我在使用最短路径算法正常工作时遇到问题。我有一个20 x 20 x 20阵列，其中包含代表城市之间道路的边缘权重。我没有得到城市之间最短路径的正确结果。非常感谢任何帮助。
我的二维数组看起来像：X轴=城市1-20，y轴=城市1-20。
X 732 X 212 X X X X X X X X X X X X X X 36 X
66 X X X X X X X 111 X X 29 X X X X 65 X 14 X
390 17 X X X X X X 11 X 38 X X 122 X X 211 78 X X
X X 273 X 29 X X X X X X 42 X X X X X X X X
X X X 122 X X X X 32 X X X X X X 12 X X X 102
62 X X X 211 X X 132 X X X 871 X X X X X X X X
20 200 X 41 X X X X X X 122 X 81 11 X X X X X X
X X 210 X X 5 X X X X X X X X X 74 X X X X
X 95 X X X X 120 X X X 2 X X X X X X X X 11
X X 925 X X X X X X X X 121 X X X X X X X 653
X 81 X 90 X X X X X X X 219 X X X 211 X X X X
X X 11 X 98 X 122 390 X X X X X X X X 121 X 122 X
719 X X X X X X X 9 X X X X X X X 26 X X 832
X X 22 X X X X X 13 182 X X X X X X X X X 219
X X X X X 22 X X X X X X X X X X X X X X
X X X X X X X X X X 73 X X X X X X 98 X X
77 X X X X X X X 200 X 21 93 X X X X X X X 190
X X X X X X X 29 X 33 X X X X 33 940 X X X 121
X 322 X X 74 219 X X X 111 X X X X X X X X X X
X X X X X X X X X X X X X X X X X X X X
到目前为止，这是我的代码：
public static void distance(){
ArrayList<String> path = new ArrayList<String>();
ArrayList<Integer> total = new ArrayList<Integer>();
int shortest = 10000; // temp value for testing
int temp;
int totalDistance = 0;
int shortNum = 0; // The city code for the next shortest path
String code = ""; //The city code
Scanner sc = new Scanner(System.in);
System.out.println("\nCity codes: ");
String d = sc.nextLine();
d = d.toUpperCase();
String[]command = d.split(" ");
if (command.length != 2){
System.out.println("You must enter 2 city codes.");
return;
}
String fromCity = command[0];
String toCity = command[1];
int fCity = find(fromCity);
int tCity = find(toCity);
fCity = fCity -1;
tCity = tCity -1;
int p = fCity;
String shortCode;
if (fCity == tCity){
System.out.println("The distance from " + cities[fCity][2] + " to " +
cities[tCity][2] + " is 0");
}
else {
while(shortNum != tCity){
for (int i = 0; i < 20; i ++){
if (roads[p][i] != "X"){
temp = Integer.parseInt(roads[p][i]);
if (temp < shortest){
shortest = temp;
shortNum = i;
code = cities[i][1];
System.out.println(code);
//p = i;
}
}
}
path.add(code);
total.add(shortest);
p = shortNum;
shortest = 10000;
}
System.out.println("The path is" + path);
for (int k = 0; k < total.size(); k ++){
totalDistance += total.get(k);
}
System.out.println("Total distance is " + totalDistance);
}
}
对于城市1和2之间的最短路径，我的计划给出了总距离276.经历了19,5,16,11
正确的解是总距离225.路径应该是19,5,9,11
谁能看到我哪里出错？
提前感谢您提供任何帮助。
答案 0 :(得分：0)
基本上，您必须在每次迭代时跟踪源节点中所有城市的最短路径。目前，您只需跟踪每次迭代时当前城市（temp变量）中相邻城市之间的最短路径。这不会产生总体最短路径。
你想使用Djistra's algorithm，它找到两个非负边缘的节点之间的最短路径。
以下是您的代码的工作版本：
// City 1 => 2 (all indices start from 0)
City[0] => City[1]
// Path: 1 => 19 => 5 =>9 => 11 => 2
Path:[0, 18, 4, 8, 10, 1]
// The distance you give is incorrect, it's 36+74+32+2+81 = 225
Distance:225
（我已取出所有用户输入，并使用整数代替道路数组的字符串）。
static int[][] roads =
{{-1, 732, -1, 212, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 36, -1},
{66, -1, -1, -1, -1, -1, -1, -1, 111, -1, -1, 29, -1, -1, -1, -1, 65, -1, 14, -1},
{390, 17, -1, -1, -1, -1, -1, -1, 11, -1, 38, -1, -1, 122, -1, -1, 211, 78, -1, -1},
{-1, -1, 273, -1, 29, -1, -1, -1, -1, -1, -1, 42, -1, -1, -1, -1, -1, -1, -1, -1},
{-1, -1, -1, 122, -1, -1, -1, -1, 32, -1, -1, -1, -1, -1, -1, 12, -1, -1, -1, 102},
{62, -1, -1, -1, 211, -1, -1, 132, -1, -1, -1, 871, -1, -1, -1, -1, -1, -1, -1, -1},
{20, 200, -1, 41, -1, -1, -1, -1, -1, -1, 122, -1, 81, 11, -1, -1, -1, -1, -1, -1},
{-1, -1, 210, -1, -1, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, 74, -1, -1, -1, -1},
{-1, 95, -1, -1, -1, -1, 120, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, 11},
{-1, -1, 925, -1, -1, -1, -1, -1, -1, -1, -1, 121, -1, -1, -1, -1, -1, -1, -1, 653},
{-1, 81, -1, 90, -1, -1, -1, -1, -1, -1, -1, 219, -1, -1, -1, 211, -1, -1, -1, -1},
{-1, -1, 11, -1, 98, -1, 122, 390, -1, -1, -1, -1, -1, -1, -1, -1, 121, -1, 122, -1},
{719, -1, -1, -1, -1, -1, -1, -1, 9, -1, -1, -1, -1, -1, -1, -1, 26, -1, -1, 832},
{-1, -1, 22, -1, -1, -1, -1, -1, 13, 182, -1, -1, -1, -1, -1, -1, -1, -1, -1, 219},
{-1, -1, -1, -1, -1, 22, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 73, -1, -1, -1, -1, -1, -1, 98, -1, -1},
{77, -1, -1, -1, -1, -1, -1, -1, 200, -1, 21, 93, -1, -1, -1, -1, -1, -1, -1, 190},
{-1, -1, -1, -1, -1, -1, -1, 29, -1, 33, -1, -1, -1, -1, 33, 940, -1, -1, -1, 121},
{-1, 322, -1, -1, 74, 219, -1, -1, -1, 111, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}};
public static List<Integer> shortestPath(int fCity, int tCity){
// keep track of the distance and path from source to all nodes
Map<Integer, Integer> distToSource = new HashMap<Integer, Integer>(20);
Map<Integer, Integer> paths = new HashMap<Integer, Integer>(20);
// initialize the distance to source for all nodes
distToSource.put(fCity, 0);
for(int i=0; i<20; i++)
if( i != fCity )
distToSource.put(i,Integer.MAX_VALUE);
// start at source and find shortest path to destination
int shortest_index = fCity, shortest_dist, edge;
while(shortest_index != tCity){
shortest_dist = Integer.MAX_VALUE;
shortest_index = -1;
// find shortest path from all options in distToSource
for(Map.Entry<Integer, Integer> e : distToSource.entrySet()){
if( e.getValue() < shortest_dist ){
shortest_dist = e.getValue();
shortest_index = e.getKey();
}
}
// no path to destination
if(shortest_index < 0)
return null;
//remove the shortest node
distToSource.remove(shortest_index);
//update all edges out of node 'shortest_index'
for(Integer i : distToSource.keySet()){
edge = roads[shortest_index][i];
if (edge > 0 && shortest_dist + edge < distToSource.get(i)){
distToSource.put(i, shortest_dist + edge);
paths.put(i, shortest_index);
}
}
}
// create path by working backwards from destination to source
Deque<Integer> path = new ArrayDeque<Integer>();
path.add(shortest_index);
while(paths.containsKey(shortest_index)){
path.addFirst(paths.get(shortest_index));
shortest_index = paths.get(shortest_index);
}
return new ArrayList<Integer>(path);
}
public static int distance(List<Integer> path){
int dist = 0;
for(int i=0; i<path.size()-1; i++)
dist += roads[path.get(i)][path.get(i+1)];
return dist;
}
public static void main(String[] args) {
int fCity = 0, tCity = 1;
List<Integer> path = shortestPath(fCity, tCity);
System.out.println("City["+ fCity + "] => City[" + tCity + "]");
System.out.println("Path:" + path);
System.out.println("Distance:" + distance(path));
}