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NC51341. Wedding

描述

Up to thirty couples will attend a wedding feast, at which they will be seated on either side of a long table. The bride and groom sit at one end, opposite each other, and the bride wears an elaborate headdress that keeps her from seeing people on the same side as her. It is considered bad luck to have a husband and wife seated on the same side of the table. Additionally, there are several pairs of people conducting adulterous relationships (both different-sex and same-sex relationships are possible), and it is bad luck for the bride to see both members of such a pair. Your job is to arrange people at the table so as to avoid any bad luck.

输入描述

The input consists of a number of test cases, followed by a line containing 0 0. Each test case gives n, the number of couples, followed by the number of adulterous pairs, followed by the pairs, in the form "4h 2w" (husband from couple 4, wife from couple 2), or "10w 4w", or "3h 1h". Couples are numbered from 0 to n-1 with the bride and groom being 0w and 0h.

输出描述

For each case, output a single line containing a list of the people that should be seated on the same side as the bride. If there are several solutions, any one will do. If there is no solution, output a line containing "bad luck".

示例1

输入:

10 6
3h 7h
5w 3w
7h 6w
8w 3w
7h 3w
2w 5h
0 0

输出:

1h 2h 3w 4h 5h 6h 7h 8h 9h

原站题解

上次编辑到这里,代码来自缓存 点击恢复默认模板

C++(g++ 7.5.0) 解法, 执行用时: 2ms, 内存消耗: 480K, 提交时间: 2023-01-16 12:54:15

#include<cstdio>
#include<cctype>
#include<vector>
#include<cstring>
#include<algorithm>
#define maxn 100
using namespace std;
int n,m;
int fir[maxn],nxt[maxn*maxn],to[maxn*maxn],tot;
bool flag;
void read(int &a,bool &b)
{
    char c;a=0;
    while(!isdigit(c=getchar()));
    while(isdigit(c)) a=a*10+c-'0',c=getchar();
    b=(c=='w');
}
void line(int x,int y)
{
    nxt[++tot]=fir[x];
    fir[x]=tot;
    to[tot]=y;
}
void add(int u,bool x,int v,bool y)
{
    u=u*2+x,v=v*2+y;
    line(u,v^1);
    line(v,u^1);
}
int dfn[maxn],low[maxn],stk[maxn],tp,scc[maxn],scnt,tim;
void tarjan(int u)
{
    dfn[u]=low[u]=++tim;
    stk[++tp]=u;
    for(int i=fir[u];i;i=nxt[i])
        if(!dfn[to[i]]) tarjan(to[i]),low[u]=min(low[u],low[to[i]]);
        else if(!scc[to[i]]) low[u]=min(low[u],dfn[to[i]]);
    if(dfn[u]==low[u])
    {
        ++scnt;
        do
        {
            if(scc[stk[tp]^1]==scnt) flag=1;
            scc[stk[tp]]=scnt;
        }while(stk[tp--]!=u);
    }
}
int Q[maxn],in[maxn],cf[maxn];
vector<int>e[maxn];
bool mark[maxn];
void Topsort()
{
    int h=1,t=0,u;
    for(int i=1;i<=scnt;i++)
        if(!in[i]) Q[++t]=i;
    while(h<=t)
    {
        u=Q[h++];
        if(!mark[cf[u]]) mark[u]=1;
        for(int i=e[u].size()-1;i>=0;i--)
            if((--in[e[u][i]])==0) Q[++t]=e[u][i];
    }
}
void init()
{
    tim=scnt=tot=flag=tp=0;
    memset(in,0,sizeof in);
    memset(cf,0,sizeof cf);
    memset(fir,0,sizeof fir);
    memset(dfn,0,sizeof dfn);
    memset(scc,0,sizeof scc);
    memset(mark,0,sizeof mark);
    for(int i=1;i<=2*n;i++) e[i].clear();
}
int main()
{
    int x,y;
    bool u,v;
    while(scanf("%d%d",&n,&m),n)
    {
        init();
        line(1,0);
        for(int i=1;i<=m;i++)
        {
            read(x,u);
            read(y,v);
            add(x,u,y,v);
        }
        n*=2;
        for(int i=0;i<n&&!flag;i++)
            if(!dfn[i]) tarjan(i);
        if(flag) {puts("bad luck");continue;}
        for(int u=0;u<n;u++)
            for(int i=fir[u];i;i=nxt[i])
                if(scc[u]!=scc[to[i]]) e[scc[to[i]]].push_back(scc[u]),in[scc[u]]++;
        for(int i=0;i<n;i++)
            cf[scc[i]]=scc[i^1];
        Topsort();
        for(int i=2;i<n;i+=2)
        {
            if(i>2) putchar(' ');
            if(mark[scc[i]]) printf("%dw",i/2);
            else printf("%dh",i/2);
        }
        putchar('\n');
    }
}

C++ 解法, 执行用时: 4ms, 内存消耗: 848K, 提交时间: 2021-08-04 11:34:23

#include<bits/stdc++.h>
#define PI acos(-1.0)
#define E 1e-6
#define MOD 16007
#define INF 0x3f3f3f3f
#define N 10001
#define LL long long
using namespace std;
bool vis[N*2];
int Stack[N*2],top;
vector<int> G[N*2];
void init(int n){
    memset(vis,false,sizeof(vis));
    for(int i=0;i<2*n;i++)
        G[i].clear();
}
void addOrClause(int x,int xVal,int y,int yVal){
    x=x*2+xVal;
    y=y*2+yVal;
    G[x^1].push_back(y);
    G[y^1].push_back(x);
}
void addAndClause(int x,int xval,int y,int yval) {
    x=x*2+xval;
    y=y*2+yval;
    G[x].push_back(y);
}
bool dfs(int x){
    if(vis[x^1])
        return false;
 
    if(vis[x])
        return true;
    vis[x]=true;
 
    Stack[top++]=x;
 
    for(int i=0;i<G[x].size();i++)
        if(!dfs(G[x][i]))
            return false;
 
    return true;
}
bool twoSAT(int n){
    for(int i=0;i<2*n;i+=2){
        if(!vis[i] && !vis[i+1]){
            top=0;
 
            if(!dfs(i)){
                while(top>0)
                    vis[Stack[--top]]=false;
 
                if(!dfs(i+1))
                    return false;
            }
        }
    }
    return true;
}
int main(){
    int n,m;
    while(scanf("%d%d",&n,&m)!=EOF&&(n+m)){
 
        init(n*2);
 
        addAndClause(0,1,0,0);//新娘在左
        addAndClause(1,0,1,1);//新郎在右
 
        //n-1对夫妇
        for(int i=1;i<n;i++){
            //拆点
            int a=i*2;//妻子
            int b=i*2+1;//丈夫
 
            //初始条件
            addAndClause(a,0,b,1);
            addAndClause(a,1,b,0);
            addAndClause(b,0,a,1);
            addAndClause(b,1,a,0);
        }
 
        for(int i=0;i<m;i++){
            int a,b;//有奸情的两个人
            char ch1[10],ch2[10];
 
            scanf("%d%s%d%s",&a,ch1,&b,ch2);
 
            //拆点
            if(ch1[0]=='w')
                a=a*2;//妻子
            else
                a=a*2+1;//丈夫
            if(ch2[0]=='w')
                b=b*2;//妻子
            else
                b=b*2+1;//丈夫
 
            //添加限制条件
            addAndClause(a,1,b,0);
            addAndClause(b,1,a,0);
        }
 
        if(!twoSAT(n*2))
            printf("bad luck\n");
        else{
            for(int i=2;i<2*n;i+=2){
                if(vis[i*2])
                    printf("%dw ",i/2);
                if(vis[(i+1)*2])
                    printf("%dh ",i/2);
            }
            printf("\n");
        }
    }
 
    return 0;
}

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