PAT 1003 emergency

學習djstra演算法

虛擬碼:

設d[0]=0, 其他d[i]=INF
迴圈n次{
	在所有為標號結點中選出d值最小結點x
	給結點x標記
	對於x出發的所有邊(x,y), 更新d[y]=min{d[y], d[x]+w(x,y)}
}

總結:

迴圈內主要分為兩部分

1. 找出當前結點的最短的路徑
2. 根據找出的最短路徑的結點, 來更新dist表: 若該結點相鄰的邊比原來小,則更新

#include <stdio.h>
#define INF 99999999
#define MAX 501
int src, tar;

void dijkstra(int
 
 g[][MAX], int n,int team[MAX]){
    int x, y, i, m;
    int dist[MAX];
    int v[MAX];
    int count[MAX];
    int dt[MAX]; //src到當前路徑的最大隊伍數
    for(i=0; i < n; i++){
        v[i] = 0;
        dt[i] = team[src];
        count[i] = 1;
        dist[i] = g[src][i];
        if(dist[i] != INF && i !=
 
 src){ 	//此處特別注意!!!(i=src)改了 30分鐘, 第二個案例過不了
            dt[i] = team[i]+team[src];
        }
    }
    count[src] = 1;
    v[src] = 1;
    for(i=0; i < n; i++){
        m = INF;
        for(y=0; y < n; y++){ //得到權值最小的邊
            if(!v[y] && dist[y] <= m){
                m = dist[x=y];
            }
 

        }
        if(m == INF || x == tar) break;
        v[x] = 1;
        for(y=0; y < n; y++){ //更新dist
            if(dist[x]+g[x][y] < dist[y]){
                dist[y] = dist[x]+g[x][y];
                dt[y] = dt[x] + team[y];
                count[y] = count[x];
            }else if(dist[x]+g[x][y] == dist[y]){
                if (dt[x] + team[y] > dt[y])
                    dt[y] = dt[x] + team[y];
                    count[y] += count[x];
            }
        }
    }
    printf("%d %d",count[tar], dt[tar]);
}

int main(void){
    int n, m;
    scanf("%d %d %d %d", &n, &m, &src, &tar);
    int i, j;
    int team[MAX];
    int g[MAX][MAX];
    for(i = 0;i < n; i++){
        for(j = 0; j < n; j++){
            g[i][j] = INF;
        }
    }
    g[src][src] = 0;
    for(i =0; i < n; i++){
        scanf("%d", &team[i]);
    }

    int t,k,w;
    for(i = 0;i < m; i++){
        scanf("%d %d %d", &t, &k, &w);
        g[t][k] = g[k][t] = w;
    }

    dijkstra(g, n, team);
    return 0;
}

DFS 演算法

注意剪枝

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

public class Main{
	static int INF = 999999999;
	static boolean[] visited;
	static int path;
	static int team;
	static int len = INF;
	static int n;
	static int m;
	static int src, tar;
	static int[] city;
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		n = sc.nextInt(); // citiy_num
		m = sc.nextInt(); // rods_num
		src = sc.nextInt();
		tar = sc.nextInt();
		int i;
		city = new int[n];
		int[][] g = new int[n][n];
		for (i = 0; i < n; i++)
			Arrays.fill(g[i], INF);

		visited = new boolean[n];
		for (i = 0; i < n; i++) {
			city[i] = sc.nextInt();
			g[i][i] = 0;
			visited[i] = false;
		}

		for (i = 0; i < m; i++) {
			int r = sc.nextInt();
			int c = sc.nextInt();
			int w = sc.nextInt();
			g[r][c] = w;
			g[c][r] = w;
		}
		sc.close();
		
		visited[src] = true;
		Dfs(g, src, city[src], 0);
		System.out.printf("%d %d", path, team);
	}
	
	public static void Dfs(int[][] g,int cur, int teamCount,  int curLen){
		
		if(curLen > len){
			return ;
		}
		if(cur == tar){
			if(curLen < len){
				len = curLen;
				path = 1;
				team = teamCount;
			}else if (curLen == len){
				path ++;
				if(team < teamCount){
					team = teamCount;
				}
			}
			return ;
		}
		for(int i = 0; i < n; i++){
			if(!visited[i] && g[cur][i] != INF){
				
				visited[i] = true;
				Dfs(g, i, teamCount + city[i], curLen+g[cur][i]);
				visited[i] = false;
			}
		}
	}
	
}