Homework Help is Here – Start Your Trial Now!
Engineering
Computer Science
problem 2 please  Ans to problem 1 is  #include using namespace std;   vector  targetSum(vector  &a , int &target) { int n = a.size(); for(int i = 0 ; i < n - 1 ; i++) for(int j = i + 1 ; j < n ; j++) { if(a[i] + a[j] == target) return {i + 1 , j + 1}; } return {}; }   int main() { vector  a = {1 , 4 , 5 , 11 , 12}; int target = 9; for(int &x : targetSum(a , target)) cout << x << " "; cout << '\n'; }

problem 2 please  Ans to problem 1 is  #include using namespace std;   vector  targetSum(vector  &a , int &target) { int n = a.size(); for(int i = 0 ; i < n - 1 ; i++) for(int j = i + 1 ; j < n ; j++) { if(a[i] + a[j] == target) return {i + 1 , j + 1}; } return {}; }   int main() { vector  a = {1 , 4 , 5 , 11 , 12}; int target = 9; for(int &x : targetSum(a , target)) cout << x << " "; cout << '\n'; }

Database System Concepts
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
See similar textbooks
icon
Related questions
Question

problem 2 please 

Ans to problem 1 is 

#include <bits/stdc++.h>
using namespace std;
 
vector <int> targetSum(vector <int> &a , int &target)
{
int n = a.size();
for(int i = 0 ; i < n - 1 ; i++)
for(int j = i + 1 ; j < n ; j++)
{
if(a[i] + a[j] == target)
return {i + 1 , j + 1};
}
return {};
}
 
int main()
{
vector <int> a = {1 , 4 , 5 , 11 , 12};
int target = 9;
for(int &x : targetSum(a , target))
cout << x << " ";
cout << '\n';
}
Problem 1. Assume that you were given N cents (N is an integer) and you were asked to break up the N cents into coins consisting of 1 cent, 2 cents and 5 cents. Write a dynamic- programming based recursive algorithm, which returns the smallest (optimal) number of coins needed to solve this problem. For example, if your algorithm is called A, and N = 13, then A(N) = A(13) returns 4, since 5+5+2+1 = 13 used the smallest (optimal) number of coins. In contrast, 5+5+1+1+1 is not an optimal answer. Problem 2. Draw the recursion tree for algorithm in Problem 1, where N = 7. Derive the complexity bound of the algorithm in Problem 1. You do not need to prove the complexity bound formally, just derive it by analyzing each component in your algorithm. Problem 3. Construct a memoized algorithm for the problem described in Problem 1 and derive its time complexity. You do not need to prove the complexity bound formally, just derive it by analyzing each component in your algorithm. Problem 4. Assume that you were given N cents (N is an integer) and you were asked to break up the N cents into coins consisting of 1 cent, 2 cents and 5 cents. Prove that a greedy algorithm always gives the optimal solution. Problem 5. Assume that you were given N cents (N is an integer) and you were asked to break up the N cents into coins consisting of 1 cent, 6 cents and 7 cents. Prove that a greedy algorithm may not always give the optimal solution.
Transcribed Image Text:Problem 1. Assume that you were given N cents (N is an integer) and you were asked to break up the N cents into coins consisting of 1 cent, 2 cents and 5 cents. Write a dynamic- programming based recursive algorithm, which returns the smallest (optimal) number of coins needed to solve this problem. For example, if your algorithm is called A, and N = 13, then A(N) = A(13) returns 4, since 5+5+2+1 = 13 used the smallest (optimal) number of coins. In contrast, 5+5+1+1+1 is not an optimal answer. Problem 2. Draw the recursion tree for algorithm in Problem 1, where N = 7. Derive the complexity bound of the algorithm in Problem 1. You do not need to prove the complexity bound formally, just derive it by analyzing each component in your algorithm. Problem 3. Construct a memoized algorithm for the problem described in Problem 1 and derive its time complexity. You do not need to prove the complexity bound formally, just derive it by analyzing each component in your algorithm. Problem 4. Assume that you were given N cents (N is an integer) and you were asked to break up the N cents into coins consisting of 1 cent, 2 cents and 5 cents. Prove that a greedy algorithm always gives the optimal solution. Problem 5. Assume that you were given N cents (N is an integer) and you were asked to break up the N cents into coins consisting of 1 cent, 6 cents and 7 cents. Prove that a greedy algorithm may not always give the optimal solution.
Expert Solution
steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Randomized Select Algorithm
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
Recommended textbooks for you
Database System Concepts
Database System Concepts
Computer Science
ISBN:
9780078022159
Author:
Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:
McGraw-Hill Education
Starting Out with Python (4th Edition)
Starting Out with Python (4th Edition)
Computer Science
ISBN:
9780134444321
Author:
Tony Gaddis
Publisher:
PEARSON
Digital Fundamentals (11th Edition)
Digital Fundamentals (11th Edition)
Computer Science
ISBN:
9780132737968
Author:
Thomas L. Floyd
Publisher:
PEARSON
C How to Program (8th Edition)
C How to Program (8th Edition)
Computer Science
ISBN:
9780133976892
Author:
Paul J. Deitel, Harvey Deitel
Publisher:
PEARSON
Database Systems: Design, Implementation, & Manag…
Database Systems: Design, Implementation, & Manag…
Computer Science
ISBN:
9781337627900
Author:
Carlos Coronel, Steven Morris
Publisher:
Cengage Learning
Programmable Logic Controllers
Programmable Logic Controllers
Computer Science
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
SEE MORE TEXTBOOKS