oblem, the order of the items when sorted by increasing weight is the same as their order when sorted by decreasing value. Give an e cient algorithm to nd an optimal solution to this variant of the knapsack problem, and argue that your algorith
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Suppose that in a 0-1 knapsack problem, the order of the items when sorted by increasing weight is the same as their order when sorted by decreasing value. Give an e cient
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- 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?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 FalseFor a double knapsack problem, assume follwoing 2 algorithms used. (1) Use the regular subset sum knapsack algorithm to pick a maximum-value solution S1 that fits in the first knapsack, and then use it again on the remaining items to pick a maximum-value solution S2 that fits in the second knapsack. (2) Use the Knapsack algorithm to pick a maximum-value solution S that would fit in a knapsack with capacity C1+C2, then partition S arbitrarily into two sets S1 and S2 with total sizes at most C1 and C2, respectively. Which of the following statements are true? (Choose all that apply.) a) Algorithm (1) is guaranteed to produce an optimal solution to the double-knapsack problem but algorithm (2) is not. b) Algorithm (2) is guaranteed to produce an optimal solution to the double-knapsack problem but algorithm (1) is not. c) Algorithm (1) is guaranteed to produce an optimal solution to the double-knapsack problem when C1=C2. d) Neither algorithm is guaranteed to produce an…
- 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 FalseIf a Genetic Algorithm only finds local optimal solutions, what should be done to find a better one globally?Suppose we have a heuristic h that over-estimates h* by at most epsilon (i.e., for all n, 0<= h(n) <= h*(n)+epsilon). Show that A* search using h will get a goal whose cost is guaranteed to be at most epsilon more than that of the optimal goal.
- Consider the following search problem, represented as a graph. The start state is S and the only goal state is G. For questions which require a heuristic, use the table given below. Please simulate the UCS search algorithm and find the optimal path. Please simulate the A* search algorithm and find the optimal path.Constructing an Optimal Solution:algorithm LCSWithAdvice x1, ... , xi, y1, ... , yj, birdAdvice pre- & post-cond: Same as LCS except with advice.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. 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.
- Using the image provided, please answer the following questions. (a). Find a path from a to g in the graph G using the search strategy of depth-first search. Is the returned solution path an optimal one? Give your explanation and remarks on "why-optimal" or "why-non-optimal". (b). Find a path from a to g in the graph G using the search strategy of breadth-first search. Is the returned solution path an optimal one? Give your explanation and remarks on "why-optimal" or "why-non-optimal".(c). Find a path from a to g in the graph G using the search strategy of least-cost first search. Is the returned solution path an optimal one? Give your explanation and remarks on "why-optimal" or "why-non-optimal". (d). Find a path from a to g in the graph G using the search strategy of best-first search. The heuristics for these nodes are: h(a,25); h(b, 43); h(c,5); h(d, 64); h(g, 0). Is the returned solution path an optimal one? Give your explanation and remarks on "why-optimal or "why-non-optimal".…Develop a dynamic programming algorithm for the knapsack problem: given n items of know weights w1, . . . , wn and values v1, . . . ,vn and a knapsack of capacity W, find the most valuable subset of the items that fit into the knapsack. We assume that all the weights and the knapsack’s capacity are positive integers, while the item values are positive real numbers. (This is the 0-1 knapsack problem). Analyze the structure of an optimal solution. Give the recursive solution. Give a solution to this problem by writing pseudo code procedures. Analyze the running time for your algorithms.Apply the bottom-up dynamic programming algorithm to the followinginstance of the knapsack problem: Item Weight Value 1 3 $25 2 2 $30 3 1 $15 4 4 $40 5 5 $50 Capacity W = 8.