Problem 15 (#2.3.30).If f and f◦g are one-to-one, does it follow that g must be one-to-one? Justify your answer.
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- Plz sir must solve this question.The Manhattan Tourist Problem (1) Given setting in Figure 6.4, calculate exact number of different paths by dynamic programming. (2) For a general setting, i.e., from source(0,0) to sink (n, m), how many different paths by dynamic programming?1 4 3 3 4 1 0 4 3 N 5 1The Manhattan Tourist Problem (1) Given setting in Figure 6.4, calculate exact number of different paths by counting principle. (2) For a general setting, i.e., from source(0,0) to sink (n, m), how many different paths by counting principle?
- Demonstrate that the following issue belongs to the NP class:Consider the following cryptarithmetic problem where TWO and FOUR are three and four digit numbers respectively. Which of the following constraint(s) is/are correct for modeling this problem? Assume that X1, X2 & X3 are carry overs resulting from the additions at the unit, tens and the hundreds place. Also, all digits are distinct.As we all know, heuristic or approximation algorithms may not always provide the best solution to a problem, but they are very efficient in terms of polynomial time. (a) Propose an approximation method for the travelling salesman problem (TSP) and analyze the time complexity and limitations of the proposed approach. (2) Provide two examples of inputs for which the method in (a) produces the best and not-the best answers, respectively. (3) There should be between six and eight nodes in each network.
- Recall Pigou’s example discussed in class, where there are two roads that connect a source, s, and destination, t. The roads have different travel costs. Fraction x1 of the traffic flow on route 1, and the remainder x2 on route 2. Here consider the following scenario. • The first road has “infinite” capacity but is slow and requires 1 hour travel time, T1 = 1. • The second road always requires at least 15 mins, which then increases as a function of traffic density, T2 = 0.25 + 0.75x2. If drivers act in a “selfish” manner – the user optimal scenario – all the traffic will flow on the second path, as one is never worse off. Worst case scenario for path 2, both paths take one hour. So no one is incentivized to change their behavior. 1. Assume user optimal behavior, and calculate τ the expected travel time per car. 2. If instead we could control the flows, we could minimize the expected travel time. Using the expression in part (a), calculate the optimal allocation of flows x¯1 and ¯x2…Consider the version of the dining-philosophers problem in which the chopsticks are placed at the center of the table and any four of them can be used by a philosopher. In other words, a philosopher needs four chopsticks to eat. Assume that requests for chopsticks are made one at a time. Assuming that there are m=4k chopsticks and n=6k philosophers around the table, (i) How many maximum philosophers can eat simultaneously? (ii) Describe a simple rule for determining whether a particular request can be satisfied without causing deadlock given the current allocation of chopsticks to philosophers. (Hint: Use rules similar to the Banker’s algorithm.)The missionaries and cannibals problem is usually stated as follows. Three missionariesand three cannibals are on one side of a river, along with a boat that can hold one ortwo people. Find a way to get everyone to the other side without ever leaving a group of missionariesin one place outnumbered by the cannibals in that place. This problem is famous inAI because it was the subject of the first paper that approached problem formulation from ananalytical viewpoint (Amarel, 1968).b. Implement and solve the problem optimally using an appropriate search algorithm. (Mention the name of the search algorithm, and write the complete answers, Draw the answer using the searching algorithms with complete and all paths and branches.)
- Determine whether ∀x(P (x) ↔ Q(x)) and ∀x P (x) ↔∀xQ(x) are logically equivalent. Justify your answerDear Experts Give correct Answer Generate FIFO branch and bound solution for the given knapsack problem, m = 15, n = 3, (P₁, P₂P3) = (10, 6, 8) and (w₁, w₂, w3) = (10, 12, 3).Subject: DLD Simplify the following function using K-map F(W,X,Y,Z) = (1,2,4,6,8,9,10,11,14,15) G(W,X,Y,Z) = Product(2,3,6,8)+d(1,4,7,10,12,13,15)