Consider the following state for the 8-queens problem with heuristic h = number of pairs of queens that are attacking each other. What is the value of 'h' for the state obtained by moving the queen in the left-most column (circled) to the location marked X?

When Bobby’s friends visit her on the farm, she likes to show them around. Thefarm consists of n fields numbered 1, 2, . . . , n, the first of which contains her house and the n-th of whichcontains the big barn. A total of m directed paths connect the fields. The i-th path is from field ui to fieldvi, and has a nonzero length wi.1 Suppose there are k friends coming today. To show off the farm in the best way, Bobby designs a tourfor each friend that starts at her house, potentially travels through some fields, and ends at the barn.Bobby wants the total length of the k tours to be as short as possible, where the length of a tour is thetotal length of paths in the tour. However, she doesn’t want any two friends to share any path. That is,for any two friends, their tours should not have any common paths (but they can travel through the samefields). Write an LP that can calculate the shortest total length of k tours that satisfies Bobby. You canassume that at least one feasible…

6. Numpy.linalg https://numpy.org/doc/stable/reference/generated/numpy.linalg. solve.html. Generate a random, square matrix and random vector using numpy and then solve using numpy.linalg.solve(). Confirm it is a solution using 'A.dot (x)' where x is the solution from solve(). import numpy as np n=100 Numpy has its own black-box linear system solver numpy.linalg.solve(): A=np.random.rand (n,n) b=np.random.rand (n,1) I

Write the PYTHON programming to solve with breadth-first search and build node-arcs with python code for the attached problem:

Suppose that you have a maze search problem. From each numbered square in the maze, youmay move that exact number of squares horizontally or vertically in a straight line. Startingat a particular square (e.g. the top-left corner), find a path to the goal square marked "G".3 4 1 3 1 3 3 3 G 2 3 1 2 2 3 4 2 3 3 3 4 1 4 3 2 Describe the State Space components of this problem. Then solve the problem using breadthirst search and the depth first search. Hint: Indicate the changes to the Open and ClosedQueues in solving this problem for each type of search.