Q5 50 Create a divide and conquer algorithm for multiplication you do not need to analyze the runtime though, based on this equation. Let X be an integer with n digits. We divide X into: • XL: First [n/3] digits (approximately one-third of the digits) XR: Last n[n/3] digits (approximately two-thirds of the digits) Similarly, we break Y into: • Y: First [n/3] digits YR: Last n [n/3] digits Representing X and Y XXL 102/3 + XR Y Y 102/3 + YR Multiplying X and Y To multiply X and Y: XXY = (XL 102/3 + XR) × (YL · 102n/3+YR)
Q5 50 Create a divide and conquer algorithm for multiplication you do not need to analyze the runtime though, based on this equation. Let X be an integer with n digits. We divide X into: • XL: First [n/3] digits (approximately one-third of the digits) XR: Last n[n/3] digits (approximately two-thirds of the digits) Similarly, we break Y into: • Y: First [n/3] digits YR: Last n [n/3] digits Representing X and Y XXL 102/3 + XR Y Y 102/3 + YR Multiplying X and Y To multiply X and Y: XXY = (XL 102/3 + XR) × (YL · 102n/3+YR)
Programming Logic & Design Comprehensive
9th Edition
ISBN:9781337669405
Author:FARRELL
Publisher:FARRELL
Chapter6: Arrays
Section: Chapter Questions
Problem 19RQ
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Please solve the following
![Q5
50
Create a divide and conquer algorithm for multiplication you do not need to analyze the
runtime though, based on this equation.
Let X be an integer with n digits. We divide X into:
•
XL: First [n/3] digits (approximately one-third of the digits)
XR: Last n[n/3] digits (approximately two-thirds of the digits)
Similarly, we break Y into:
•
Y: First [n/3] digits
YR: Last n [n/3] digits
Representing X and Y
XXL 102/3 + XR
Y Y 102/3 + YR
Multiplying X and Y
To multiply X and Y:
XXY = (XL 102/3 + XR) × (YL · 102n/3+YR)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F963c82ed-fd9a-4657-9173-14563717e6ee%2Fa8898f12-add9-43a3-a939-cff6112724d5%2Fwk8i6sf_processed.png&w=3840&q=75)
Transcribed Image Text:Q5
50
Create a divide and conquer algorithm for multiplication you do not need to analyze the
runtime though, based on this equation.
Let X be an integer with n digits. We divide X into:
•
XL: First [n/3] digits (approximately one-third of the digits)
XR: Last n[n/3] digits (approximately two-thirds of the digits)
Similarly, we break Y into:
•
Y: First [n/3] digits
YR: Last n [n/3] digits
Representing X and Y
XXL 102/3 + XR
Y Y 102/3 + YR
Multiplying X and Y
To multiply X and Y:
XXY = (XL 102/3 + XR) × (YL · 102n/3+YR)
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