HDU2228栈深搜树哈希/同构

Posted 2021-09-07 hesorchen

题目

Same or not

给出两个01字符串，表示两棵树上的深搜方式。其中0表示向深层递归，1表示回溯。问两个字符串有没有可能是在同一颗树上生成的。

求解

根据深搜的性质，先用栈建树。建好两棵树之后，求出树的重心，然后以重心为根，进行树哈希，利用哈希值判断两棵树是否同构即可。

代码

#include <bits/stdc++.h>
using namespace std;
const int N = 1e4 + 5;

vector<int> mp[N];

int siz[N], mx[N];
void init()
{
    for (int i = 0; i < N; i++)
        mp[i].clear();
}
char s[N];

void add(int u, int v)
{
    mp[u].emplace_back(v);
    mp[v].emplace_back(u);
}
int rd[N];
int n;
int dfs(int u, int fa)
{
    int res = 0;
    siz[u] = 0;
    for (auto v : mp[u])
    {
        if (v == fa)
            continue;
        int val = dfs(v, u);
        siz[u] += val;
        res = max(res, val);
    }
    mx[u] = max(res, n - (siz[u] + 1));
    return siz[u] + 1;
}

const long long mod = 1e9 + 7;
long long Hash(int u, int fa)
{
    long long res = 1;
    vector<long long> vec;
    for (auto v : mp[u])
    {
        if (v == fa)
            continue;
        int val = Hash(v, u);
        vec.emplace_back(val);
    }
    sort(vec.begin(), vec.end());
    for (auto it : vec)
    {
        res = ((res * 13331 + it) ^ 1333331) % mod;
    }
    return res;
}
vector<pair<int, long long>> solve()
{
    init();
    int cnt = 1;
    vector<int> st;
    st.emplace_back(1);
    int len = strlen(s + 1);
    n = len / 2 + 1;
    for (int i = 1; i <= len; i++)
    {
        if (s[i] == '0')
        {
            ++cnt;
            add(st.back(), cnt);
            st.emplace_back(cnt);
        }
        else
            st.pop_back();
    }
    dfs(1, -1);
    int maxx = 0x3f3f3f3f;
    for (int i = 1; i <= n; i++)
        maxx = min(maxx, mx[i]);
    vector<pair<int, long long>> centr;
    for (int i = 1; i <= n; i++)
        if (maxx == mx[i])
            centr.emplace_back(make_pair(Hash(i, -1), i));
    return centr;
}

int main()
{
    srand(time(NULL));
    for (int i = 0; i < N; i++)
        rd[i] = rand();
    int t;
    cin >> t;
    while (t--)
    {
        scanf("%s", s + 1);
        vector<pair<int, long long>> vec1 = solve();
        scanf("%s", s + 1);
        vector<pair<int, long long>> vec2 = solve();
        bool flag = 1;
        if (vec1.size() == vec2.size())
        {
            sort(vec1.begin(), vec1.end());
            sort(vec2.begin(), vec2.end());
            for (int i = 0; i < vec1.size(); i++)
                if (vec1[i].first != vec2[i].first)
                    flag = 0;
        }
        else
            flag = 0;
        puts(flag ? "True" : "False");
    }
    return 0;
}