Write down a summation version of the run-time of each of thefollowing two algorithms and then figure out and prove the asymptotic complexity(-set) of that run-time function.(a) FUNCTION Wa(n = N)x < 0i 1WHILE i < n² DOx + +i ← 5iRETURN(x)(b) FUNCTION W₁(n = N)x < 0FOR1 TO ² DOj← 3WHILE j ≤ i DOx + +j← 2jRETURN(x)

write down a summation version of the runtime of each of the following algorithms and then figure…

Answered: (a) FUNCTION Wa(n = N) x i 0 1 WHILE…

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(a) FUNCTION Wa(n = N) x i 0 1 WHILE in² DO

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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Concept explainers

LUP Decomposition

LU decomposition stands for Lower-Upper decomposition. LU decomposition is the factorization of the lower triangular matrix and an upper triangular matrix. It is very useful in linear algebra and numerical analysis. A permutation matrix is usually included in the product. Gaussian elimination in a matrix form is known as LU decomposition, When inverting a matrix or evaluating its determinant, this is a crucial step. Tadeusz Banachiewicz, a Polish mathematician, first proposed the LU decomposition in 1938.

Question

Write down a summation version of the run-time of each of the
following two algorithms and then figure out and prove the asymptotic complexity
(-set) of that run-time function.
(a) FUNCTION Wa(n = N)
x < 0
i 1
WHILE i < n² DO
x + +
i ← 5i
RETURN(x)
(b) FUNCTION W₁(n = N)
x < 0
FOR
1 TO ² DO
j← 3
WHILE j ≤ i DO
x + +
j← 2j
RETURN(x)

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