Find the values of mand n if Km.n has an Euler path. (Check all that apply.) Check All That Apply Km, n has an Euler path when both mand n are even. Km.n has an Euler path when both mand n are odd. Km, n has an Euler path if m=2 and n is odd. Km,n has an Euler path if n= 2 and m is odd. TL Km,n has an Euler path when m= n=1.

7. For n 2 1, in how many out of the n! permutations T = (T(1), 7(2),..., 7 (n)) of the numbers {1, 2, ..., n} the value of 7(i) is either i – 1, or i, or i +1 for all 1 < i < n? Example: The permutation (21354) follows the rules while the permutation (21534) does not because 7(3) = 5. Hint: Find the answer for small n by checking all the permutations and then find the recursive formula depending on the possible values for 1(n).

Suppose a salesperson is planning a sales trip that includes n cities. Each city is connected to some of the other cities by a road. To minimize travel time, the salesperson wants to determine the shortest route that starts at the salesperson’s home city, visits each of the cities once, and ends up at the home city. This problem of finding the shortest route is called the Travelling Salesperson Problem (TSP) and is a well-known problem that can be solved using Dynamic Programming. Research about the TSP problem and find an algorithm based on Dynamic Programming for that. Explain the approach, the algorithm, and its time complexity. Use an example to explain the way the algorithm operates

Let x and y be integers such that x = 3 (mod 10) and y = 5 (mod 10). Find the integer z such that 97x + 3y³ z (mod 10) and 0 ≤ z ≤9.