UVA 208 Firetruck （DFS+剪枝）

题意：构造出一张图，给出一个点，字典序输出所有从1到该点的路径

思路：这道题裸搜的话会超时，所以要进行必要的剪枝，刚开始我时用一个dfs从目标点开始搜，dfs能到达的点说明通过这个带你可以到达目标点，这样会超时，所以需要换另一种方法，这里我用的是flody，也可以用并查集。

代码：

#include <map>
#include <set>
#include <cmath>
#include <queue>
#include <stack>
#include <cstdio>
#include <vector>
#include <iomanip>
#include <cstdlib>
#include <cstring>
#include <iostream>
#include <algorithm>
#define ll long long
#define mod 1000000007
#define mem(a) memset(a,0,sizeof(a))

using namespace std;
const int maxn = 20 + 5, inf = 0x3f3f3f3f;

bool vis[maxn];
int floyd[maxn][maxn];
int d[maxn];
bool G[maxn][maxn];
int n,cnt,Maxn,len;
void print(){
    cnt++;
    cout<<1;
    for(int i = 1 ; i < len ; i ++ ){
        cout<<" "<<d[i];
    }
    cout<<endl;
}
void dfs(int cur,int dd){
    if(cur==n){
        len = dd;
        print();
        return;
    }
    else{
        for(int i = 1 ; i <= Maxn ; i ++ ){
            if(!vis[i]&&G[cur][i]&&floyd[n][i] != maxn){
                d[dd] = i;
                vis[i] = true;
                dfs(i,dd+1);
                vis[i] = false;
            }
        }
    }
}
int main(){
//    freopen("in.txt","r",stdin);
//    freopen("out.txt","w",stdout);
    int kase = 1 ;
    while(scanf("%d",&n)!=EOF){
        memset(G,false,sizeof(G));
        memset(vis,false,sizeof(vis));
        for(int i = 1 ; i <= 21 ; i ++ )
            for(int j = 1 ; j <= 21 ; j ++ )
                floyd[i][j] = maxn;
        Maxn = 0;
        cnt = 0;
        printf("CASE %d:\n",kase++);
        int a,b;
        while(scanf("%d %d",&a,&b)!=EOF&&(a||b)){
            G[a][b] = G[b][a] = true;
            floyd[a][b] = floyd[b][a] = 1;
            if(Maxn < a ) Maxn = a;
            if(Maxn < b ) Maxn = b;
        }
        for (int k = 1; k <= Maxn ; k ++ )
            for (int i = 1; i <= Maxn ; i ++ )
                for (int j = 1; j <= Maxn ; j ++ )
                    if (floyd[i][k] + floyd[k][j] < floyd[i][j])
                        floyd[i][j] = floyd[i][k] + floyd[k][j];
        vis[1] = true ;
        dfs(1,1);
        printf("There are %d routes from the firestation to streetcorner %d.\n",cnt,n);
    }
}