Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 35.5, Problem 4E
Program Plan Intro
To describe the method to modify the approximation scheme provided in this section in order to get good approximation to the smallest value not less than t that is a sum of some subset of the given input list.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Explian this C program
#include <stdio.h>
unsigned int rotateRight(unsigned int num, unsigned int bits) {
unsignedint bit_count =sizeof(unsignedint) *8;
bits = bits % bit_count; // Handle cases where bits >= bit_count
return (num >> bits) | (num << (bit_count - bits));
}
int main() {
unsignedint num, bits;
printf("Enter a number: ");
scanf("%u", &num);
printf("Enter the number of bits to shift: ");
scanf("%u", &bits);
printf("After rotation: %u\n", rotateRight(num, bits));
return0;
}
Explian thiS C program
#include<stdio.h>
int countSetBits(int n) { int count = 0; while (n) { count += n & 1; n >>= 1; } return count;}
int main() { int num; printf("Enter a number: "); scanf("%d", &num); printf("Output: %d units\n", countSetBits(num)); return 0;}
Please provide the Mathematica code
Chapter 35 Solutions
Introduction to Algorithms
Ch. 35.1 - Prob. 1ECh. 35.1 - Prob. 2ECh. 35.1 - Prob. 3ECh. 35.1 - Prob. 4ECh. 35.1 - Prob. 5ECh. 35.2 - Prob. 1ECh. 35.2 - Prob. 2ECh. 35.2 - Prob. 3ECh. 35.2 - Prob. 4ECh. 35.2 - Prob. 5E
Ch. 35.3 - Prob. 1ECh. 35.3 - Prob. 2ECh. 35.3 - Prob. 3ECh. 35.3 - Prob. 4ECh. 35.3 - Prob. 5ECh. 35.4 - Prob. 1ECh. 35.4 - Prob. 2ECh. 35.4 - Prob. 3ECh. 35.4 - Prob. 4ECh. 35.5 - Prob. 1ECh. 35.5 - Prob. 2ECh. 35.5 - Prob. 3ECh. 35.5 - Prob. 4ECh. 35.5 - Prob. 5ECh. 35 - Prob. 1PCh. 35 - Prob. 2PCh. 35 - Prob. 3PCh. 35 - Prob. 4PCh. 35 - Prob. 5PCh. 35 - Prob. 6PCh. 35 - Prob. 7P
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.Similar questions
- Explian this C program code. #include <stdio.h> void binary(unsigned int n) { if (n /2!=0) { binary(n /2); } printf("%d", n %2); } int main() { unsignedint number =33777; unsignedchar character ='X'; printf("Number: %u\n", number); printf("Binary: "); binary(number); printf("\nDecimal: %u\nHexadecimal: 0x%X\n\n", number, number); printf("Character: %c\n", character); printf("ASCII Binary: "); binary(character); printf("\nASCII Decimal: %u\nASCII Hexadecimal: 0x%X\n", character, character); return0; }arrow_forwardDesign a dynamic programming algorithm for the Longest Alternating Subsequence problem described below: Input: A sequence of n integers Output: The length of the longest subsequence where the numbers alternate between being larger and smaller than their predecessor The algorithm must take O(n²) time. You must also write and explain the recurrence. Example 1: Input: [3, 5, 4, 1, 3, 6, 5, 7, 3, 4] Output: 8 ([3, 5, 4, 6, 5, 7, 3, 4]) Example 2: Input: [4,7,2,5,8, 3, 8, 0, 4, 7, 8] Output: 8 ([4, 7, 2, 5, 3, 8, 0,4]) (Take your time with this for the subproblem for this one)arrow_forwardDesign a dynamic programming algorithm for the Coin-change problem described below: Input: An amount of money C and a set of n possible coin values with an unlimited supply of each kind of coin. Output: The smallest number of coins that add up to C exactly, or output that no such set exists. The algorithm must take O(n C) time. You must also write and explain the recurrence. Example 1: Input: C24, Coin values = = [1, 5, 10, 25, 50] Output: 6 (since 24 = 10+ 10+1+1 +1 + 1) Example 2: Input: C = 86, Coin values = [1, 5, 6, 23, 35, 46, 50] Output: 2 (since 86 = 46+35+5)arrow_forward
- Design a dynamic programming algorithm for the Longest Common Subsequence problem de- scribed below Input: Two strings x = x1x2 xm and y = Y1Y2... Yn Output: The length of the longest subsequence that is common to both x and y. . The algorithm must take O(m n) time. You must also write and explain the recurrence. (I want the largest k such that there are 1 ≤ i₁ < ... < ik ≤ m and 1 ≤ j₁ < ... < jk ≤ n such that Xi₁ Xi2 Xik = Yj1Yj2 ··· Yjk) Example 1: Input: x = 'abcdefghijklmnopqrst' and y = 'ygrhnodsh ftw' Output: 6 ('ghnost' is the longest common subsequence to both strings) Example 2: Input: x = 'ahshku' and y = ‘asu' Output: 3 ('asu' is the longest common subsequence to both strings)arrow_forwardDesign a dynamic programming algorithm for the problem described below Input: A list of numbers A = = [a1,..., an]. Output: A contiguous subsequence of numbers with the maximum sum. The algorithm must take O(n) time. You must also write and explain the recurrence. (I am looking for an i ≥ 1 and k ≥ 0 such that a + ai+1 + ···ai+k has the largest possible sum among all possible values for i and k.) Example 1: Input: A[5, 15, -30, 10, -5, 40, 10]. Output: [10, 5, 40, 10] Example 2: Input: A = [7, 5, 7, 4, -20, 6, 9, 3, -4, -8, 4] Output: [6,9,3]arrow_forwardDesign a dynamic programming algorithm for the Longest Increasing Subsequence problem described below: Input: A sequence of n integers Output: The length of the longest increasing subsequence among these integers. The algorithm must take O(n²) time. You must also write and explain the recurrence. Example 1: Input: [5, 3, 6, 8, 4, 6, 2, 7, 9, 5] Output: 5 ([3, 4, 6, 7, 9]) Example 2: Input: [12, 42, 66, 73, 234, 7, 543, 16] Output: 6 ([42, 66, 73, 234, 543])arrow_forward
- Design a dynamic programming algorithm for the Subset Sum problem described below: Input: A set of n integers A and an integer s Output: A subset of A whose numbers add up to s, or that no such set exists. The algorithm must take O(n·s) time. You must also write and explain the recurrence. Example 1: Input: A = {4, 7, 5, 2, 3}, s = 12 Output: {7,2,3} Example 2: Input: A{4, 7, 5,3}, s = 6 Output: 'no such subset'arrow_forwardTECNOLOGIE DEL WEB 2023/2023 (VER 1.1) Prof. Alfonso Pierantonio 1. Project Requirements The project consists in designing and implementing a Web application according to the methodology and the technologies illustrated and developed during the course. This document describe cross-cutting requirements the application must satisfy. The application must be realized with a combination of the following technologies: PHP MySQL HTML/CSS JavaScript, jQuery, etc templating The requirements are 2. Project size The application must have at least 18 SQL tables The number of SQL tables refers to the overall number of tables (including relation normalizations). 3. Methodology The application must be realized by adopting separation of logics, session management, and generic user management (authentication/permissions). Missing one of the above might correspond to a non sufficient score for the project. More in details: 3.1 Separation of Logics The separation of logics has to be realizse by using…arrow_forwardWrite a C program to calculate the function sin(x) or cos(x) using a Taylor series expansion around the point 0. In other words, you will program the sine or cosine function yourself, without using any existing solution. You can enter the angles in degrees or radians. The program must work for any input, e.g. -4500° or +8649°. The function will have two arguments: float sinus(float radians, float epsilon); For your own implementation, use one of the following relations (you only need to program either sine or cosine, you don't need both): Tip 1: Of course, you cannot calculate the sum of an infinite series indefinitely. You can see (if not, look in the program) that the terms keep getting smaller, so there will definitely be a situation where adding another term will not change the result in any way (see problem 1.3 – machine epsilon). However, you can end the calculation even earlier – when the result changes by less than epsilon (a pre-specified, sufficiently small number, e.g.…arrow_forward
- Write a C program that counts the number of ones (set bits) in the binary representation of a given number. Example:Input: 13 (binary 1101)Output: 3 unitsarrow_forwardI need help to resolve or draw the diagrams. thank youarrow_forwardYou were requested to design IP addresses for the following network using the addressblock 166.118.10.0/8, connected to Internet with interface 168.118.40.17 served by the serviceprovider with router 168.118.40.1/20.a) Specify an address and net mask for each network and router interface in the table provided. b) Give the routing table at Router 1.c) How will Router 1 route the packets with destinationi) 168.118.10.5ii) 168.118.10.103iii) 168.119.10.31iii) 168.118.10.153arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole
C++ Programming: From Problem Analysis to Program...Computer ScienceISBN:9781337102087Author:D. S. MalikPublisher:Cengage Learning
COMPREHENSIVE MICROSOFT OFFICE 365 EXCEComputer ScienceISBN:9780357392676Author:FREUND, StevenPublisher:CENGAGE L- Programming Logic & Design ComprehensiveComputer ScienceISBN:9781337669405Author:FARRELLPublisher:Cengage
C++ for Engineers and ScientistsComputer ScienceISBN:9781133187844Author:Bronson, Gary J.Publisher:Course Technology Ptr
Systems ArchitectureComputer ScienceISBN:9781305080195Author:Stephen D. BurdPublisher:Cengage Learning
Operations Research : Applications and Algorithms
Computer Science
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Brooks Cole
C++ Programming: From Problem Analysis to Program...
Computer Science
ISBN:9781337102087
Author:D. S. Malik
Publisher:Cengage Learning
COMPREHENSIVE MICROSOFT OFFICE 365 EXCE
Computer Science
ISBN:9780357392676
Author:FREUND, Steven
Publisher:CENGAGE L
Programming Logic & Design Comprehensive
Computer Science
ISBN:9781337669405
Author:FARRELL
Publisher:Cengage
C++ for Engineers and Scientists
Computer Science
ISBN:9781133187844
Author:Bronson, Gary J.
Publisher:Course Technology Ptr
Systems Architecture
Computer Science
ISBN:9781305080195
Author:Stephen D. Burd
Publisher:Cengage Learning