結果

問題 No.463 魔法使いのすごろく🎲
コンテスト
ユーザー heno239
提出日時 2022-10-17 21:12:14
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 27 ms / 2,000 ms
コード長 8,789 bytes
コンパイル時間 2,297 ms
コンパイル使用メモリ 169,092 KB
最終ジャッジ日時 2025-02-08 07:46:15
ジャッジサーバーID
（参考情報） 		judge3 / judge4
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 36
権限があれば一括ダウンロードができます

ソースコード

diff # 

#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#include<iostream>
#include<string>
#include<cstdio>
#include<vector>
#include<cmath>
#include<algorithm>
#include<functional>
#include<iomanip>
#include<queue>
#include<ciso646>
#include<random>
#include<map>
#include<set>
#include<bitset>
#include<stack>
#include<unordered_map>
#include<unordered_set>
#include<utility>
#include<cassert>
#include<complex>
#include<numeric>
#include<array>
#include<chrono>
using namespace std;

//#define int long long
typedef long long ll;

typedef unsigned long long ul;
typedef unsigned int ui;
//constexpr ll mod = 998244353;
constexpr ll mod = 1000000007;
const ll INF = mod * mod;
typedef pair<int, int>P;

#define rep(i,n) for(int i=0;i<n;i++)
#define per(i,n) for(int i=n-1;i>=0;i--)
#define Rep(i,sta,n) for(int i=sta;i<n;i++)
#define rep1(i,n) for(int i=1;i<=n;i++)
#define per1(i,n) for(int i=n;i>=1;i--)
#define Rep1(i,sta,n) for(int i=sta;i<=n;i++)
#define all(v) (v).begin(),(v).end()
typedef pair<ll, ll> LP;

template<typename T>
void chmin(T& a, T b) {
	a = min(a, b);
}
template<typename T>
void chmax(T& a, T b) {
	a = max(a, b);
}
template<typename T>
void cinarray(vector<T>& v) {
	rep(i, v.size())cin >> v[i];
}
template<typename T>
void coutarray(vector<T>& v) {
	rep(i, v.size()) {
		if (i > 0)cout << " "; cout << v[i];
	}
	cout << "\n";
}
ll mod_pow(ll x, ll n, ll m = mod) {
	if (n < 0) {
		ll res = mod_pow(x, -n, m);
		return mod_pow(res, m - 2, m);
	}
	if (abs(x) >= m)x %= m;
	if (x < 0)x += m;
	//if (x == 0)return 0;
	ll res = 1;
	while (n) {
		if (n & 1)res = res * x % m;
		x = x * x % m; n >>= 1;
	}
	return res;
}
//mod should be <2^31
struct modint {
	int n;
	modint() :n(0) { ; }
	modint(ll m) {
		if (m < 0 || mod <= m) {
			m %= mod; if (m < 0)m += mod;
		}
		n = m;
	}
	operator int() { return n; }
};
bool operator==(modint a, modint b) { return a.n == b.n; }
bool operator<(modint a, modint b) { return a.n < b.n; }
modint operator+=(modint& a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= (int)mod; return a; }
modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += (int)mod; return a; }
modint operator*=(modint& a, modint b) { a.n = ((ll)a.n * b.n) % mod; return a; }
modint operator+(modint a, modint b) { return a += b; }
modint operator-(modint a, modint b) { return a -= b; }
modint operator*(modint a, modint b) { return a *= b; }
modint operator^(modint a, ll n) {
	if (n == 0)return modint(1);
	modint res = (a * a) ^ (n / 2);
	if (n % 2)res = res * a;
	return res;
}

ll inv(ll a, ll p) {
	return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p);
}
modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); }
modint operator/=(modint& a, modint b) { a = a / b; return a; }
const int max_n = 1 << 21;
modint fact[max_n], factinv[max_n];
void init_f() {
	fact[0] = modint(1);
	for (int i = 0; i < max_n - 1; i++) {
		fact[i + 1] = fact[i] * modint(i + 1);
	}
	factinv[max_n - 1] = modint(1) / fact[max_n - 1];
	for (int i = max_n - 2; i >= 0; i--) {
		factinv[i] = factinv[i + 1] * modint(i + 1);
	}
}
modint comb(int a, int b) {
	if (a < 0 || b < 0 || a < b)return 0;
	return fact[a] * factinv[b] * factinv[a - b];
}
modint combP(int a, int b) {
	if (a < 0 || b < 0 || a < b)return 0;
	return fact[a] * factinv[a - b];
}

ll gcd(ll a, ll b) {
	a = abs(a); b = abs(b);
	if (a < b)swap(a, b);
	while (b) {
		ll r = a % b; a = b; b = r;
	}
	return a;
}
using ld = long double;
//typedef long double ld;
typedef pair<ld, ld> LDP;
const ld eps = 1e-10;
const ld pi = acosl(-1.0);
template<typename T>
void addv(vector<T>& v, int loc, T val) {
	if (loc >= v.size())v.resize(loc + 1, 0);
	v[loc] += val;
}
/*const int mn = 2000005;
bool isp[mn];
vector<int> ps;
void init() {
	fill(isp + 2, isp + mn, true);
	for (int i = 2; i < mn; i++) {
		if (!isp[i])continue;
		ps.push_back(i);
		for (int j = 2 * i; j < mn; j += i) {
			isp[j] = false;
		}
	}
}*/

//[,val)
template<typename T>
auto prev_itr(set<T>& st, T val) {
	auto res = st.lower_bound(val);
	if (res == st.begin())return st.end();
	res--; return res;
}

//[val,)
template<typename T>
auto next_itr(set<T>& st, T val) {
	auto res = st.lower_bound(val);
	return res;
}
using mP = pair<modint, modint>;
mP operator+(mP a, mP b) {
	return { a.first + b.first,a.second + b.second };
}
mP operator+=(mP& a, mP b) {
	a = a + b; return a;
}
mP operator-(mP a, mP b) {
	return { a.first - b.first,a.second - b.second };
}
mP operator-=(mP& a, mP b) {
	a = a - b; return a;
}
LP operator+(LP a, LP b) {
	return { a.first + b.first,a.second + b.second };
}
LP operator+=(LP& a, LP b) {
	a = a + b; return a;
}
LP operator-(LP a, LP b) {
	return { a.first - b.first,a.second - b.second };
}
LP operator-=(LP& a, LP b) {
	a = a - b; return a;
}

mt19937 mt(time(0));

const string drul = "DRUL";
string senw = "SENW";
//DRUL,or SENW
int dx[4] = { 1,0,-1,0 };
int dy[4] = { 0,1,0,-1 };
//-----------------------------------------

typedef long double Data;
typedef vector<Data> Array;
typedef vector<Array> mat;

bool is_zero(Data dat) { return abs(dat) < eps; }
mat operator-(mat a) {
	rep(i, a.size())rep(j, a[0].size())a[i][j] = -a[i][j];
	return a;
}
mat operator+(mat lhs, mat& rhs) {
	rep(i, lhs.size())rep(j, lhs[0].size())lhs[i][j] += rhs[i][j];
	return lhs;
}
mat operator-(mat lhs, mat& rhs) {
	rep(i, lhs.size())rep(j, lhs[0].size())lhs[i][j] -= rhs[i][j];
	return lhs;
}
mat operator*(const mat& lhs, const mat& rhs) {
	mat ret(lhs.size(), Array(rhs[0].size(), 0));
	rep(i, lhs.size())rep(j, rhs[0].size())rep(k, rhs.size()) {
		ret[i][j] += lhs[i][k] * rhs[k][j];
	}
	return ret;
}
//no verify
int rankMat(mat a) {
	const int n = a.size(), m = a[0].size();
	int r = 0;
	for (int i = 0; r < n && i < m; ++i) {
		int pivot = r;
		for (int j = r + 1; j < n; ++j)
			if (abs(a[j][i]) > abs(a[pivot][i]))pivot = j;
		swap(a[pivot], a[r]);
		if (is_zero(a[r][i]))continue;
		for (int k = m - 1; k >= i; --k)
			a[r][k] = a[r][k] / a[r][i];
		for (int j = r + 1; j < n; ++j) {
			for (int k = m - 1; k >= i; --k) {
				a[j][k] = fma(-a[r][k], a[j][i], a[j][k]);
			}
		}
		++r;
	}
	return r;
}
mat scalar(int sz, Data k) {
	mat ret(sz, Array(sz, 0));
	rep(i, sz)ret[i][i] = k;
	return ret;
}
//行列累乗
mat operator^(const mat& lhs, const ll n) {
	if (n == 0)return scalar(lhs.size(), 1);
	mat ret = (lhs * lhs) ^ (n / 2);
	if (n % 2) {
		ret = ret * lhs;
	}
	return ret;
}

Data det(mat a) {
	const int n = a.size();
	Data D = Data(1);
	for (int i = 0; i < n; ++i) {
		int pivot = i;
		for (int j = i + 1; j < n; ++j) {
			if (abs(a[j][i]) > abs(a[pivot][i]))pivot = j;
		}
		swap(a[pivot], a[i]);
		D = D * a[i][i] * Data(i != pivot ? -1 : 1);
		if (is_zero(a[i][i]))break;
		Data coef = (Data)1 / a[i][i];
		for (int j = i + 1; j < n; ++j) {
			if (a[j][i] == (Data)0)continue;
			for (int k = n - 1; k >= i; --k) {
				a[j][k] = a[j][k] - a[i][k] * a[j][i] * coef;
			}
		}
	}
	return D;
}

pair<mat, vector<int>> LUPDecomposition(mat a) {
	int n = a.size();
	vector<int> perm(n);
	iota(begin(perm), end(perm), 0);
	rep(i, n) {
		int pivot = i;
		for (int j = i + 1; j < n; ++j)
			if (abs(a[j][i]) > abs(a[pivot][i]))pivot = j;
		swap(a[pivot], a[i]);
		swap(perm[pivot], perm[i]);
		for (int j = i + 1; j < n; ++j) {
			a[j][i] /= a[i][i];
			for (int k = i + 1; k < n; ++k) {
				a[j][k] -= a[i][k] * a[j][i];
			}
		}
	}
	return make_pair(a, perm);
}
Array LUPBackSubstitution(mat& LU, vector<int>& perm, Array a) {
	int n = LU.size();
	Array tmp(n);
	rep(i, n)tmp[i] = a[perm[i]];
	swap(tmp, a);
	rep(i, n) {
		rep(j, i) {
			a[i] -= a[j] * LU[i][j];
		}
	}
	for (int i = n - 1; i >= 0; --i) {
		for (int j = i + 1; j < n; ++j) {
			a[i] -= a[j] * LU[i][j];
		}
		a[i] /= LU[i][i];
	}
	return a;
}

//Ax=bのxを返す
Array calc(mat A, Array b) {
	pair<mat, vector<int>> p = LUPDecomposition(A);
	return LUPBackSubstitution(p.first, p.second, b);
}

void solve() {
	int n, m; cin >> n >> m;
	vector<int> c(n);
	rep1(i, n-2)cin >> c[i];
	mat A(n - 1, Array(n - 1));
	Array b(n - 1);
	rep(i, n - 1) {
		A[i][i] += 1;
		rep1(j, m) {
			int to = i + j;
			if (to >= n)to = 2 * (n - 1) - to;
			if (to < n - 1) {
				A[i][to] -= 1 / (ld)m;
				b[i] += c[to]/(ld)m;
			}
		}
	}
	auto a = calc(A, b);
	//coutarray(a);
	vector<ld> dp(n);
	per(i, n - 1) {
		if (i + m >= n - 1) {
			dp[i] = 0;
		}
		else {
			//decide
			ld val1 = INF;
			rep1(j, m) {
				chmin(val1, a[i + j] + c[i + j]);
			}
			//random
			ld val2 = 0;
			rep1(j, m) {
				val2 += (dp[i + j] + c[i + j]) / (ld)m;
			}
			dp[i] = min(val1, val2);
		}
	}
	cout << dp[0] << "\n";
}





signed main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	cout << fixed << setprecision(10);
	//init_f();
	//init();
	//expr();
	//while(true)
	//int t; cin >> t; rep(i, t)
	solve();
	return 0;
}
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