洛谷 P6378 [PA2010]Riddle

传送门

对于每个点在其所在的部分中考虑，每个点用 (a_i) 来表示，对其新增一个状态 (pre_i) 表示在该部分前 (i) 个点中是否存在被选为关键点。

(a_i longrightarrow pre_{a_i} , pre_{a_i}^prime longrightarrow a_i^prime)

(pre_{a_{i-1}} longrightarrow pre_{a_i} , pre_{a_i}^prime longrightarrow pre_{a_{i-1}}^prime)

(pre_{a_{i-1}} longrightarrow a_i^prime , a_i longrightarrow pre_{a_{i-1}}^prime)

#include <bits/stdc++.h>

using namespace std;
using ll = long long;
using p = pair<int, int>;
const double pi(acos(-1));
const int inf(0x3f3f3f3f);
const int mod(1e9 + 7);
const int maxn(4e6 + 10);
const int maxm(1e7 + 10);
int ecnt, head[maxn], a[maxn];
int tim, dfn[maxn], low[maxn];
int scnt, id[maxn];
bool vis[maxn];
stack<int> st;

struct edge {
    int to, nxt;
} edges[maxm];

template<typename T = int>
inline const T read()
{
    T x = 0, f = 1;
    char ch = getchar();
    while (ch < '0' || ch > '9') {
        if (ch == '-') f = -1;
        ch = getchar();
    }
    while (ch >= '0' && ch <= '9') {
        x = (x << 3) + (x << 1) + ch - '0';
        ch = getchar();
    }
    return x * f;
}

template<typename T>
inline void write(T x, bool ln)
{
    if (x < 0) {
        putchar('-');
        x = -x;
    }
    if (x > 9) write(x / 10, false);
    putchar(x % 10 + '0');
    if (ln) putchar(10);
}

inline int getPrev(int x, int n, bool prev1)
{
    return x + (prev1 ? n * 2 : n * 3);
}

void addEdge(int u, int v)
{
    edges[ecnt].to = v;
    edges[ecnt].nxt = head[u];
    head[u] = ecnt++;
}

void tarjan(int u)
{
    dfn[u] = low[u] = ++tim;
    st.push(u);
    vis[u] = true;
    for (int i = head[u]; compl i; i = edges[i].nxt) {
        int v = edges[i].to;
        if (not dfn[v]) {
            tarjan(v);
            low[u] = min(low[u], low[v]);
        } else if (vis[v]) {
            low[u] = min(low[u], dfn[v]);
        }
    }
    if (dfn[u] == low[u]) {
        ++scnt;
        int v = -1;
        do {
            v = st.top();
            st.pop();
            vis[v] = false;
            id[v] = scnt;
        } while (u not_eq v);
    }
}

bool check(int n)
{
    for (int i = 1; i <= n; ++i) {
        if (id[i] == id[i + n] or id[getPrev(i, n, true)] == id[getPrev(i, n, false)]) {
            return false;
        }
    }
    return true;
}

int main()
{
#ifdef ONLINE_JUDGE
#else
    freopen("input.txt", "r", stdin);
#endif
    memset(head, -1, sizeof head);
    int n = read(), m = read(), k = read();
    while (m--) {
        int u = read(), v = read();
        addEdge(u + n, v);
        addEdge(v + n, u);
    }
    while (k--) {
        int w = read();
        for (int i = 1; i <= w; ++i) {
            a[i] = read();
            addEdge(a[i], getPrev(a[i], n, true));
            addEdge(getPrev(a[i], n, false), a[i] + n);
        }
        for (int i = 2; i <= w; ++i) {
            addEdge(getPrev(a[i - 1], n, true), getPrev(a[i], n, true));
            addEdge(getPrev(a[i], n, false), getPrev(a[i - 1], n, false));
            addEdge(getPrev(a[i - 1], n, true), a[i] + n);
            addEdge(a[i], getPrev(a[i - 1], n, false));
        }
    }
    for (int i = 1; i <= n * 4; ++i) {
        if (not dfn[i]) {
            tarjan(i);
        }
    }
    puts(check(n) ? "TAK" : "NIE");
    return 0;
}