2021第十二届蓝桥杯省赛真题：路径

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import java.util.Scanner;
import java.util.Arrays;

public class Main {
    static final int INF = 0x3f3f3f3f;
    static final int N = 2030;
    static int[][] g = new int[N][N];
    static int[] dist = new int[N];
    static boolean[] s = new boolean[N];
    public static void main(String[] args) {
        //初始化图和距离
        for(int i = 1; i <= 2021; i++) {
            for(int j = i; j <= 2021; j++) {
                if(j - i > 21) {
                    g[i][j] = g[j][i] = INF;
                } else {
                    g[i][j] = g[j][i] = lcm(i, j);
                }
            }
        }
        Arrays.fill(dist, INF);
        dist[1] = 0;

        //朴素DijKstra
        for(int i = 1; i <= 2021; i++) {
            int v = -1;
            for(int j = 1; j <= 2021; j++) {
                if(!s[j] && (v == -1 || dist[v] > dist[j])) {
                    v = j;
                }
            }
            s[v] = true;
            for(int j = 1; j <= 2021; j++) {
                dist[j] = Math.min(dist[j], dist[v] + g[v][j]);
            }
        }

        System.out.println(dist[2021]);
    }
    
    //求最大公约数
    public static int gcd(int a, int b) {
        //递归方式性能差些，但是写法简单
        //return b == 0 ? a : gcd(b, a % b);
        int t;
        while(b != 0) {
            t = a % b;
            a = b;
            b = t;
        }
        return a;
    }
    //求最小公倍数
    public static int lcm(int a, int b) {
        return a * b / gcd(a, b);
    }
}