题目描述

算法1 2-sat算法，思路分分钟，写代码20分钟，然而各种细节调了一下午

C++ 代码

#include<cstring>
#include<cmath>
#include<cstdio>
using namespace std;

#define a first
#define b second

typedef pair<int, int> PII;

const int N = 210, M = 10010;

PII edges[M];

int st[2 * M]; // is in loop

//tarjan
int dfn[M * 2], low[M * 2], ts, stk[M * 2], top, ins[M * 2];
int id[M * 2], cnt;

int h[M * 2], e[2000010], ne[2000010], idx;

int mp[N];

int n, m;

void add(int a, int b)
{
    e[idx] = b, ne[idx] = h[a], h[a] = idx ++; 
}

bool is_cross(int i, int j)//check if two edges cross
{
    int ia = mp[edges[i].a], ib = mp[edges[i].b];
    if(ia > ib) swap(ia, ib);
    int ja = mp[edges[j].a], jb = mp[edges[j].b];
    if(ja > jb) swap(ja, jb);
    if(ia < ja && ib < jb && ib > ja) return true;
    if(ja < ia && jb < ib && jb > ia) return true; 
    return false;
}

void tarjan(int u)
{
    dfn[u] = low[u] = ++ ts;
    stk[++ top ] = u, ins[u] = true;
    for(int i = h[u]; ~i; i = ne[i])
    {
        int j = e[i];
        if(!dfn[j])
        {
            tarjan(j);
            low[u] = min(low[u], low[j]);
        }
        else if(ins[j]) low[u] = min(dfn[j], low[u]);
    }
    if(dfn[u] == low[u])
    {
        ++ cnt;
        int k;
        do{
            k = stk[top --];
            ins[k] = false;
            id[k] = cnt;
        }while(k != u);
    }
}

int main()
{
    int t;
    scanf("%d", &t);
    while(t --)
    {
        scanf("%d%d", &n, &m);
        memset(h, -1, sizeof h);
        memset(st, 0, sizeof st);
        memset(mp, 0, sizeof mp);
        memset(dfn, 0, sizeof dfn);
        memset(low, 0, sizeof low);
        memset(id, 0, sizeof id);
        ts = 0, cnt = 0;
        idx = 0;
        for(int i = 1; i <= m; ++ i)
        {
            int a, b;
            scanf("%d%d", &a, &b);
            edges[i] = {a, b};
        }
        for(int i = 1; i <= n; ++ i)
        {
            int x;
            scanf("%d", &x);
            mp[x] = i;  
        }
        if(m > (n * 3 - 6))
        {
            puts("NO");
            continue;
        }
        for(int i = 1; i <= m; ++ i)
        {
            int a = edges[i].a, b = edges[i].b;
            if((abs(mp[a] - mp[b]) == 1) || (abs(mp[a] - mp[b]) == n - 1)) 
                st[i] = true, st[i + m] = true; 
        }
        //for(int i = 1; i <= m; ++ i) 
        //  printf("%d %d %d %d\n", i, edges[i].a, edges[i].b, st[i]);
        for(int i = 1; i <= m; ++ i)
            if(st[i]) continue;
            else 
                for(int j = 1; j < i; ++ j)
                    if(st[j]) continue;
                    else if(is_cross(i, j))
                    {
                        //printf("%d %d\n", i, j);
                        add(i, j + m), add(j, i + m);
                        add(i + m, j), add(j + m, i);
                    }
        for(int i = 1; i <= 2 * m; ++ i)
            if(!st[i] && !dfn[i])
                tarjan(i);
        bool tag = true;
        //for(int i = 1; i <= 2 * m; ++ i)
        //  printf("%d ", id[i]);
        for(int i = 1; i <= m; ++ i)
            if(!st[i] && id[i] == id[i + m])
                {
                    tag = false;
                    break;  
                }
        if(tag) printf("YES\n");
        else printf("NO\n");
    }
    return 0;
}