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depth-first search wastes considerable time not only exploring this chain, but also backtracking to the goal The Breadth-First Search The opposite of the depth-first search is the breadth-first search In this method, each node on the same level is checked before the search proceeds to the next deeper level This traversal method is shown here with C as the goal:
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To make the route-seeking program perform a breadth-first search, you only need to alter the procedure isflight( ), as shown here:
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void isflight(char *from, char *to) { int d, dist; char anywhere[20]; while(dist=find(from, anywhere)) { /* breadth-first modification */ if(d=match(anywhere, to)) { push(from, to, dist); push(anywhere, to, d);
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Page 626 return; } } /* try any connection */ if(dist=find(from, anywhere)) { push(from, to, dist); isflight(anywhere, to); } else if(tos>0) { pop(from, to, &dist); isflight(from, to); } }
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As you can see, only the first condition has been altered Now all connecting cities to the departure city are checked to see if they connect with the destination city Substitute this version of isflight( ) in the program and run it The solution is
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The solution is optimal Figure 25-6 shows the breadth-first path to the solution Analysis of the Breadth-First Search In this example, the breadth-first search performed very well by finding the first solution without backtracking As it turned out, this was also the optimal solution In fact, the first three solutions that would be found are the best three routes there are However, remember that this result does not generalize to other situations because the path depends upon the physical organization of the information as it is stored in the computer The example does illustrate, however, how radically different depth-first and breadth-first searches are A disadvantage to breadth-first searching becomes apparent when the goal is several layers deep In this case, a breadth-first search expends substantial effort to find the goal In general, you choose between depth-first and breadth-first searching by making an educated guess about the most likely position of the goal Adding Heuristics You have probably guessed by now that both the depth-first and breadth-first search routines are blind They are methods of looking for a solution that rely solely upon
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Figure 25-6 The breadth-first path to a solution
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moving from one goal to the other without any educated guesswork on the part of the computer This may be fine for certain controlled situations where you know that one method is better than the other However, a generalized AI program needs a search procedure that is on the average superior to either of these two techniques The only way to achieve such a search is to add heuristic capabilities Heuristics are simply rules that qualify the possibility that a search is proceeding in the correct direction For example, imagine that you are lost in the woods and need a drink of water The woods are so thick that you cannot see far ahead, and the trees are too big to climb and get a look around However, you know that rivers, streams, and ponds are most likely in valleys; that animals frequently make paths to their watering
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places; that when you are near water it is possible to ''smell" it; and that you can hear running water So, you begin by moving downhill because water is unlikely to be uphill Next you come across a deer trail that also runs downhill Knowing that this may lead to water, you follow it You begin to hear a slight rushing off to your left Knowing that this may be water, you cautiously move in that direction As you move, you begin to detect the increased humidity in the air; you can smell the water Finally, you find a stream and have your drink As you can see, heuristic information, although neither precise nor guaranteed, increases the chances that a search method will find a goal quickly, optimally, or both In short, it increases the odds in favor of a quick success You may think that heuristic information could easily be included in programs designed for specific applications, but that it would be impossible to create generalized heuristic searches This is not the case Most often, heuristic search methods are based on maximizing or minimizing some aspect of the problem In fact, the two heuristic approaches that we will look at use opposite heuristics and yield different results Both of these searches will be built upon the depth-first search routines The Hill-Climbing Search In the problem of scheduling a flight from New York to Los Angeles, there are two possible constraints that a passenger may want to minimize The first is the number of connections that have to be made The second is the length of the route Remember, the shortest route does not necessarily imply the fewest connections A search algorithm that attempts to find as a first solution a route that minimizes the number of connections uses the heuristic that the longer the length of the flight, the greater the likelihood that it takes the traveler closer to the destination; therefore, the number of connections is minimized In the language of AI, this is called hill climbing The hill-climbing algorithm chooses as its next step the node that appears to place it closest to the goal (that is, farthest away from the current position) It derives its name from the analogy of a hiker being lost in the dark, halfway up a mountain Assuming that the hiker's camp is at the top of the mountain, even in the dark the hiker knows that each step that goes up is a step in the right direction Working only with the information contained in the flight-scheduling knowledge base, here is how to incorporate the hill-climbing heuristic into the routing program: Choose the connecting flight that is as far away as possible from the current position in the hope that it will be closer to the destination To do this, modify the find( ) routine as shown here:
/* Given from, find the farthest away "anywhere" */ int find(char *from, char *anywhere) {
Page 629 int pos, dist; pos=dist = 0; find_pos = 0; while(find_pos < f_pos) { if(!strcmp(flight[find_pos]from, from) && !flight[find_pos]skip) { if(flight[find_pos]distance>dist) { pos = find_pos; dist = flight[find_pos]distance; } } find_pos++; } if(pos) { strcpy(anywhere, flight[pos]to); flight[pos]skip = 1; return flight[pos]distance; } return 0 }
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