(a) On the grid shown in picture,number the nodes expanded(in order)fora depth-first search from s to g, given that the order of the operators is up,left, right, then down. Assume there is a cycle check.(b) For the same grid, number the nodes expanded, in order, for a best-firstsearch from s to g. Manhattan distance should be used as the evaluationfunction. The Manhattan distance between two points is the distance in thex-direction plus the distance in the y-direction. It corresponds to the distancetraveled along city streets arranged in a grid. Assume multiple-path prun-ing. What is the first path found?(c) On the same grid, number the nodes expanded, in order, for a heuristicdepth-first search from s to g, given Manhattan distance as the evaluationfunction. Assume a cycle check. What is the path found? (d) Number the nodes in order for an A∗ search, with multiple-path pruning,for the same graph. What is the path found?(e) Show how to solve the same problem using dynamic programming. Givethe dist value for each node, and show which path is found.(f) Based on this experience, discuss which algorithms are best suited for thisproblem.(g) Suppose that the graph extended infinitely in all directions. That is, there isno boundary, but s, g, and the blocks are in the same positions relative toeach other. Which methods would no longer find a path? Which would bethe best method, and why?