Consider a currency system that has the following coins and their values: dollar (100 cents), quarter (25 cents), dime (10 cents), nickel (5 cents) and 1-cent coins. (A unit-value coin is always required). Suppose we want to give a change of value n cents in such a way that the total number of coins n is minimized. Design a greedy algorithm to solve this problem.

Q: Given a value `value`, if we want to make change for `value` cents, and we have infinite supply of…

A: 1. Create a list `dp` of size (value + 1) and initialize all elements to 0.2. Set `dp[0]` to 1,…

Q: Write a recurrence that would be used in dynamic programming for the following problem: Given a rod…

A: #include<stdio.h>#include<limits.h> // this is mainly used for the finding of two…

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

A: Answer: We need to write which algorithms would be acceptable so we will see in the more details…

Q: Given a set B of n planar points, construct an efficient algorithm to determine whether or not there…

A: 1. take three points from user.2. sort the points.3. fins slope and 2nd plane.4. check whether the…

Q: sorting algorithm is in O(n2) in the worst case. It takes 2 seconds to sort 10,000  records, i.e. n…

A: As per the given information, we are supposed to solve the two parts provided.

Q: We have two input arrays, an array A with n elements, and an array B with m elements, where m 2 n.…

A: Brute force algorithm would require us to perform linear search. Best case algorithm would require…

Q: Let m be a randomly chosen non-negative integer having at most n decimal digits, i.e. an integer in…

A: Let m be randomly chosen non-negative integer having at most n digits, i.e.,an integer in the…

Q: We want to send n cargo by n truck. Each truck can move only one cargo and receives different costs…

A: We want to send n cargo by n truck. Each truck can move only one cargo and receives different costs…

Q: Problem 5. Let S be a perhaps multi-set of n integers. Give an algorithm to determine whether 5 has…

A: Task : Given the multiset S and value k. The task is to find the algorithm to determine whether S…

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: A divide-and-conquer algorithm's recurrence is 3T(n/3) + vn, thus T(n) E Pick one: a. None O(vn log…

A: We are given a recurrence relation and we are asked which option is correct for it after solving it.…

Q: Many scheduling problems can be solved using greedy algorithms. A classic problem is as follows:…

A: A greedy algorithm is a problem-solving approach that makes locally optimal choices at each step in…

Q: Write A First Greedy Algorithm Example: The Coin-Changing Problem and explain it with code

A: The coin - changing problem :  It is the most easiest thing to understand . The coin changing…

Q: Cryptography Algorithm Q: Say that x^2 = y^2 mod n, but x != y mod n and x != −y mod n. (a) Show…

A: Non Trivial factor: It is the opposite of trivial factor. The non trivial factor of the number is…

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: Given an array of digits D[1, . . . , n], find the largest multiple of three that can be formed by…

A: When there are multiple questions, we must answer the first one.

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: Algorithm A search using the heuristic h(n) = α for some fixed constant α > 0 is guaranteed to find…

A: Algorithm -> A search heuristic h(n) = α fixed constant α > 0 We have to verify the statement…

Q: Algorithm MultiplyMatrix for(i = 0; i < n; ++i)         for(j = 0; j < n; ++j)…

A: Innermost loop k iterating n times. now, loop j is varying from 0 to n-1. So, j iterating n times.…

Q: You are given a set of n (closed) intervals on a line: [a1, bi], [a2, b2], ., [an, bn]. Design an…

A: Answer is given below

Q: Assuming you possess a total of 'm' dollars, and are accompanied by a group of 'n' friends. For…

A: Imagine that you have a total of 'm' dollars, and you are in the company of 'n' friends. Each of…

Q: The Coin-Changing Problem Is A Good First Example Of A Greedy Algorithm To Write describe it with…

A: Introduction: The coin-changing problem is a well-known problem in computer science that involves…

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: The input is a set of jobs j1, j2, ..., jN, each of which takes one time unit to complete. Each job…

A: Answer is given below-

Q: Many scheduling problems can be solved using greedy algorithms. A classic problem is as follows:…

A: It is possible to invent several greedy algorithms for the problem.

Q: Implement the divide-and-conquer O(n) time

A: Coded using C++.

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: You are going to purchase items from a store that can carry a maximal weight of 'w' into your…

A: Given: You are going to purchase items from a store that can carry a maximal weight of 'w' into your…

Q: not handwritten    Design a divide and conquer algorithm to solve the following problem in Θ(n log…

A: In this question we need to write an algorithm which finds indices i and j which maximizes the value…

Q: Design and analyze asymptotically a divide-conquer algorithm for the following problem: input: a…

A: Introduction : Algorithm A: Input: s, a string of length n Output: the number of substrings of s…

Q: A bottle factory produces bottles of equal mass. During a production, the weight of one of the…

A: Input:First-line contains T number of test cases.For each of the T-test cases, the first line…

Q: find running Time complexity T(n) and Space complexity S(n). Also   show in big-O notation.

A: Time Complexity is the amount of time required for program execution Generally, each statement takes…

Q: Devise a divide-and-conquer algorithm that multiplies a matrix A and a matrix B (both of them are…

A: The algorithm to multiply two matrices A and B of size n×n in O(n^(log 7 base 2)) time using the…

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…

Q: What is the heuristic function of greedy best-first search? O f(n) not equals to h(n) f(n) less than…

A: According to the question The Best Greedy Search attempts to expand the area around the goal, on the…