Luogu 2921 [USACO08DEC]在农场万圣节Trick or Treat on the Farm

基环树森林，然而我比较菜，直接tarjan找环。

发现缩点之后变成了DAG，每一个点往下走一定会走到一个环，缩点之后搜一遍看看会走到哪个环以及那个环的编号是多少，答案就是环的$siz$$ + $要走的路程。

比较垃圾的我忘记了判重边WA了好多发……

时间复杂度$O(n)$。

Code：

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

const int N = 1e5 + ;
const int inf =  << ;

int n, to[N], dfsc = , dfn[N], low[N], cur[N];
int scc = , siz[N], top = , sta[N], bel[N], dis[N];
int tot = , head[N];
bool vis[N], isCur[N];

struct Edge {
    int to, nxt;
} e[N];

inline void add(int from, int ver) {
    e[++tot].to = ver;
    e[tot].nxt = head[from];
    head[from] = tot;
}

inline void read(int &X) {
    X = ; char ch = ; int op = ;
    for(; ch > ''|| ch < ''; ch = getchar())
        if(ch == '-') op = -;
    for(; ch >= '' && ch <= ''; ch = getchar())
        X = (X << ) + (X << ) + ch - ;
    X *= op;
}

inline int min(int x, int y) {
    return x > y ? y : x;
}

inline int max(int x, int y) {
    return x > y ? x : y;
}

void tarjan(int x) {
    dfn[x] = low[x] = ++dfsc;
    sta[++top] = x, vis[x] = ;

    int y = to[x];
    if(!dfn[y]) {
        tarjan(y);
        low[x] = min(low[x], low[y]);
    } else if(vis[y]) low[x] = min(low[x], dfn[y]);

    if(low[x] == dfn[x]) {
        ++scc;
        for(; sta[top + ] != x; --top) {
            bel[sta[top]] = scc;
            siz[scc]++;
            vis[sta[top]] = ;
        }
    }
}

void dfs(int x) {
    vis[x] = ;
    if(isCur[x]) {
        dis[x] = , cur[x] = x;
        return;
    }
    for(int i = head[x]; i; i = e[i].nxt) {
        int y = e[i].to;
        if(!vis[y]) dfs(y);
        dis[x] = dis[y] + , cur[x] = cur[y];
    }
}

int main() {
//    freopen("testdata.in", "r", stdin);
//    freopen("mine.out", "w", stdout);

    read(n);
    for(int i = ; i <= n; i++) read(to[i]);

    for(int i = ; i <= n; i++)
        if(!dfn[i]) tarjan(i);

/*    for(int i = 1; i <= n; i++)
        printf("%d ", bel[i]);
    printf("\n");   */
    for(int i = ; i <= n; i++)
        if(to[i] == i) isCur[bel[i]] = ;
    for(int i = ; i <= scc; i++)
        if(siz[i] >= ) isCur[i] = ;

    for(int i = ; i <= n; i++) {
        if(bel[i] == bel[to[i]]) continue;
        add(bel[i], bel[to[i]]);
    }    

    for(int i = ; i <= scc; i++)
        if(!vis[i]) dfs(i);

/*    for(int i = 1; i <= scc; i++)
        printf("%d ", cur[i]);
    printf("\n");   */

    for(int i = ; i <= n; i++) {
        if(isCur[bel[i]]) printf("%d\n", siz[bel[i]]);
        else printf("%d\n", dis[bel[i]] + siz[cur[bel[i]]]);
    }

    return ;
}