[BJOI2015]树的同构

嘟嘟嘟




判断树的同构的方法就是树上哈希。




如果树是一棵有根树，那么只要从根节点出发dfs，每一个节点的哈希值等于按传统方式算出来的子树的哈希值的结果。需要注意的是，算完子树的哈希值后要先排序再加起来，因为交换两棵子树对于判断同构不影响。




对于无根树，我们应该选一个点，满足树的标号改变后树的形态没有变。所以就选重心好了。重心可能有两个（一条边的两个端点上），所以分别求一遍哈希取max（min）即可。




结果这题卡我的哈希（可能是我太菜了），最后写成ret = ((ret * base) | t[i]) % mod才过，自然溢出都不出行。

#include<cstdio>
#include<iostream>
#include<cmath>
#include<algorithm>
#include<cstring>
#include<cstdlib>
#include<cctype>
#include<vector>
#include<stack>
#include<queue>
using namespace std;
#define enter puts("")
#define space putchar(' ')
#define Mem(a, x) memset(a, x, sizeof(a))
#define In inline
typedef long long ll;
typedef unsigned long long ull;
typedef double db;
const int INF = 0x3f3f3f3f;
const db eps = 1e-8;
const ull base = 19260817;
const ull mod = 1e9 + 7;
const int maxn = 55;
inline ll read()
{
  ll ans = 0;
  char ch = getchar(), last = ' ';
  while(!isdigit(ch)) last = ch, ch = getchar();
  while(isdigit(ch)) ans = (ans << 1) + (ans << 3) + ch - '0', ch = getchar();
  if(last == '-') ans = -ans;
  return ans;
}
inline void write(ll x)
{
  if(x < 0) x = -x, putchar('-');
  if(x >= 10) write(x / 10);
  putchar(x % 10 + '0');
}

int m, n;
struct Edge
{
  int nxt, to;
}e[maxn << 1];
int head[maxn], ecnt = -1;
In void addEdge(int x, int y)
{
  e[++ecnt] = (Edge){head[x], y};
  head[x] = ecnt;
}

int siz[maxn], dp[maxn], G = INF;
In void dfs1(int now, int _f)
{
  siz[now] = 1; dp[now] = 0;
  for(int i = head[now], v; ~i; i = e[i].nxt)
    {
      if((v = e[i].to) == _f) continue;
      dfs1(v, now);
      siz[now] += siz[v];
      dp[now] = max(dp[now], siz[v]);
    }
  dp[now] = max(dp[now], n - siz[now]);
  G = min(G, dp[now]);
}

ull ans[maxn];
In ull dfs2(int now, int _f)
{
  ull ret = 1343247397;
  vector<ull> tp;
  for(int i = head[now], v; ~i; i = e[i].nxt)
    {
      if((v = e[i].to) == _f) continue;
      tp.push_back(dfs2(v, now));
    }
  sort(tp.begin(), tp.end());
  for(int i = 0; i < (int)tp.size(); ++i) ret = ((ret * base) ^ tp[i]);
  return ret;
}

In void init()
{
  Mem(head, -1); ecnt = -1;
  G = INF;
}

int main()
{
  //freopen("2.in", "r", stdin);
  //freopen("ha.out", "w", stdout);
  m = read();
  for(int i = 1; i <= m; ++i)
    {
      init();
      n = read();
      for(int j = 1; j <= n; ++j)
	{
	  int x = read();
	  if(x) addEdge(x, j), addEdge(j, x);
	}
      dfs1(1, 0);
      for(int j = 1; j <= n; ++j)
	if(dp[j] == G) ans[i] = max(ans[i], dfs2(j, 0));
    }
  for(int i = 1; i <= m; ++i)
    for(int j = 1; j <= i; ++j)
      if(ans[i] == ans[j]) {write(j), enter; break;}
  return 0;
}