Use the Backtracking algorithm for the 0-1 Knapsack problem (Algorithm 5.7) to maximize the profit for the following problem instance. Show the actions step by step. Pi i Pi Wi Wi 1 $20 2 $30 25 10 6 3 $35 7 5 W = 9 4 $12 3 4 5 $3 1 3
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- 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.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 = 21Consider navigating the maze shown below (same maze used in the homework). (N M 4 2 K 2 2 2 E B G 2 2 F H 2 The maze is represented as a graph with edge costs as shown on the edges. The edge cost is 1 for all edges where the cost is not shown. Let B be the initial state and G is the goal state. The heuristic cost of every node to reach G is : h(n) Th A 5.1 B 4.1 C 3.9 D 14 E 2.2 IF 3.8 G 0 IH 3.7 IJ 7 IK 16 L 14 IM 0.5 IN 1.5 IP 1.8 S 4.5 Show the steps of an A* search starting from B to goal G: . Show the frontier and explored set in every iteration (i.e., complete the above table) List the vertices in the order they are expanded.
- A robot can move horizontally or vertically to any square in the same row or in the same column of a board. Find the number of the shortest paths by which a robot can move from one corner of a board to the diagonally opposite corner. The length of a path is measured by the number of squares it passes through, including the first and the least squares. Write the recurrence relation if you solve the problem by a dynamic programming algorithm.Algorithm to An iterative solution to Towers of Hanoi.in: triplet S = s0, s1, s2 representing the current game stateout: triplet R = r0, r1, r2 representing the new game statelocal: pole indices a, b, z ∈ {0, 1, 2}; disc numbers g, h ∈ [2, n]; last(Q) = Q|Q|−1, if1 ≤ |Q|, otherwise, last(Q) = +∞Correct answer will be upvoted else downvoted. Computer science. You are given three positive (more prominent than nothing) integers c, d and x. You need to track down the number of sets of positive integers (a,b) with the end goal that balance c⋅lcm(a,b)−d⋅gcd(a,b)=x holds. Where lcm(a,b) is the most un-normal various of an and b and gcd(a,b) is the best normal divisor of an and b. Input The primary line contains one integer t (1≤t≤104) — the number of experiments. Each experiment comprises of one line containing three integer c, d and x (1≤c,d,x≤107). Output For each experiment, print one integer — the number of sets (a,b) to such an extent that the above uniformity holds.
- Given an array of integers, find the longest non-decreasing subsequences (the subsequence does not need to be consecutive). For example, A = [8,5,2,10,3,6,9,7] contains the longest subsequences [2,3,6,9] and [2,3,6,7].a. Formulate the recursive relation of the optimal solution (do not miss the base case); b. Design a bottom-up (iterative) algorithm to calculate the length of the longest non-decreasing subsequences (pseudo code); c. Analyze the complexity of your algorithm.Let pn(x) be the probability of selling the house to the highest bidder when there are n people, and you adopt the Look-Then-Leap algorithm by rejecting the first x people. For all positive integers x and n with x < n, the probability is equal to p(n(x))= x/n (1/x + 1/(x+1) + 1/(x+2) + … + 1/(n-1)) If n = 100, use the formula above to determine the integer x that maximizes the probability n = 100 that p100(x). For this optimal value of x, calculate the probability p100(x). Briefly discuss the significance of this result, explaining why the Optimal Stopping algorithm produces a result whose probability is far more than 1/n = 1/100 = 1%.2. Honest Goblins are Easy to Find At Hogwarts a new shipment of n goblins has arrived. To be of any use, a goblin must be completely truthful (never lies). Unfortunately, not all of the n goblins in the shipment are truth tellers. Only some are truth-tellers, and some are deceivers. It is your task to design an algorithm to separate the truth-teller goblins from the deceiver goblins. To do this, you have one tool available: You may combine any two goblins and have them state whether the other goblin is a truth-teller or a deceiver. A truth-teller will always say correctly what the other goblin is, but a deceiver may lie (but also may sometimes tell the truth to REALLY confuse you). For any two goblins that you test, the following can be concluded from the goblin responses: Goblin A says Goblin B says Conclusion B is a truth-teller A is a truth-teller both are truth-tellers or both are deceivers B is a truth-teller A is a deceiver at least one is a deceiver B is a deceiver A is a…
- Correct answer will be upvoted else Multiple Downvoted. Computer science. Allow us to characterize the terrorizing worth of a succession as the amount of the number of slopes and the number of valleys in the arrangement. You can change precisely one integer in the succession to any number that you need, or let the grouping stay unaltered. What is the base terrorizing esteem that you can accomplish? Input The main line of the input contains a solitary integer t (1≤t≤10000) — the number of experiments. The portrayal of the experiments follows. The main line of each experiment contains a solitary integer n (1≤n≤3⋅105). The second line of each experiment contains n space-isolated integers a1, a2, ..., an (1≤ai≤109). It is ensured that the amount of n over all experiments doesn't surpass 3⋅105. Output For each experiment, print a solitary integer — the base terrorizing esteem that you can accomplish.Hi please answer the following follow up questions as well, posted them as another question. Question 4 For the 9-tile soring problem, assume that you start from this initial state 7 2 4 5 6 8 3 1 The Goal State is: 1 2 3 4 5 6 7 8 The cost of moving any tile is 1. Let the heuristic function h(n) = number of misplaced tiles. For the shown configuration, there are four options for the next move: Move 5 to the right Move 6 to the left Move 2 down Move 3 up Each of these moves has a value f(n) = h(n) + g(n). If we choose to Move 5 to the right, then g(n) = 1. That is, it took us one step to reach this state from the initial state. h(n) = number of misplaced tiles. The misplaced tiles are {7,4,8,3,1}. So the number of misplaced tiles = h(n) = 5. If we choose to Move 6 to the left, g(n) is still = 1, but h(n) will change because the number of misplaced tiles is different. A* works by computing f(n) = h(n) + g(n) for each of these possible moves. Then it…With T=4, n=12 and A=(3,5,8,8,9,16,29,41,50,63,64,67). Draw the corresponding walkthrough as shown in P.146.