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The Art of Java
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To find a route between New York and Los Angeles, several support methods are needed. The first is match( ), which determines if there is a flight between two cities. If no such flight exists, it returns zero; or if there is a flight, it returns the distance between the two cities. This method is shown here:
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/* If there is a flight between from and to, return the distance of flight; otherwise, return 0. */ int match(String from, String to) { for(int i=numFlights-1; i > -1; i--) { if(flights[i].from.equals(from) && flights[i].to.equals(to) && !flights[i].skip) { flights[i].skip = true; // prevent reuse return flights[i].distance; } } return 0; // not found }
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The next support method is find( ). Given a departure city, find( ) searches the database for any connection. If a connection is found, the FlightInfo object associated with that connection is returned. Otherwise, null is returned. Thus, the difference between match( ) and find( ) is that match( ) determines if there is a flight between two specific cities, whereas find( ) determines if there is a flight from a given city to any other city. The find( ) method follows:
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// Given from, find any connection. FlightInfo find(String from) { for(int i=0; i < numFlights; i++) { if(flights[i].from.equals(from) && !flights[i].skip) { FlightInfo f = new FlightInfo(flights[i].from, flights[i].to, flights[i].distance); flights[i].skip = true; // prevent reuse return f; } }
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return null; }
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In both match( ) and find( ), connections that have the skip field set to 1 are bypassed. Also, if a connection is found, its skip field is set. This manages backtracking from dead ends, preventing the same connections from being tried over and over again. Now consider the code that actually finds the connecting flights. It is contained in the isflight( ) method, the key routine in finding a route between two cities. It is called with the names of the departure and destination cities.
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// Determine if there is a route between from and to. void isflight(String from, String to) { int dist; FlightInfo f; // See if at destination. dist = match(from, to); if(dist != 0) { btStack.push(new FlightInfo(from, to, dist)); return; } // 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. f = (FlightInfo) btStack.pop(); isflight(f.from, f.to); } }
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Let s examine this method closely. First, the flight database is checked by match( ) to see if there is a flight between from and to. If there is, the goal has been reached, the connection is pushed onto the stack, and the method returns. Otherwise, it uses find( ) to find a connection between from and any place else. The find( ) method returns the FlightInfo object describing the connection, if one is found, or null if no connecting flights are available. If there is such a flight, this connection is stored in f, the current flight is pushed onto the backtrack stack, and isflight( ) is called recursively, with the city in f.to becoming the new departure city. Otherwise, backtracking takes place. The previous node is removed from the stack and isflight( ) is called recursively. This process continues until the goal is found.
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For example, if isflight( ) is called with New York and Chicago, the first if would succeed and isflight( ) would terminate because there is a direct flight from New York to Chicago. The situation is more complex when isflight( ) is called with New York and Calgary. In this case, the first if would fail because there is no direct flight connecting these two cities. Next, the second if is tried by attempting to find a connection between New York and any other city. In this case, find( ) first finds the New York to Chicago connection, this connection is pushed onto the backtrack stack, and isflight( ) is called recursively with Chicago as the starting point. Unfortunately, there is no path from Chicago to Calgary and several false paths are followed. Eventually, after several recursive calls to isflight( ) and substantial backtracking, the connection from New York to Toronto is found, and Toronto connects to Calgary. This causes isflight( ) to return, unraveling all recursive calls in the process. Finally, the original call to isflight( ) returns. You might want to try adding println( ) statements in isflight( ) to see precisely how it works with various departure and destination cities. It is important to understand that isflight( ) does not actually return the solution it generates it. Upon exit from isflight( ), the backtrack stack contains the route between New York and Calgary. That is, the solution is contained in btStack. Furthermore, the success or failure of isflight( ) is determined by the state of the stack. An empty stack indicates failure; otherwise, the stack holds a solution. In general, backtracking is a crucial ingredient in AI-based search techniques. Backtracking is accomplished through the use of recursion and a backtrack stack. Almost all backtracking situations are stack-like in operation that is, they are first in, last out. As a path is explored, nodes are pushed onto the stack as they are encountered. At each dead end, the last node is popped off the stack and a new path, from that point, is tried. This process continues until either the goal is reached or all paths have been exhausted. You need one more method, called route( ), to complete the entire program. It displays the path and the total distance. The route( ) method is shown here:
// Show the route and total distance. void route(String to) { Stack rev = new Stack(); int dist = 0; FlightInfo f; int num = btStack.size(); // Reverse the stack to display route. for(int i=0; i < num; i++) rev.push(btStack.pop()); for(int i=0; i < num; i++) { f = (FlightInfo) rev.pop(); System.out.print(f.from + " to "); dist += f.distance; }
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