https://ac.nowcoder.com/acm/contest/5675/J
题意
给出两棵同构的树，问最少修改多少点，让两棵树相同，即根节点相同，非根节点父亲节点的编号相同。
题解
设(dp[u1][u2])为(tree1)的子树根节点为(u1)，(tree2)的子树根节点为(u2)，子树中最多能匹配的点。
我们先对树做一遍hash，方便判断哪些子树是同构的。
按sz从小到大枚举两颗树的子树，如果同构，就计算这两棵子树匹配，最多有多少节点可以相同。
对于这两棵子树的同构子树，用一张图记录i和j子树之间匹配的答案，即(G[i][j]=dp[v1[i]][v2[j]])用KM算法进行转移，算出最大的匹配值，再加上根节点是否相同，就是这两棵子树匹配的答案，由于是按sz从小到大枚举，子树的子树匹配答案已经被计算出。
最后答案即为(n-dp[t1.rt][t2.rt])
代码
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
struct READ {
inline char read() {
#ifdef _WIN32
return getchar();
#endif
static const int IN_LEN = 1 << 18 | 1;
static char buf[IN_LEN], *s, *t;
return (s == t) && (t = (s = buf) + fread(buf, 1, IN_LEN, stdin)), s == t ? -1 : *s++;
}
template <typename _Tp> inline READ & operator >> (_Tp&x) {
static char c11, boo;
for(c11 = read(),boo = 0; !isdigit(c11); c11 = read()) {
if(c11 == -1) return *this;
boo |= c11 == '-';
}
for(x = 0; isdigit(c11); c11 = read()) x = x * 10 + (c11 ^ '0');
boo && (x = -x);
return *this;
}
} in;
const int N = 505;
#define pii pair<int, int>
mt19937_64 rdn(time(0));
int n;
ull key[N];
struct tree {
ull hs[N];
int sz[N];
vector<int> G[N];
int rt = 0;
vector<pii> f;
void read() {
for (int i = 1; i <= n; i++) {
int x; in >> x;
if (x == 0) rt = i;
else {
G[i].push_back(x);
G[x].push_back(i);
}
}
dfs(rt, 0);
for (int i = 1; i <= n; i++) f.push_back(pii(sz[i], i));
sort(f.begin(), f.end());
}
void dfs(int u, int fa) {
sz[u] = 1;
hs[u] = key[sz[u]];
for (int v : G[u]) {
if (v == fa) continue;
dfs(v, u);
sz[u] += sz[v];
hs[u] += key[sz[v]] * hs[v];
}
}
} t1, t2;
struct KM {
int G[N][N];
bool visx[N], visy[N];
int lx[N], ly[N];
int slack[N];
int linker[N];
int pre[N];
const int inf = 1e9 + 50;
int n;
void bfs(int k) {
int x, y = 0, yy = 0, delta;
memset(pre, 0, sizeof(pre));
fill(slack + 1, slack + n + 1, inf);
linker[y] = k;
while (1) {
x = linker[y]; delta = inf; visy[y] = true;
for (int i = 1; i <= n; i++) {
if (!visy[i]) {
if (slack[i] > lx[x] + ly[i] - G[x][i]) {
slack[i] = lx[x] + ly[i] - G[x][i];
pre[i] = y;
}
if (slack[i] < delta) delta = slack[i], yy = i;
}
}
for (int i = 0; i <= n; i++) {
if (visy[i]) lx[linker[i]] -= delta, ly[i] += delta;
else slack[i] -= delta;
}
y = yy;
if (linker[y] == -1) break;
}
while (y) linker[y] = linker[pre[y]], y = pre[y];
}
int calc(int nn) {
n = nn;
for (int i = 1; i <= n; i++) {
lx[i] = ly[i] = 0;
linker[i] = -1;
}
// for (int i = 1; i <= n; i++) {
// for (int j = 1; j <= n; j++) {
// printf("%d ", G[i][j]);
// }
// puts("");
// }
for (int i = 1; i <= n; i++) {
memset(visy, false, sizeof(visy));
bfs(i);
}
int ans = 0;
for (int i = 1; i <= n; i++) {
if (linker[i]) ans += G[linker[i]][i];
}
return ans;
}
} km;
int dp[N][N];
int main() {
in >> n;
for (int i = 0; i <= n; i++) key[i] = rdn();
t1.read(); t2.read();
for (auto x : t1.f) {
for (auto y : t2.f) {
int u1 = x.second, u2 = y.second;
if (t1.hs[u1] == t2.hs[u2]) {
set<ull> val;
map<ull, vector<int>> m1, m2;
for (int v1 : t1.G[u1]) val.insert(t1.hs[v1]), m1[t1.hs[v1]].push_back(v1);
for (int v2 : t2.G[u2]) m2[t2.hs[v2]].push_back(v2);
int ans = 0;
for (ull v : val) {
auto v1 = m1[v], v2 = m2[v];
for (int i = 0; i < v1.size(); i++) {
for (int j = 0; j < v2.size(); j++) {
km.G[i+1][j+1] = dp[v1[i]][v2[j]];
}
}
ans += km.calc(v1.size());
}
dp[u1][u2] = ans + (u1 == u2);
//printf("%d %d %d %d
", u1, u2, ans, dp[u1][u2]);
}
}
}
printf("%d
", n - dp[t1.rt][t2.rt]);
return 0;
}