A#Details
R1
Optimize computation using parallel processing
R2
Optimize computation by maintaining a map of previous sequences





Analysis

Map/Graph lookup for sequence truncation

The goal of computing the collatz sequence for a particular number is to iterate the sequence to 1.   Since we have previously computed sequences that we will eventually revisit when running higher numbers - we must optimize collatz sequence generation by storing previous sequences for query.  For example, the trivial sequence 8,4,2,1 is a subset of 32,16,8,4,2,1

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