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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
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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.
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