bzoj 1217 [HNOI2003]消防局的设立 贪心

题面

题目传送门

解法

树形dp表示感觉太烦，不太会写

考虑贪心

显然每一次应该选深度最大且没有被覆盖的点，然后找到它的爷爷，然后暴力更新

当然，距离大一点贪心也是正确的

时间复杂度：\(O(n)\)

代码

#include <bits/stdc++.h>
#define N 100010
using namespace std;
template <typename node> void chkmax(node &x, node y) {x = max(x, y);}
template <typename node> void chkmin(node &x, node y) {x = min(x, y);}
template <typename node> void read(node &x) {
	x = 0; int f = 1; char c = getchar();
	while (!isdigit(c)) {if (c == '-') f = -1; c = getchar();}
	while (isdigit(c)) x = x * 10 + c - '0', c = getchar(); x *= f;
}
struct Edge {
	int next, num;
} e[N * 3];
int n, k, t, cnt, d[N], vis[N], fa[N];
void add(int x, int y) {
	e[++cnt] = (Edge) {e[x].next, y};
	e[x].next = cnt;
}
void bfs() {
	queue <int> q; q.push(1);
	int len = 1; d[1] = 1; fa[1] = 1;
	while (!q.empty()) {
		int x = q.front(); q.pop();
		for (int p = e[x].next; p; p = e[p].next) {
			int k = e[p].num;
			if (fa[k]) continue;
			d[++len] = k, q.push(k);
			fa[k] = x;
		}
	}
}
void dfs(int x, int fa, int s) {
	vis[x] = 1; if (s == k) return;
	for (int p = e[x].next; p; p = e[p].next) {
		int k = e[p].num;
		if (k != fa) dfs(k, x, s + 1);
	}
}
int main() {
	read(n); cnt = n, k = 2;
	for (int i = 2; i <= n; i++) {
		int x; read(x);
		add(x, i), add(i, x);
	}
	bfs(); int ans = 0;
	for (int i = n; i; i--)
		if (!vis[d[i]]) {
			int x = d[i]; ans++;
			for (int j = k; j; j--) x = fa[x];
			dfs(x, 0, 0);
		}
	cout << ans << "\n";
	return 0;
}