CF 1138 E. Museums Tour

E. Museums Tour

链接

分析：

　　按时间建出分层图，每个点形如(u,t)，表示u在在t个时刻的点，tarjan缩点。每个强连通分量中的点都能经过，然后DAG上dp。

代码：

#include<cstdio>
#include<algorithm>
#include<cstring>
#include<iostream>
#include<cmath>
#include<cctype>
#include<set>
#include<queue>
#include<vector>
#include<map>
#define getid(a, b) ((a - 1) * d + b + 1)
using namespace std;
typedef long long LL;

inline int read() {
    int x=0,f=1;char ch=getchar();for(;!isdigit(ch);ch=getchar())if(ch=='-')f=-1;
    for(;isdigit(ch);ch=getchar())x=x*10+ch-'0';return x*f;
}

const int N = 5000005;
struct Graph { 
    int head[N], nxt[N], to[N], En;
    inline void add_edge(int u,int v) {
        ++En; to[En] = v, nxt[En] = head[u]; head[u] = En;
    }
}G1, G2;
int dfn[N], low[N], sk[N], bel[N], vis[N], siz[N], dp[N], TimeIndex, SCC, top;
char s[100001][51];

void tarjan(int u) {
    dfn[u] = low[u] = ++TimeIndex; sk[++top] = u; vis[u] = 1;
    for (int i = G1.head[u]; i; i = G1.nxt[i]) {
        int v = G1.to[i];
        if (!dfn[v]) tarjan(v), low[u] = min(low[u], low[v]);
        else if (vis[v]) low[u] = min(low[u], dfn[v]);
    }
    if (low[u] == dfn[u]) {
        ++SCC;
        do { vis[sk[top]] = 0; bel[sk[top]] = SCC; top--; } while (sk[top + 1] != u);
    }
}
int dfs(int u) { // DAG上dp 
    if (dp[u]) return dp[u];
    int ans = 0;
    for (int i = G2.head[u]; i; i = G2.nxt[i]) 
        ans = max(ans, dfs(G2.to[i]));
    dp[u] = siz[u] + ans;
    return dp[u];    
}
int main() {
    int n = read(), m = read(), d = read(), tot = n * d;
    for (int i = 1; i <= m; ++i) {
        int u = read(), v = read();
        for (int j = 0; j < d; ++j) 
            G1.add_edge(getid(u, j), getid(v, (j + 1) % d));
    }
    for (int i = 1; i <= n; ++i) scanf("%s", s[i]);
    for (int i = 1; i <= tot; ++i) if (!dfn[i]) tarjan(i);
    for (int i = 1; i <= n; ++i) {
        for (int j = 0; j < d; ++j) {
            int x = getid(i, j);
            if (s[i][j] == '1' && vis[bel[x]] != i) vis[bel[x]] = i, siz[bel[x]] ++; // 每个点在一个强连通分量中只能计算一次 
            for (int k = G1.head[x]; k; k = G1.nxt[k]) 
                if (bel[x] != bel[G1.to[k]]) G2.add_edge(bel[x], bel[G1.to[k]]);
        }
    }
    cout << dfs(bel[1]);
    return 0;
}