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.

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.

Related questions

Q: Write a Python program to give changes for the least number of bills and coins. • Assume the…

A: num = float(input("Enter the currency: ")) #entering amounttemp = float(0)for i in range(11):…

Q: Write a C program to solve the fractional knapsack problem. For example, the weights and values of 3…

A: Here is the c program. I have provided source code screenshot in the below steps. See below steps…

Q: Given the locations of the gas stations in some arbitrary order, describe an algorithm that finds an…

A: Below I have used "k - problem center " Greedy algo:

Q: Design a greedy algorithm to make change for n cents using the least number of coins among quarters…

A: 1)Consider n<5, then use n pennies.consider 5<=n<`0, then use n-5 pennies and 1…

Q: Show that the greedy algorithm for making change for n cents using quarters, dimes, nickels, and…

Q: The classic example of following a greedy algorithm is making change. Let’s say you buy some items…

A: 1. Create a list of available coin denominations (e.g., quarters, dimes, nickels, and pennies).2.…

Q: Assume A = [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0]. Create a greedy algorithm with the…

A: It is a finite sequence of well-defined, computer-implementable instructions, typically to solve a…

Q: There are 3 algorithms to solve the same problem. Let n = problem size. Suppose that their runtime…

Q: A student has been asked to put some parcels on a shelf. The parcels all weigh different amounts,…

A: Greedy algorithm A greedy algorithm is any algorithm that follows the problem-solving heuristic of…

Q: We want to purchase an item of price and for that, we have an unlimited (!) supply of three types of…

A: The dynamic programming algorithm for problem 4 will be: 1. We will make a 1-D dp array where dp[i]…

Q: Given two strings X[1, . . . , n] and Y [1, . . . , m], find the minimum number of steps required to…

A: Subproblem: We will traverse both the string from either side(left or right). Let's traverse the…

Q: There are n different sizes of boxes, from 1 to n. There is an unlimited supply of boxes of each…

A: Hi there, Please find your solution below, I hope you would find my solution useful and helpful.…

Q: Suppose that each person in a group of n people votes for exactly two people from a slate of…

A: a) We can use the following stages to create a divide-and-conquer algorithm that identifies the…

Q: numerous bouquet combinations, including two 5-rose bouquets (total profit of $70), and a 4-rose…

A: Roses 1 2 3 4 5 Profit $5 $15 $24 $30…

Q: Find the best solution for the 0-1 knapsack problem using backtracking algorithm. We have 5 items…

A: The above question is solved in step 2 and step 3 :-

Q: Using a Population-based Algorithm (E.g. Genetic Algorithm or Ant Colony Optimisation algorithms)…

A: According to the information given:- We have to follow the instruction in order to get the desired…

Q: Kruskal's MSP algorithm is an example of following type of algorithm Divide and Conquer Dynamic…

A: Kruskal's Minimum Spanning Tree (MST) algorithm is an example of a Greedy algorithm.In Kruskal's…

Question

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

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1: Introducing the concept

VIEW

Step 2: Proving that greedy algorithm may not always give optimal solution

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, data-structures-and-algorithms and related others by exploring similar questions and additional content below.

Similar questions

Given an array of intervals I[1, . . . , n] where I[i] = [si, fi], find the minimumnumber of intervals you need to remove to make the rest of the intervals non-overlapping. Precisely define the subproblem.Provide the recurrence equation.Describe the algorithm in pseudocode to compute the optimal value.Describe the algorithm in pseudocode to print out an optimal solution.
Find the best solution for the 0-1 knapsack problem using backtracking algorithm. We have 5 items with price and weight: $50 $30 $40 $100 $20 10 1. 2. 3. 2 4. 10 5. 5 Limitation on the weight is: W = 21
TRUE OR FALSE N Queen's problem can be effectively solved using a divide-and-conquer algorithm.
For x = [7 3 9 10 15] and y= [18 2 9 12 4], what is obtained for z when using z = find(x
consider a jewler who shows a collection of diamonds to a person. all diamonds have different integer ounce weights and are laid out in a single row on the table. what is the largest weight amount of diamonds that the person can take, provided that the person cannot select adjacent diamonds? use standard pseudocode notation similar to python to write a dynamic programming bottom up algorithm that solves this problem for any n number of diamonds.
computes and returns the smallest positive integer n for which 1+2+3+...+n equals or exceeds the value of "goal".
The classic example of following a greedy algorithm is making change. Let’s say you buy some items at the store and the change from your purchase is 63 cents. How does the clerk determine the change to give you? If the clerkfollows a greedy algorithm, he or she gives you two quarters, a dime, and three pennies. That is the smallest number of coins that will equal 63 cents (given that we don’t allow fifty-cent pieces). It has been proven that an optimal solution for coin changing can always be found using the current American denominations of coins. However, if we introduce some other denomination to the mix, the greedy algorithm doesn’t produce an optimal solution.Write a program that uses a greedy algorithm to make change (this code assumes change of less than one dollar).