最小生成树的扩展应用

news2025/1/13 15:40:37

1146. 新的开始 - AcWing题库

//建立一个虚拟远点
import java.util.*;

public class Main{
    static int N = 310;
    static int[][] w = new int[N][N];
    static int[] dist = new int[N];
    static boolean[] st = new boolean[N];
    static int n, res;
    
    public static int prim(){
        Arrays.fill(dist, 0x3f3f3f3f);
        dist[0] = 0;

        for(int i = 0; i < n + 1; i ++){
            int t = -1;
            for(int j = 0; j < n + 1; j ++){
                if(!st[j] && (t == -1 || dist[t] > dist[j])){
                    t = j;
                }
            }
            st[t] = true;
            res += dist[t];
            
            for(int j = 0; j < n + 1; j ++){
                dist[j] = Math.min(dist[j], w[t][j]);//t点到这个点的距离短还是虚拟远点到这个点的距离短
            }
        }
        return res;
    }
    
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        n = sc.nextInt();
        
        for(int i = 1; i <= n; i ++){//虚拟远点到每个点的距离
            w[0][i] = sc.nextInt();
            w[i][0] = w[0][i];
        }
        
        for(int i = 1; i <= n; i ++){
            for(int j = 1; j <= n; j ++){
                w[i][j] = sc.nextInt();
            }
        }
        
        System.out.print(prim());
    }
}

1145. 北极通讯网络 - AcWing题库

找到一个最小的d值，将所有权值大于d的边删去，整个图形连通块的数量不超过k条

import java.util.*;

class PII_1{
    int x, y;
    public PII_1(int x, int y){
        this.x = x;
        this.y = y;
    }
}

class PII_2 implements Comparable<PII_2>{
    int a, b;
    double c;
    public PII_2(int a, int b, double c){
        this.a = a;
        this.b = b;
        this.c = c;
    }
    
    public int compareTo(PII_2 o){
        return Double.compare(c, o.c);
    }
}

public class Main{
    static int N = 510, M = N * N;
    static PII_1[] a = new PII_1[M];
    static PII_2[] q = new PII_2[M];
    static int[] p = new int[M];
    static int n, k, m;
    
    public static double get_dist(PII_1 a, PII_1 b){
        int dx = a.x - b.x;
        int dy = a.y - b.y;
        return Math.sqrt(dx * dx + dy * dy);
    }
    
    public static int find(int x){
        if(p[x] != x) p[x] = find(p[x]);
        return p[x];
    }
    
    public static void Kruskal(){
        Arrays.sort(q, 0, m);//一定要记得排序
        
        int cnt = n;
        double res = 0.0;
        for(int i = 0; i < m; i ++){
            if(cnt <= k) break;
            int a = q[i].a;
            int b = q[i].b;
            double c = q[i].c;
            a = find(a);
            b = find(b);
            if(a != b){
                p[a] = b;
                cnt --;
                res = c;
            }
        }
        System.out.printf("%.2f", res);
    }
    
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        n = sc.nextInt();
        k = sc.nextInt();
        
        for(int i = 0; i < n; i ++) p[i] = i;
        
        for(int i = 0; i < n; i ++){
            int x = sc.nextInt();
            int y = sc.nextInt();
            a[i] = new PII_1(x, y);//每个村庄的坐标
        }
        
        for(int i = 0; i < n; i ++){
            for(int j = 0; j < n; j ++){//村庄与村庄之间两两的距离
                q[m ++] = new PII_2(i, j, get_dist(a[i], a[j]));
            }
        }
        
        Kruskal();
    }
}

346. 走廊泼水节 - AcWing题库

import java.util.*;

class PII implements Comparable<PII>{
    int a, b, c;
    public PII(int a, int b, int c){
        this.a = a;
        this.b = b;
        this.c = c;
    }
    public int compareTo(PII o){
        return Integer.compare(c, o.c);
    }
}

public class Main{
    static int N = 6010, n;
    static int[] p = new int[N];
    static int[] size = new int[N];
    static PII[] q = new PII[N];
    
    public static int find(int x){
        if(p[x] != x) p[x] = find(p[x]);
        return p[x];
    }
    
    public static void Kruskal(){
        Arrays.sort(q, 0, n - 1);
        int res = 0;
        
        for(int i = 0; i < n - 1; i ++){
            int a = q[i].a;
            int b = q[i].b;
            int c = q[i].c;
            a = find(a);
            b = find(b);
            if(a != b){
                res += (size[a] * size[b] - 1) * (c + 1);//权值加1
                p[a] = b;
                size[b] += size[a];
            }
        }
        System.out.println(res);
    }
    
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        int T = sc.nextInt();
        while(T -- > 0){
            n = sc.nextInt();
            for(int i = 1; i <= n; i ++){
                p[i] = i;
                size[i] = 1;
            }
            
            for(int i = 0; i < n - 1; i ++){
                int a = sc.nextInt();
                int b = sc.nextInt();
                int c = sc.nextInt();
                q[i] = new PII(a, b, c);//先把点加进去
            }
            
            Kruskal();
        }
    }
}