9.8.3. Uniform Cost Search Problem

edge connecting it to a node already pIUUUUUU f two nodes on the open list Algorithm) always produces a minimum spanning tree. 2 In our discussion above we never considered the possibility with the exact same priority value. act same priority value. Carefully check that our claims above are correct, in the ranteed to find a path to each node such that there is no shorter path, whichevo choice we make when there are more than one minimum re are more than one minimum entry in the queue. a portion of Manhattan Island and P9.8.3 Let Mn be a labeled directed graph as follows, I rith i 0, From (i, j) to (i, j+ 1) (north), whenever i is even and j 0. Note that (0, 0) is a source node. Assume that the weight of each north-south edge is 1 and that the weight of each east-west edge is 3 (reflecting the fact that east-west blocks are longer in Manhattan). Find the distance from (1,1) to (3, 3) in M4, justifying your answer by referring to the behavior of a uniform-cost search of M4 starting from (1,1). algorithm (in English or pseudo-Java) that takes n and two nodes u and u in Mn, and returns Give an the distance from u to v if it exists. 3.4 Prove that for any natural n, with n > 1, there exists an undirected graph with n nodes, positive natural edge weights, and nodes s and t, such that a uniform-cost search from s examines all the nodes whereas the optimal path from s to t consists of a single edge 5 Let G be an undirected graph with positive edge weights, and let s and t be nodes Stntnu prove a theorem characterizing the sot nf nodul edge connecting it to a node already pIUUUUUU f two nodes on the open list Algorithm) always produces a minimum spanning tree. 2 In our discussion above we never considered the possibility with the exact same priority value. act same priority value. Carefully check that our claims above are correct, in the ranteed to find a path to each node such that there is no shorter path, whichevo choice we make when there are more than one minimum re are more than one minimum entry in the queue. a portion of Manhattan Island and P9.8.3 Let Mn be a labeled directed graph as follows, I rith i 0, From (i, j) to (i, j+ 1) (north), whenever i is even and j 0. Note that (0, 0) is a source node. Assume that the weight of each north-south edge is 1 and that the weight of each east-west edge is 3 (reflecting the fact that east-west blocks are longer in Manhattan). Find the distance from (1,1) to (3, 3) in M4, justifying your answer by referring to the behavior of a uniform-cost search of M4 starting from (1,1). algorithm (in English or pseudo-Java) that takes n and two nodes u and u in Mn, and returns Give an the distance from u to v if it exists. 3.4 Prove that for any natural n, with n > 1, there exists an undirected graph with n nodes, positive natural edge weights, and nodes s and t, such that a uniform-cost search from s examines all the nodes whereas the optimal path from s to t consists of a single edge 5 Let G be an undirected graph with positive edge weights, and let s and t be nodes Stntnu prove a theorem characterizing the sot nf nodul<><><><>