POJ 3683 Priest John's Busiest Day

POJ_3683

这是一个2-SAT的问题，其实算法以及构图并不难想，但是编码的复杂度比较高。

在构图的时候，我们需要判断两段时间是否相交，比较容易的办法就是if(s1<t2&&t1>s2)，其中[s1,t1]、[s2,t2]为两段时间。

#include<stdio.h>
#include<string.h>
#include<stdlib.h>
#define MAXD 2010
#define MAXM 4000010
int S[MAXD], T[MAXD], D[MAXD], N;
int Gfirst[MAXD], Gnext[MAXM], Gv[MAXM], Ge;
int gfirst[MAXD], gnext[MAXM], gv[MAXM], ge, dg[MAXD][MAXD], del[MAXD];
int dfn[MAXD], color[MAXD], low[MAXD], cnt, col;
int ins[MAXD], s[MAXD], top, group[MAXD][MAXD], num[MAXD];
int topo[MAXD], vis[MAXD], t, ans[MAXD], res;
int cmp(const void * _p,const void * _q)
{
    int *p = (int *)_p;
    int *q = (int *)_q;
    return *p - *q;
}
void add_G(int i, int j)
{
    Gv[Ge] = j;
    Gnext[Ge] = Gfirst[i];
    Gfirst[i] = Ge;
    Ge ++;
}
void add_g(int i, int j)
{
    gv[ge] = j;
    gnext[ge] = gfirst[i];
    gfirst[i] = ge;
    ge ++;    
}
void init()
{
    int i, j, a, b;
    char str[10];
    for(i = 0; i < N; i ++)
    {
        scanf("%s", str);
        sscanf(str, "%d:%d", &a, &b);
        S[i] = a * 60 + b;
        scanf("%s", str);
        sscanf(str, "%d:%d", &a, &b);
        T[i] = a * 60 + b;
        scanf("%d", &D[i]);
    }
    Ge = 0;
    memset(Gfirst, -1, sizeof(Gfirst));
    for(i = 0; i < N; i ++)
    {
        int si0 = S[i], si1 = T[i] - D[i], ti0 = S[i] + D[i], ti1 = T[i];
        for(j = i + 1; j < N; j ++)
        {
            int sj0 = S[j], sj1 = T[j] - D[j], tj0 = S[j] + D[j], tj1 = T[j];
            if(si0 < tj0 && ti0 > sj0)
            {
                add_G(2 * i, 2 * j + 1);
                add_G(2 * j, 2 * i + 1);
            }
            if(si0 < tj1 && ti0 > sj1)
            {
                add_G(2 * i, 2 * j);
                add_G(2 * j + 1, 2 * i + 1);
            }
            if(si1 < tj0 && ti1 > sj0)
            {
                add_G(2 * i + 1, 2 * j + 1);
                add_G(2 * j, 2 * i);
            }
            if(si1 < tj1 && ti1 > sj1)
            {
                add_G(2 * i + 1, 2 * j);
                add_G(2 * j + 1, 2 * i);
            }
        }
    }
}
void tarjan(int u)
{
    int i, e;
    dfn[u] = low[u] = ++ cnt;
    for(e = Gfirst[u]; e != -1; e = Gnext[e])
    {
        if(!dfn[Gv[e]])
        {
            s[top ++] = Gv[e];
            ins[Gv[e]] = 1;
            tarjan(Gv[e]);
            if(low[Gv[e]] < low[u])
                low[u] = low[Gv[e]];
        }
        else if(ins[Gv[e]] && dfn[Gv[e]] < low[u])
            low[u] = dfn[Gv[e]];
    }
    if(low[u] == dfn[u])
    {
        for(i = 0, s[top] = -1; s[top] != u; i ++)
        {
            top --;
            ins[s[top]] = 0;
            color[s[top]] = col;
            group[col][i] = s[top];
        }
        num[col] = i;
        col ++;
    }
}
void dfs(int u)
{
    int e;
    vis[u] = 1;
    for(e = gfirst[u]; e != -1; e = gnext[e])
        if(!vis[gv[e]])
            dfs(gv[e]);
    topo[-- t] = u;
}
void toposort()
{
    int i;
    t = col;
    memset(vis , 0, sizeof(vis));
    for(i = 0; i < col; i ++)
        if(!vis[i])
            dfs(i);
}
void del_g(int u)
{
    int e;
    del[u] = 1;
    for(e = gfirst[u]; e != -1; e = gnext[e])
        if(!del[gv[e]])
            del_g(gv[e]);
}
int com()
{
    int i, j, e;
    cnt = top = col = 0;
    memset(dfn, 0, sizeof(dfn));
    memset(ins, 0, sizeof(ins));
    for(i = 0; i < 2 * N; i ++)
        if(!dfn[i])
        {
            s[top ++] = i;
            ins[i] = 1;
            tarjan(i);
        }
    for(i = 0; i < 2 * N; i ++)
    {
        if(color[i] == color[i ^ 1])
            return 0;
    }
    ge = 0;
    memset(gfirst, -1, sizeof(gfirst));
    memset(dg, 0, sizeof(dg));
    for(i = 0; i < 2 * N; i ++)
        for(e = Gfirst[i]; e != -1; e = Gnext[e])
            if(color[i] != color[Gv[e]] && !dg[color[Gv[e]]][color[i]])
            {
                dg[color[Gv[e]]][color[i]] = 1;
                add_g(color[Gv[e]], color[i]);
            }
    toposort();
    memset(del, 0, sizeof(del));
    res = 0;
    for(i = 0; i < col; i ++)
        if(!del[topo[i]])
        {
            del[topo[i]] = 1;
            for(j = 0; j < num[topo[i]]; j ++)
            {
                int p = group[topo[i]][j];
                ans[res ++] = p;
                if(!del[color[p ^ 1]])
                    del_g(color[p ^ 1]);
            }
        }
    return 1;
}
void printpath()
{
    int i;
    qsort(ans, res, sizeof(ans[0]), cmp);
    for(i = 0; i < res; i ++)
    {
        int p = ans[i] / 2;
        if(ans[i]%2 == 0)
        {
            printf("%02d:%02d ", S[p] / 60, S[p] % 60);
            printf("%02d:%02d\n", (S[p] + D[p]) / 60, (S[p] + D[p]) % 60);
        }
        else
        {
            printf("%02d:%02d ", (T[p] - D[p]) / 60, (T[p] - D[p]) % 60);
            printf("%02d:%02d\n", T[p] / 60, T[p] % 60);
        }
    }
}
int main()
{
    while(scanf("%d", &N) == 1)
    {
        init();
        if(com())
        {
            printf("YES\n");
            printpath();
        }
        else
            printf("NO\n");
    }
    return 0;    
}