#441879 (C++14) No.75 回数の期待値の問題

• 問題: No.75 回数の期待値の問題
• ユーザー: ysuzuki5321
• 提出日時: 2020-03-09 21:25:50
• 言語: C++14 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 6 ms / 5,000 ms
• コード長: 13,475 bytes
• コンパイル時間: 1,646 ms
• コンパイル使用メモリ: 132,088 KB
• 実行使用メモリ: 6,820 KB
• 最終ジャッジ日時: 2024-11-14 07:48:46
• 合計ジャッジ時間: 2,467 ms
• ジャッジサーバーID （参考情報）: judge5 / judge2

ファイルパターン	結果
sample	AC * 4
other	AC * 16

ソースコード

#include <stdio.h>
#include <sstream>
#include <string.h>
#include <vector>
#include <map>
#include <algorithm>
#include <utility>
#include <set>
#include <cctype>
#include <queue>
#include <stack>
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <deque>
#include <limits>
#include <iomanip>
#include <ctype.h>
#include <unordered_map>
#include <random>
#include <numeric>
#include <iostream>
#include <array>

#define _USE_MATH_DEFINES
#include <iostream>
#include <math.h>
using namespace std;
#define rep(x,n) for(int x = 0;x < n;x++)
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef pair<int, char> pic;
int dx[] = { -1,0,1,0 };
int dy[] = { 0,-1,0,1 };
#define bit(x,v) ((ll)x << v)

const ll INF = 1000000007;
const int MAX = 1000010;
const int MOD = 1000000007;

long long fac[MAX], finv[MAX], inv[MAX];
void COMinit() {
	fac[0] = fac[1] = 1;
	finv[0] = finv[1] = 1;
	inv[1] = 1;
	for (int i = 2; i < MAX; i++) {
		fac[i] = fac[i - 1] * i % MOD;
		inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD;
		finv[i] = finv[i - 1] * inv[i] % MOD;
	}
}

// 二項係数計算
long long COM(int n, int k) {
	if (n < k) return 0;
	if (n < 0 || k < 0) return 0;
	return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
}

ll gcd(ll a, ll b) {
	if (b == 0) return a;
	return gcd(b, a % b);
}
int pr[100010];
int lank[100010];
void uini(int n) {
	for (size_t i = 0; i <= n; i++)
	{
		pr[i] = i;
		lank[i] = 1;
	}
}

int parent(int x) {
	if (x == pr[x]) return x;
	return pr[x] = parent(pr[x]);
}

int same(int x, int y) {
	return parent(x) == parent(y);
}

bool unit(int x, int y) {
	int px = parent(x);
	int py = parent(y);

	if (px == py) return false;
	if (lank[py] < lank[px]) {
		pr[py] = px;
		lank[px] += lank[py];
	}
	else {
		pr[px] = py;
		lank[py] += lank[px];
	}
	return true;
}

ll bit[200010];
int max_n = 200000;
int pm = 0;
void add(int x) {

	while (max_n >= x)
	{
		bit[x]++;
		x += x & -x;
	}
}
void sub(int x) {
	while (max_n >= x)
	{
		bit[x]--;
		x += x & -x;
	}
}
ll merge(ll* a, int left, int mid, int right) {
	ll n1 = mid - left;
	ll n2 = right - mid;
	vector<int> L(n1 + 1);
	vector<int> R(n2 + 1);
	for (size_t i = 0; i < n1; i++)
	{
		L[i] = a[left + i];
	}
	for (size_t i = 0; i < n2; i++)
	{
		R[i] = a[mid + i];
	}

	L[n1] = INF;
	R[n2] = INF;
	ll i = 0;
	ll j = 0;
	ll r = 0;
	for (size_t k = left; k < right; k++)
	{
		if (L[i] <= R[j]) {
			a[k] = L[i];
			i++;
		}
		else {
			a[k] = R[j];
			r += n1 - i;
			j++;
		}
	}
	return r;
}
ll merge2(pair<int, char>* a, int left, int mid, int right) {
	ll n1 = mid - left;
	ll n2 = right - mid;
	vector<pair<int, char>> L(n1 + 1);
	vector<pair<int, char>> R(n2 + 1);
	for (size_t i = 0; i < n1; i++)
	{
		L[i] = a[left + i];
	}
	for (size_t i = 0; i < n2; i++)
	{
		R[i] = a[mid + i];
	}

	L[n1] = make_pair(INF, ' ');
	R[n2] = make_pair(INF, ' ');
	ll i = 0;
	ll j = 0;
	ll r = 0;
	for (size_t k = left; k < right; k++)
	{
		if (L[i].first <= R[j].first) {
			a[k] = L[i];
			i++;
		}
		else {
			a[k] = R[j];
			r += n1 - i;
			j++;
		}
	}
	return r;
}
ll mergeSort2(pair<int, char>* a, int left, int right) {
	ll res = 0;
	if (left + 1 < right) {
		int mid = (left + right) / 2;
		res = mergeSort2(a, left, mid);
		res += mergeSort2(a, mid, right);
		res += merge2(a, left, mid, right);
	}
	return res;
}
ll mergeSort(ll* a, int left, int right) {
	ll res = 0;
	if (left + 1 < right) {
		int mid = (left + right) / 2;
		res = mergeSort(a, left, mid);
		res += mergeSort(a, mid, right);
		res += merge(a, left, mid, right);
	}
	return res;
}
int partition(pair<int, char>* a, int p, int r) {
	pair<int, char> x = a[r];
	int i = p - 1;
	for (size_t j = p; j < r; j++)
	{
		if (a[j].first <= x.first) {
			i++;
			swap(a[i], a[j]);
		}
	}
	swap(a[i + 1], a[r]);
	return i + 1;
}
void quick(pair<int, char>* a, int p, int r) {
	if (p < r) {
		int q = partition(a, p, r);
		quick(a, p, q - 1);
		quick(a, q + 1, r);
	}
}

ll n;
int ci = 0;
ll P[1000010];
struct Node {
	int key;
	int priority;
	Node* parent, * left, * right;
	Node(int key, int priority);
	Node() {}
};
Node NIL;
Node::Node(int key, int priority) : key(key), priority(priority) {
	left = &NIL;
	right = &NIL;
}
Node* root = new Node();
void cenrec(Node* k) {
	if (k->key == NIL.key) return;
	cenrec(k->left);
	cout << " " << k->key;
	cenrec(k->right);
}
void fastrec(Node* k)
{
	if (k->key == NIL.key) return;
	cout << " " << k->key;
	fastrec(k->left);
	fastrec(k->right);
}
void insert(Node* v) {
	Node* y = &NIL;
	Node* x = root;
	while (x->key != NIL.key)
	{
		y = x;
		if (v->key < x->key) {
			x = x->left;
		}
		else {
			x = x->right;
		}
	}
	v->parent = y;
	if (y->key == NIL.key) {
		root = v;
	}
	else if (v->key < y->key) {
		y->left = v;
	}
	else {
		y->right = v;
	}

}

Node* find(Node* k, ll v)
{
	if (k->key == NIL.key) return &NIL;
	if (k->key == v) return k;
	if (v < k->key) return find(k->left, v);
	return find(k->right, v);
}
void delp12(Node* x) {
	if (x->key == NIL.key)  return;
	Node* l = x->left;
	Node* r = x->right;
	Node* pr = x->parent;

	if (l->key == NIL.key
		&& r->key == NIL.key) {
		if (pr->left == x) {
			pr->left = &NIL;
		}
		else pr->right = &NIL;
	}
	else if (l->key != NIL.key) {
		if (pr->left == x) {
			pr->left = l;
		}
		else pr->right = l;
		l->parent = pr;
	}
	else if (r->key != NIL.key) {
		if (pr->left == x) {
			pr->left = r;
		}
		else pr->right = r;
		r->parent = pr;
	}
}
Node* get_next(Node* k) {
	if (k->key == NIL.key) return &NIL;
	Node* res = get_next(k->left);
	if (res->key != NIL.key) return res;
	return k;
}
void del(Node* x) {

	if (x->key == NIL.key) return;
	Node* l = x->left;
	Node* r = x->right;
	Node* pr = x->parent;

	if (l->key != NIL.key && r->key != NIL.key) {
		Node* nex = get_next(r);
		x->key = nex->key;
		delp12(nex);
	}
	else {
		delp12(x);
	}
}
Node* rightRotate(Node* t) {
	Node* s = t->left;
	t->left = s->right;
	s->right = t;
	return s;
}
Node* leftRotate(Node* t) {
	Node* s = t->right;
	t->right = s->left;
	s->left = t;
	return s;
}
Node* _insert(Node* t, int key, int priority) {
	if (t->key == NIL.key) {
		return new Node(key, priority);
	}
	if (key == t->key) {
		return t;
	}

	if (key < t->key) {
		t->left = _insert(t->left, key, priority);
		if (t->priority < t->left->priority) {
			t = rightRotate(t);
		}
	}
	else {
		t->right = _insert(t->right, key, priority);
		if (t->priority < t->right->priority) {
			t = leftRotate(t);
		}
	}
	return t;
}
Node* delete1(Node* t, int key);
Node* _delete(Node* t, int key) {
	if (t->left->key == NIL.key && t->right->key == NIL.key) {
		return &NIL;
	}
	else if (t->left->key == NIL.key) {
		t = leftRotate(t);
	}
	else if (t->right->key == NIL.key) {
		t = rightRotate(t);
	}
	else
	{
		if (t->left->priority > t->right->priority) {
			t = rightRotate(t);
		}
		else
			t = leftRotate(t);
	}
	return delete1(t, key);
}
Node* delete1(Node* t, int key) {
	if (t->key == NIL.key) {
		return &NIL;
	}
	if (key < t->key) {
		t->left = delete1(t->left, key);
	}
	else if (key > t->key) {
		t->right = delete1(t->right, key);
	}
	else return _delete(t, key);
	return t;
}
int H;
int left(int i) {
	return i * 2 + 1;
}
int right(int i) {
	return i * 2 + 2;
}
struct edge {
	int from, to;
	ll val;
	edge(int from, int to, ll val) : from(from), to(to), val(val) {}
};
int k;
int _rank[1010];
int temp[1010];
bool compare_sa(int i, int j) {
	if (_rank[i] != _rank[j]) return _rank[i] < _rank[j];
	else {
		int ri = i + k <= n ? _rank[i + k] : -1;
		int rj = j + k <= n ? _rank[j + k] : -1;
		return ri < rj;
	}
}
void construct_sa(string S, int* sa) {
	n = S.length();

	for (size_t i = 0; i <= n; i++)
	{
		sa[i] = i;
		_rank[i] = i < n ? S[i] : -1;
	}

	for (k = 1; k <= n; k *= 2)
	{
		sort(sa, sa + n + 1, compare_sa);

		// saはソート後の接尾辞の並びになっている、rankは元の位置のindexを保持したまま、更新されている。
		// ピンとこなかった部分
		temp[sa[0]] = 0;
		for (size_t i = 1; i <= n; i++)
		{
			temp[sa[i]] = temp[sa[i - 1]] + (compare_sa(sa[i - 1], sa[i]) ? 1 : 0);
		}
		for (size_t i = 0; i <= n; i++)
		{
			_rank[i] = temp[i];
		}
	}
}
bool contain(string S, int* sa, string T) {
	int a = 0, b = S.length();
	// sa は 接尾辞が辞書順に並んでいる、入っているのはその位置のインデックス
	while (b - a > 1) {
		int c = (a + b) / 2;
		if (S.compare(sa[c], T.length(), T) < 0) a = c;
		else b = c;
	}
	return S.compare(sa[b], T.length(), T) == 0;
}


#define bit(x,v) ((ll)x << v)

class BIT {

	static const int MAX_N = 500010;
public:
	BIT() { memset(bit, 0, sizeof(bit)); }
	ll bit[MAX_N + 1], n;
	ll sum(int i) {
		ll s = 0;
		while (i > 0)
		{
			s += bit[i];
			i -= i & -i;
		}
		return s;
	}

	void add(int i, int x) {
		while (i <= n)
		{
			bit[i] += x;
			i += i & -i;
		}
	}


};
struct UnionFind {
	vector<int> A;
	UnionFind(int n) : A(n, -1) {}
	int find(int x) {
		if (A[x] < 0) return x;
		return A[x] = find(A[x]);
	}
	void unite(int x, int y) {
		x = find(x), y = find(y);
		if (x == y) return;
		if (A[x] > A[y]) swap(x, y);
		A[x] += A[y];
		A[y] = x;
	}
	int ngroups() {
		int ans = 0;
		for (auto a : A) if (a < 0) ans++;
		return ans;
	}
};
void yes() { cout << "Yes\n"; exit(0); }
void no() { cout << "No\n"; exit(0); }
vector<ll> getp(ll n) {

	vector<ll> res;
	ll a = 2;
	if (n % 2 == 0) {
		res.push_back(2);
		while (n % 2 == 0)n /= 2;
	}

	for (ll i = 3; i * i <= n; i += 2)
	{
		if (n % i == 0) {
			res.push_back(i);
			while (n % i == 0)n /= i;
		}
	}
	if (n != 1) res.push_back(n);
	return res;
}
vector<ll> getp2(ll n) {

	vector<ll> res;
	ll a = 2;
	if (n % 2 == 0) {

		while (n % 2 == 0) { n /= 2; res.push_back(2); }
	}

	for (ll i = 3; i * i <= n; i += 2)
	{
		if (n % i == 0) {

			while (n % i == 0) { n /= i; res.push_back(i); }
		}
	}
	if (n != 1) res.push_back(n);
	return res;
}
vector<pll> getp3(ll n) {
	vector<pll> res;
	ll a = 2;
	int si = 0;
	if (n % 2 == 0) {

		res.push_back(make_pair(2, 0));
		while (n % 2 == 0) { n /= 2; res[si].second++; }
		si++;
	}

	for (ll i = 3; i * i <= n; i += 2)
	{
		if (n % i == 0) {
			res.push_back(make_pair(i, 0));
			while (n % i == 0) { n /= i; res[si].second++; }
			si++;
		}
	}
	if (n != 1) { res.push_back(make_pair(n,1)); }
	return res;
}

vector<ll> getDivisors(ll n) {

	vector<ll> res;
	ll a = 2;
	res.push_back(1);
	for (ll i = 2; i * i <= n; i++)
	{

		if (n % i == 0) {
			res.push_back(i);
			if (n / i != i)
				res.push_back(n / i);
		}
	}
	return res;
}

struct ve {
public:
	vector<ve> child;
	int _t = INF;
	ve(int t) :_t(t) {}
	ve(ve _left, ve _right) {
		_t = _left._t + _right._t;
		child.push_back(_left);
		child.push_back(_right);
	}
	bool operator<(const ve& t) const {
		return _t > t._t;
	}
};

vector<bool> elas(ll n) {
	vector<bool> r(n);
	fill(r.begin(), r.end(), 1);
	r[0] = 0;
	r[1] = 0;
	for (ll i = 2; i * i < n; i++)
	{
		if (!r[i]) continue;
		ll ti = i * 2;
		while (ti < n)
		{
			r[ti] = false;
			ti += i;
		}
	}
	return r;
}
bool isPrime(ll v) {
	for (ll i = 2; i * i <= v; i++)
	{
		if (v % i == 0) return false;
	}
	return true;
}

ll getpow(ll b,ll x, ll md) {

	ll t = b;
	ll res = 1;
	while (x > 0)
	{
		if (x & 1) {
			res *= t;
			res %= md;
		}
		x >>= 1;
		t *= t;
		t %= md;
	}
	return res;
}
ll getpow(ll b, ll x) {

	return getpow(b, x, INF);
}
class SegTree {

public :
	const static int MAX_N = 100010;
	const static int DAT_SIZE = (1 << 18) - 1;
	int N, Q;
	int A[MAX_N];
	
	
	ll data[DAT_SIZE], datb[DAT_SIZE];
	void init(int _n) {
		N = 1;
		while (N < _n) N <<= 1;
		memset(data, 0, sizeof(data));
		memset(datb, 0, sizeof(datb));
	}
	void init(int _n,ll iv) {
		N = 1;
		while (N < _n) N <<= 1;
		rep(i, DAT_SIZE) {
			data[i] = iv;
			datb[i] = iv;
		}
	}
	void add(int a, int b, int x) {
		add(a, b + 1, x, 0, 0, N);
	}
	void add(int a, int b, int x, int k, int l, int r) {
		if (a <= l && r <= b) {
			data[k] += x;
		}
		else if (l < b && a < r) {
			datb[k] += (min(b, r) - max(a, l)) * x;
			add(a, b, x, k * 2 + 1, l, (l + r) / 2);
			add(a, b, x, k * 2 + 2, (l + r)/2, r);
		}
	}

	void change(int a, int b, int x) {
		change(a, b + 1, x, 0, 0, N);
	}
	void change(int a, int b, int x, int k, int l, int r) {
		if (a <= l && r <= b) {
			data[k] = x;
		}
		else if (l < b && a < r) {
			datb[k] = x;
			change(a, b, x, k * 2 + 1, l, (l + r) / 2);
			change(a, b, x, k * 2 + 2, (l + r) / 2, r);
		}
	}

	ll sum(int a, int b) {
		return sum(a, b + 1, 0, 0, N);
	}
	ll sum(int a, int b, int k, int l, int r) {
		if (b <= l || r <= a) {
			return 0;
		}
		if (a <= l && r <= b) {
			return data[k] * (r - l) + datb[k];
		}

		ll res = (min(b, r) - max(a, l)) * data[k];
		res += sum(a, b, k * 2 + 1, l, (l + r) / 2);
		res += sum(a, b, k * 2 + 2, (l + r) / 2, r);
		return res;
	}
};
ll divRm(string s, ll x) {

	ll r = 0;
	for (size_t i = 0; i < s.size(); i++)
	{
		r *= 10;
		r += s[i] - '0';
		r %= x;
	}
	return r;
}
ll cmbi(ll x, ll b) {

	ll res = 1;
	for (size_t i = 0; i < b; i++)
	{
		res *= x - i;
		res %= INF;
		res *= inv[b - i];
		res %= INF;
	}
	return res;
}

void solv() {
	
	cin >> n;

	double dp[300];
	memset(dp, 0, sizeof(dp));
	rep(i, 1000) {

		for (int i = 1; i <= n; i++)
		{
			double tmp = 1;
			for (int j = 1; j <= 6; j++)
			{
				if (i == j) continue;
				if (i < j) {
					tmp += dp[n] / 6.0;
				}
				else {
					tmp += dp[i - j] / 6.0;
				}
			}
			dp[i] = tmp;
		}
	}

	cout << fixed << setprecision(10) << dp[n] << endl;
}

int main() {
	//COMinit();
	solv();
	return 0;
}