第十二届蓝桥杯 JavaA组试题D 路径 Dijkstra算法

本文链接：https://blog.youkuaiyun.com/intwei/article/details/122820357

这篇博客主要展示了如何实现Dijkstra算法来计算图中两点间的最短路径。作者首先初始化了一个二维距离矩阵，并填充了无穷大值，然后通过循环迭代更新节点的距离，最终得出从起点到终点的最短距离。博客还包含了欧几里得距离的计算方法（lcm函数）作为边的权重。

摘要生成于 C知道，由 DeepSeek-R1 满血版支持，前往体验 >

答案：10266837

public class Main {
    static int n = 2022;
    static int[] prev = new int[n];//前驱
    static int[] dis = new int[n];//距离
    static int INF = 0x3f3f3f3f;

    public static void main(String[] args){
        int[][] map = new int[n][n];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                map[i][j]=INF;
            }
        }
        for (int i = 1; i < n; i++) {
            for (int j = i + 1; j < n && j <= i + 21; j++) {
                if (j > 0) {
                    map[i][j] = map[j][i] = lcm(i,j);
                }
            }
        }
        dijkstra(1,prev,dis,map);
        System.out.println(dis[2021]);
    }

    public static void dijkstra(int vs,int[] prev,int[] dis,int[][] map){
        boolean[] vis = new boolean[map.length];
        for(int i = 1;i<map.length;i++){
            prev[i] = 0;
            vis[i] = false;
            dis[i] = map[vs][i];
        }
        vis[vs] = true;
        dis[vs] = 0;
        int k = 0;
        for(int i = 2;i<map.length;i++){
            int min = INF;
            for(int j = 0;j<map.length;j++){
                if(vis[j] == false && dis[j] < min){
                    min = dis[j];
                    k = j;
                }
            }
            vis[k] = true;
            for(int j = 0;j<map.length;j++){
                int temp = (map[k][j] == INF ? INF :(min + map[k][j]));
                if(vis[j] == false && temp < dis[j]){
                    prev[j] = k;
                    dis[j] = temp;
                }
            }
        }
    }

    public static int gcd(int a,int b){
        return b == 0 ? a : gcd(b,a%b);
    }
    public static int lcm(int a, int b) {
        int gc = gcd(a, b);
        return a * b / gc;
    }
}