cf280C. Game on Tree(期望线性性)

题意

题目链接

Sol

开始想的dp，发现根本不能转移(貌似只能做链)

根据期望的线性性，其中\(ans = \sum_{1 * f(x)}\)

\(f(x)\)表示删除\(x\)节点的概率，显然\(x\)节点要被删除，那么它的祖先都不能被删除，因此概率为\(\frac{1}{deep[x]}\)

#include<bits/stdc++.h>
#define Pair pair<int, int>
#define MP(x, y) make_pair(x, y)
#define fi first
#define se second
//#define int long long
#define LL long long
#define ull unsigned long long
#define Fin(x) {freopen(#x".in","r",stdin);}
#define Fout(x) {freopen(#x".out","w",stdout);}
using namespace std;
const int MAXN = 1e6 + 10, mod = 1e9 + 7, INF = 1e9 + 10;
const double eps = 1e-9;
template <typename A, typename B> inline bool chmin(A &a, B b){if(a > b) {a = b; return 1;} return 0;}
template <typename A, typename B> inline bool chmax(A &a, B b){if(a < b) {a = b; return 1;} return 0;}
template <typename A, typename B> inline LL add(A x, B y) {if(x + y < 0) return x + y + mod; return x + y >= mod ? x + y - mod : x + y;}
template <typename A, typename B> inline void add2(A &x, B y) {if(x + y < 0) x = x + y + mod; else x = (x + y >= mod ? x + y - mod : x + y);}
template <typename A, typename B> inline LL mul(A x, B y) {return 1ll * x * y % mod;}
template <typename A, typename B> inline void mul2(A &x, B y) {x = (1ll * x * y % mod + mod) % mod;}
template <typename A> inline void debug(A a){cout << a << '\n';}
template <typename A> inline LL sqr(A x){return 1ll * x * x;}
inline int read() {
    char c = getchar(); int x = 0, f = 1;
    while(c < '0' || c > '9') {if(c == '-') f = -1; c = getchar();}
    while(c >= '0' && c <= '9') x = x * 10 + c - '0', c = getchar();
    return x * f;
}
int N, dep[MAXN];
vector<int> v[MAXN];
void dfs(int x, int fa) {
	dep[x] = dep[fa] + 1;
	for(int i = 0; i < v[x].size(); i++) {
		int to = v[x][i];
		if(to == fa) continue;
		dfs(to, x);
	}
}
signed main() {
	N = read();
	for(int i = 1; i <= N - 1; i++) {
		int x = read(), y = read();
		v[x].push_back(y);
		v[y].push_back(x);
	}
	dfs(1, 0);
	double ans = 0;
	for(int i = 1; i <= N; i++) ans += 1.0 / dep[i];
	printf("%.12lf", ans);
	return 0;
}