Queen 3 Prove that repeatedly picking the largest possible denomination gives the optimal solution for the coin change problem with coin denominations 1, 7, 7^2, 7^3, ……, 7^m for some fixed m≥0. Full explain this question and text typing work only thanks
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Queen 3
Prove that repeatedly picking the largest possible denomination gives the optimal solution for the coin change problem with coin denominations 1, 7, 7^2, 7^3, ……, 7^m for some fixed m≥0.
Full explain this question and text typing work only thanks
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- Consider the problem of providing change for an amount of n-bahts while using the smallest possible quantity of coins. You may assume that each coin’s value is integer. Assume that the coins available for use have values that can be expressed as powers of c. To clarify, the denominations of the coins can be written as c0,c1,..., ck , where c is an integer greater than 1, and k is a positive integer. Prove that the greedy algorithm always yields an optimal solution.Consider 7 items along their respective weights and values I = I1, I2, I3, I4, I5, I6, I7W = 2,3,5,7,1,4,1V = 10,5,15,7,6,18,3 The capacity of knapsack W=15. Find the optimal solution of the fractional knapsackproblem. What is the complexity of finding the solution of fractional knapsack problem?The heuristic path algorithm is a best-first search in which the objective function is f(n)= 3w*g(n) + (2w+1) * h(n), 0≤w<3. For what values of w is this algorithm guaranteed to be optimal?
- he heuristic path algorithm is a best-first search in which the objective function is f(n) = (4 −w)g(n) + wh(n). For what values of w is this algorithm guaranteed to be optimal? What kind of search does this perform when w = 0? When w = 1? When w = 4?Subject : Artificial Intelligence Consider a best first search (BFS) algorithm that tries to find the optimal goal state with minimal cost. Consider heuristics h1, h2 with h1(n) > h2(n) for all states n. BFS with h1 is guaranteed to expand fewer nodes or an equal number of nodes to arrive at the optimal goal state than BFS with h2 Select one: True FalseConsider the problem of providing change for an amount of n-bahts while using the smallest possible quantity of coins. You may assume that each coin’s value is integer. Describe a greedy algorithm to make change consisting of 1-baht coins, 5-baht coins, and 10-baht coins and prove that your algorithm yields an optimal solution.
- Question 5 (greedy) Prove that repeatedly picking the largest possible denomination gives the optimal solution for the coin change problem with coin denominations 1, 7, 7^2, 7^3, ……, 7^m for some fixed m≥0. Full explain this question and text typing work onlyCalculate the optimal path from g to a using A* algorithm (as heuristic function, use the provided table)Usingthe following coindenominationsas an example: 1, 5, 20 and23, explain whythegreedy solution for thechange-making problem does not result in an optimal solution.
- What is the solution by greedy algorithm to the change-making problem with denominations 1, 3, and 4 to return the minimum number of coins for an amount of 6? Copy and paste the following expression and replace the ? mark by a number ?(4), ?(3), ?(1) (Keep the same format) Is the solution provided by greedy algorithm to the change-making problem with denominations 1, 3, and 4 to return the minimum number of coins for an amount of 6 optimal or not? prove your answerConsider the following version of Knapsack. Given are two weight limits W1 and W2, whereW1 ≤ W2. Given are also n items (w1, c1),(w2, c2), . . . ,(wn, cn), where wiis the weight and cithe cost of the i-th item. We want to find a subset of these items of the highest cost, wherethe subset weights at least W1 and at most W2. Give an O(nW2) algorithm for this problem.(Recall that the cost (respectively weight) of a subset is the sum of the costs (respectivelyweights) of the items in the subset.)The branching part of the branch and bound algorithm that Solver uses to solve integer optimization models means that the algorithm [a] creates subsets of solutions through which to search[b] searches through only a limited set of feasible integer solutions [c] identifies an incumbent solution which is optimal [d] uses a decision tree to find the optimal solution 2. The LP relaxation of an integer programming (IP) problem is typically easy to solve and provides a bound for the IP model. [a] True [b] False