Java实现Dijkstra算法的示例代码
目录
- 一 问题描述
- 二 实现
- 三 测试
一 问题描述
小明为位置1,求他到其他各顶点的距离。
二 实现
package graph.dijkstra; import java.util.Scanner; import java.util.Stack; public class Dijkstra { static final int MaxVnum = 100; // 顶点数最大值 static final int INF = 0x3f3f3f3f; //无穷大 static final int dist[] = new int[MaxVnum]; // 最短距离 static final int p[] = new int[MaxVnum]; // 前驱数组 static final boolean flag[] = new boolean[MaxVnum]; // 如果 s[i] 等于 true,说明顶点 i 已经加入到集合 S ;否则顶点 i 属于集合 V-S static int locatevex(AMGraph G, char x) { for (int i = 0; i < G.vexnum; i++) // 查找顶点信息的下标 if (x == G.Vex[i]) return i; return -1; // 没找到 } static void CreateAMGraph(AMGraph G) { Scanner scanner = new Scanner(System.in); int i, j; char u, v; int w; System.out.println("请输入顶点数:"); G.vexnum = scanner.nextInt(); System.out.println("请输入边数:"); G.edgenum = scanner.nextInt(); System.out.println("请输入顶点信息:"); // 输入顶点信息,存入顶点信息数组 for (int k = 0; k < G.vexnum; k++) { G.Vex[k] = scanner.next().charAt(0); } //初始化邻接矩阵所有值为0,如果是网,则初始化邻接矩阵为无穷大 for (int m = 0; m < G.vexnum; m++) for (int n = 0; n < G.vexnum; n++) G.Edge[m][n] = INF; System.out.println("请输入每条边依附的两个顶点及权值:"); while (G.edgenum-- > 0) { u = scanner.next().charAt(0); v = scanner.next().charAt(0); w = scanner.nextInt(); i = locatevex(G, u);// 查找顶点 u 的存储下标 j = locatevex(G, v);// 查找顶点 v 的存储下标 if (i != -1 && j != -1) G.Edge[i][j] = w; //有向图邻接矩阵 else { System.out.println("输入顶点信息错!请重新输入!"); G.edgenum++; // 本次输入不算 } } } static void print(AMGraph G) { // 输出邻接矩阵 System.out.println("图的邻接矩阵为:"); for (int i = 0; i < G.vexnum; i++) { for (int j = 0; j < G.vexnum; j++) System.out.print(G.Edge[i][j] + "\t"); System.out.println(); } } public static void main(String[] args) { AMGraph G = new AMGraph(); int st; char u; CreateAMGraph(G); System.out.println("请输入源点的信息:"); Scanner scanner = new Scanner(System.in); u = scanner.next().charAt(0); ; st = locatevex(G, u);//查找源点u的存储下标 Dijkstra(G, st); System.out.println("小明所在的位置:" + u); for (int i = 0; i < G.vexnum; i++) { System.out.print("小明:" + u + " - " + "要去的位置:" + G.Vex[i]); if (dist[i] == INF) System.out.print(" sorry,无路可达"); else System.out.println(" 最短距离为:" + dist[i]); } findpath(G, u); } public static void Dijkstra(AMGraph G, int u) { for (int i = 0; i < G.vexnum; i++) { dist[i] = G.Edge[u][i]; //初始化源点u到其他各个顶点的最短路径长度 flag[i] = false; if (dist[i] == INF) p[i] = -1; //源点u到该顶点的路径长度为无穷大,说明顶点i与源点u不相邻 else p[i] = u; //说明顶点i与源点u相邻,设置顶点i的前驱p[i]=u } dist[u] = 0; flag[u] = true; //初始时,集合S中只有一个元素:源点u for (int i = 0; i < G.vexnum; i++) { int temp = INF, t = u; for (int j = 0; j < G.vexnum; j++) //在集合V-S中寻找距离源点u最近的顶点t if (!flag[j] && dist[j] < temp) { t = j; temp = dist[j]; } if (t == u) return; //找不到t,跳出循环 flag[t] = true; //否则,将t加入集合 for (int j = 0; j < G.vexnum; j++)//更新V-S中与t相邻接的顶点到源点u的距离 if (!flag[j] && G.Edge[t][j] < INF) if (dist[j] > (dist[t] + G.Edge[t][j])) { dist[j] = dist[t] + G.Edge[t][j]; p[j] = t; } } } public static void findpath(AMGraph G, char u) { int x; Stack<Integer> S = new Stack<>(); System.out.println("源点为:" + u); for (int i = 0; i < G.vexnum; i++) { x = p[i]; if (x == -1 && u != G.Vex[i]) { System.out.println("源点到其它各顶点最短路径为:" + u + "--" + G.Vex[i] + " sorry,无路可达"); continue; } while (x != -1) { S.push(x); x = p[x]; } System.out.println("源点到其它各顶点最短路径为:"); while (!S.empty()) { System.out.print(G.Vex[S.peek()] + "--"); S.pop(); } System.out.println(G.Vex[i] + " 最短距离为:" + dist[i]); } } } class AMGraph { char Vex[] = new char[Dijkstra.MaxVnum]; int Edge[][] = new int[Dijkstra.MaxVnum][Dijkstra.MaxVnum]; int vexnum; // 顶点数 int edgenum; // 边数 }
三 测试
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