HDU 5732 Subway(树同构)

题意：

给你两个树，让你判断是否同构。

分析：

这个题目还是挺好的，主要考验了Hash的技术，如何能够把两颗树Hash出来是难点之一，题解给出了一个办法，就是把每个子树的Hash值乘以一个小质数累乘然后模一个大质数，但是只要是这种hash肯定会出现重复的情况，所以我们需要对重复的hash值进行多次检验，另外，要把这个树变成有根树，可以选择中心或者是重心，这二者是不同的，但是都是可以做的。具体的细节还是看代码吧。

代码：

//
//  Created by  CQU_CST_WuErli
//  Copyright (c) 2016 CQU_CST_WuErli. All rights reserved.
//
//#pragma comment(linker, "/STACK:102400000,102400000")
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#define CLR(x) memset(x,0,sizeof(x))
#define OFF(x) memset(x,-1,sizeof(x))
#define MEM(x,a) memset((x),(a),sizeof(x))
#define BUG cout << "I am here" << endl
#define lookln(x) cout << #x << "=" << x << endl
#define SI(a) scanf("%d", &a)
#define SII(a,b) scanf("%d%d", &a, &b)
#define SIII(a,b,c) scanf("%d%d%d", &a, &b, &c)
const int INF_INT=0x3f3f3f3f;
const long long INF_LL=0x7f7f7f7f;
const int MOD=1e9+7;
const double eps=1e-10;
const double pi=acos(-1);
typedef long long  ll;
using namespace std;
typedef pair<int, int> pii;

const int N = 111111;
const int P = 1000000007, Q = 100000007;
int pos[N];
int pre[N];
int cnt, head[N], pnt[N << 1], nxt[N << 1];
struct HashMap {
    map<string, int> mp;
    vector<string> vec;
    int ID_cnt;
    int getID(const string& name) {
        if (mp.find(name) == mp.end()) {
            mp.insert(make_pair(name, ID_cnt++));
            vec.push_back(name);
        }
        return mp[name];
    }
    void init() {
        mp.clear();
        vec.clear();
        ID_cnt = 0;
    }
};
struct Hash {
    int u;
    int value;
    Hash(int u, int value): u(u), value(value) {}
    bool operator < (const Hash& x) const {
        return value < x.value;
    }
};
vector cha[N];
vector chb[N];
void add_edge(int u, int v) {
    pnt[cnt] = v;
    nxt[cnt] = head[u];
    head[u] = cnt++;
}
pii findFarthest(int fa, int u) {
    pii ret(u, -1);
    for (int i = head[u]; ~i; i = nxt[i]) {
        int v = pnt[i];
        if (v == fa) continue;
        pii cur = findFarthest(u, v);
        if (cur.second > ret.second) {
            pre[u] = v;
            ret = cur;
        }
    }
    ret.second++;
    return ret;
}

pii findRoot() {
    int a = findFarthest(-1, 0).first;
    pii t = findFarthest(-1, a);
    for (int i =0; i < t.second / 2; i++)
        a = pre[a];
    return make_pair(a, t.second % 2 ? pre[a] : -1);
}
int dfs(int fa, int u, vector* tgt) {
    vector vec;
    for (int i = head[u]; ~i; i = nxt[i]) {
        int v = pnt[i];
        if (v == fa) continue;
        vec.push_back(Hash(v, dfs(u, v, tgt)));
    }
    sort(vec.begin(), vec.end());
    int ret = 1;
    for (int i =0; i < (int) vec.size(); i++) {
        ret = ((ll) ret * Q + vec[i].value) % P;
    }
    tgt[u].swap(vec);
    return ret;
}

bool match(vector &vs, vector& vt, int *res) {
    if (vs.size() != vt.size()) {
        return false;
    }
    for (int i = 0; i < (int)vt.size(); i++) {
        for (int j = i; j < (int) vt.size() && vs[i].value == vt[j].value; j++) {
            swap(vt[i].u, vt[j].u);
            if (match(cha[vs[i].u], chb[vt[i].u], res)) {
                goto lblMatch;
            }
        }
        return false;
        lblMatch:
        res[vs[i].u] = vt[i].u;
    }
    return true;
}

int main(int argc, char const *argv[]) {
#ifdef LOCAL
    freopen("C:\\Users\\john\\Desktop\\in.txt","r",stdin);
    // freopen("C:\\Users\\john\\Desktop\\out.txt","w",stdout);
#endif
    int n;
    while (~scanf("%d", &n)) {
        string name;
        cnt = 0;
        OFF(head);
        HashMap a, b;
        a.init(); b.init();
        for (int i = 1; i < n; i++) {
            cin >> name;
            int u = a.getID(name);
            cin >> name;
            int v = a.getID(name);
            add_edge(u, v);
            add_edge(v, u);
        }
        pii ra = findRoot();
        vector vs, vt;
        vs.push_back(Hash(ra.first, dfs(ra.second, ra.first, cha)));
        if (ra.second != -1)
            vs.push_back(Hash(ra.second, dfs(ra.first, ra.second, cha)));
        sort(vs.begin(), vs.end());
        cnt = 0;
        OFF(head);
        for (int i = 1; i < n; i++) {
            cin >> name;
            int u = b.getID(name);
            cin >> name;
            int v = b.getID(name);
            add_edge(u, v);
            add_edge(v, u);
        }
        pii rb = findRoot();
        vt.push_back(Hash(rb.first, dfs(rb.second, rb.first, chb)));
        if (rb.second != -1)
            vt.push_back(Hash(rb.second, dfs(rb.first, rb.second, chb)));
        sort(vt.begin(), vt.end());
        if (match(vs, vt, pos)) {
            for (int i = 0; i cout << a.vec[i] << ' ' << b.vec[pos[i]] << '\n';
            }
        }
    }
    return 0;
}