「SCOI2005」王室联邦

「SCOI2005」王室联邦

传送门

树分块。

考虑把树，按照节点个数每 \(B\) 个分块，把块顶作为省会。

这是具体证明

参考代码：

#include <cstdio>
#define rg register
#define file(x) freopen(x".in", "r", stdin), freopen(x".out", "w", stdout)
using namespace std;
template < class T > inline void read(T& s) {
	s = 0; int f = 0; char c = getchar();
	while ('0' > c || c > '9') f |= c == '-', c = getchar();
	while ('0' <= c && c <= '9') s = s * 10 + c - 48, c = getchar();
	s = f ? -s : s;
}

const int _ = 1010;

int tot, head[_], nxt[_ << 1], ver[_ << 1];
inline void Add_edge(int u, int v)
{ nxt[++tot] = head[u], head[u] = tot, ver[tot] = v; }

int n, B, cnt, num, rt[_], bel[_], x[_];

inline void dfs(int u, int f) {
	int tmp = num;
	for (rg int i = head[u]; i; i = nxt[i]) {
		int v = ver[i]; if (v == f) continue;
		dfs(v, u);
		if (num - tmp >= B) {
			rt[++cnt] = u;
			while (num > tmp) bel[x[num--]] = cnt;
		}
	}
	x[++num] = u;
}

int main() {
#ifndef ONLINE_JUDGE
	file("cpp");
#endif
	read(n), read(B);
	for (rg int u, v, i = 1; i < n; ++i)
		read(u), read(v), Add_edge(u, v), Add_edge(v, u);
	dfs(1, 0);
	if (!cnt) rt[++cnt] = 1;
	while (num) bel[x[num--]] = cnt;
	printf("%d\n", cnt);
	for (rg int i = 1; i <= n; ++i) printf("%d%c", bel[i], " \n"[i == n]);
	for (rg int i = 1; i <= cnt; ++i) printf("%d%c", rt[i], " \n"[i == n]);
	return 0;
}