A certain computer algorithm executes twice as many operations when it is run with an input of size k as when it is run with an input ofsize k - 1 (where k is an integer that is greater than 1). When the algorithm is run with an input of size 1, it executes seven operations. Howmany operations does it execute when it is run with an input of size 24?For each integernz 1, let s,-1 be the number of operations the algorithm executes when it is run with an input of size n. Thenfor each integer 2 1. Therefore, So, S3. Sz.is -Select-and s,=with constantSelect-,which is. So, for every integer n 2 0, s, =It follows that for an input of size 24, the numberof operations executed by the algorithm is s-Select-vwhich equalsNeed Heln?Desd

A certain computer algorithm executes twice as many operations when it is run with an input of size k as when it is run with an input of size k - 1 (where k is an integer that is greater than 1). When the algorithm is run with an input of size 1, it executes seven operations. How many operations does it execute when it is run with an input of size 24? For each integern21, let s,-1 be the number of operations the algorithm executes when it is run with an input of size n. Then and s for each integer k 2 1. Therefore, So, $y. $2 .. is -Select- with constant Select ,which is So, for every integer n 2 0, s,= It follows that for an input of size 24, the number of operations executed by the algorithm is which equals -Select-

A certain computer algorithm executes twice as many operations when it is run with an input of size k as when it is run with an input of size k - 1 (where k is an integer that is greater than 1). When the algorithm is run with an input of size 1, it executes seven operations. How many operations does it execute when it is run with an input of size 24? For each integern21, let s,-1 be the number of operations the algorithm executes when it is run with an input of size n. Then and s for each integer k 2 1. Therefore, So, $y. $2 .. is -Select- with constant Select ,which is So, for every integer n 2 0, s,= It follows that for an input of size 24, the number of operations executed by the algorithm is which equals -Select-

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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A certain computer algorithm executes twice as many operations when it is run with an input of size k as when it is run with an input of size k – 1 (where k is an integer that is greater than 1). When the algorithm is run with an input of size 1, it executes seven operations. How many operations does it execute when it is run with an input of size 26? For each integer n 2 1, let s, -1 be the number of operations the algorithm executes when it is run with an input of size n. Then s, = and s = for each integer k 2 1. Therefore, So, S1, S21 -Select--- with constant Select--- |, which is So, for every integer n 2 0, s, It follows that for an input of size 26, the number of ... is operations executed by the algorithm is s which equals ---Select--- v
1. A runner targets herself to improve her time on a certain course by 3 seconds a day. If onday 0 she runs the course in 3 minutes, how fast must she run it on day 14 to stay ontarget?2. A certain computer algorithm executes twice as many operations when it is run with aninput of size k as when it is run with an input of size k − 1 (where k is an integer that isgreater than 1). When the algorithm is run with an input of size 1, it executes sevenoperations. How many operations does it execute when it is run with an input of size 25?
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There are n different sizes of boxes, from 1 to n. There is an unlimited supply of boxes of each size t, each with a value vt . A box of size t can hold several smaller boxes of sizes a1, a2, . . . , ak as long as the sum of sizes a1 + a2 + . . . + ak is strictly less than t. Each of these boxes may be filled with yet more boxes, and so on. Design an algorithm which runs in O(n2 ) time and finds the maximum value that can be attained by taking one box, potentially with smaller boxes nested inside it.
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Suppose that you have five different algorithms (A, B, C, D and E) for solving a problem. To solve a problem of size n, the number of operations used by each algorithm is as follows. As n grows, which algorithm uses the most operations? Algorithm number of operations n2+n3 A B 2n+1 log n 100 26 + log no logn)² +1 D Algorithm C Algorithm E O Algorithm A Algorithm D Algorithm B O O
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