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From New York To Los Angeles New York to Chicago to Denver to Los Angeles Distance is 2900
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Figure 10-5
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The depth-first path to a solution
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An Analysis of the Depth-First Search
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The depth-first approach found a good solution. Also, relative to this specific problem, depth-first searching found this solution on its first try with no backtracking this is very good; but had the data been organized differently, finding a solution might have involved considerable backtracking. Thus, the outcome of this example cannot be generalized. Moreover, the performance of depth-first searches can be quite poor when a particularly long branch with no solution at the end is explored. In this case, a depth-first search wastes time not only exploring this chain but also backtracking to the goal.
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The Breadth-First Search
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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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Although thinking in terms of a binary tree structured search space makes it easy to describe the actions of a breadth-first search, many search spaces, including our flight example, are not binary trees. So precisely what constitutes breadth is a bit subjective in that it is defined by the problem at hand. As it relates to our flight example, the breadth-first approach is implemented by checking if any flight leaving the departure city connects to a flight that reaches the destination. In other words, before advancing to another level, the destinations of all connections of connecting flights are checked. To make the route-seeking program perform a breadth-first search, you need to make an alteration to isflight( ), as shown here:
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/* Determine if there is a route between from and to using breadth-first search. */ void isflight(String from, String to)
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10: AI-Based Problem Solving
{ int dist, dist2; FlightInfo f; // This stack is needed by the breadth-first search. Stack resetStck = new Stack(); // See if at destination. dist = match(from, to); if(dist != 0) { btStack.push(new FlightInfo(from, to, dist)); return; } /* Following is the first part of the breadth-first modification. It checks all connecting flights from a specified node. */ while((f = find(from)) != null) { resetStck.push(f); if((dist = match(f.to, to)) != 0) { resetStck.push(f.to); btStack.push(new FlightInfo(from, f.to, f.distance)); btStack.push(new FlightInfo(f.to, to, dist)); return; } } /* The following code resets the skip fields set by preceding while loop. This is also part of the breadth-first modification. */ int i = resetStck.size(); for(; i!=0; i--) resetSkip((FlightInfo) resetStck.pop()); // Try another connection. f = find(from); if(f != null) { btStack.push(new FlightInfo(from, to, f.distance)); isflight(f.to, to); } else if(btStack.size() > 0) { // Backtrack and try another connection.
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f = (FlightInfo) btStack.pop(); isflight(f.from, f.to); } }
Two changes have been made. First, the while loop checks all flights leaving from the departure city (from) to see if they connect with flights that arrive at the destination city. Second, if the destination is not found, the skip fields of those connecting flights are cleared by calling resetSkip( ). The connections that need to be reset are stored on their own stack, called resetStck, which is local to isflight( ). Resetting the skip flags is necessary to enable alternative paths that might involve those connections. The resetSkip( ) method is shown here:
// Reset skip field of specified flight. void resetSkip(FlightInfo f) { for(int i=0; i< numFlights; i++) if(flights[i].from.equals(f.from) && flights[i].to.equals(f.to)) flights[i].skip = false; }
To try the breadth-first search, substitute the new version of isflight( ) into the preceding search program and then add the resetSkip( ) method. When run, it produces the following solution:
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Figure 10-6 shows the breadth-first path to the solution.
An Analysis of the Breadth-First Search
In this example, the breadth-first search performed fairly well, finding a reasonable solution. As before, this result cannot be generalized because the first path to be found depends on the physical organization of the information. The example does illustrate, however, how depth-first and breadth-first searches often find different paths through the same search space. Breadth-first searching works well when the goal is not buried too deeply in the search space. It works poorly when the goal is several layers deep. In this case, a breadth-first search expends substantial effort during the backtrack stage.
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