結果

問題 No.463 魔法使いのすごろく🎲
コンテスト
ユーザー shimomire
提出日時 2016-12-15 00:54:53
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 5 ms / 2,000 ms
コード長 8,129 bytes
コンパイル時間 1,297 ms
コンパイル使用メモリ 131,740 KB
実行使用メモリ 6,820 KB
最終ジャッジ日時 2024-11-30 08:10:54
合計ジャッジ時間 2,507 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge1
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 # 

#include <cassert>// c
#include <iostream>// io
#include <iomanip>
#include <fstream>
#include <sstream>
#include <vector>// container
#include <map>
#include <set>
#include <queue>
#include <bitset>
#include <stack>
#include <algorithm>// other
#include <complex>
#include <numeric>
#include <functional>
#include <random>
#include <regex>
using namespace std;

typedef long long ll;typedef unsigned long long ull;typedef long double ld;

#define ALL(c) c.begin(),c.end()
#define IN(l,v,r) (l<=v && v < r)
template<class T> void UNIQUE(T& v){v.erase(unique(ALL(v)),v.end());}
//debug
#define DUMP(x) cerr << #x <<" = " << (x)
#define LINE() cerr<< " (L" << __LINE__ << ")"

struct range{
	struct Iter{
		int v,step;
		Iter& operator++(){v+=step;return *this;}
		bool operator!=(Iter& itr){return v<itr.v;}
		int& operator*(){return v;}
	};
	Iter i, n;
	range(int i, int n,int step):i({i,step}), n({n,step}){}
	range(int i, int n):range(i,n,1){}
	range(int n):range(0,n){}
	Iter& begin(){return i;}
	Iter& end(){return n;}
};
struct rrange{
	struct Iter{
		int v,step;
		Iter& operator++(){v-=step;return *this;}
		bool operator!=(Iter& itr){return v>itr.v;}
		int& operator*(){return v;}
	};
	Iter i, n;
	rrange(int i, int n,int step):i({i-1,step}), n({n-1,step}){}
	rrange(int i, int n):rrange(i,n,1){}
	rrange(int n) :rrange(0,n){}
	Iter& begin(){return n;}
	Iter& end(){return i;}
};

//input
template<typename T1,typename T2> istream& operator >> (istream& is,pair<T1,T2>& p){return is>>p.first>>p.second;}
template<typename T1> istream& operator >> (istream& is,tuple<T1>& t){return is >> get<0>(t);}
template<typename T1,typename T2> istream& operator >> (istream& is,tuple<T1,T2>& t){return is >> get<0>(t) >> get<1>(t);}
template<typename T1,typename T2,typename T3> istream& operator >> (istream& is,tuple<T1,T2,T3>& t){return is >>get<0>(t)>>get<1>(t)>>get<2>(t);}
template<typename T1,typename T2,typename T3,typename T4> istream& operator >> (istream& is,tuple<T1,T2,T3,T4>& t){return is >> get<0>(t)>>get<1>(t)>>get<2>(t)>>get<3>(t);}
template<typename T> istream& operator >> (istream& is,vector<T>& as){for(int i:range(as.size()))is >>as[i];return is;}
//output
template<typename T> ostream& operator << (ostream& os, const set<T>& ss){for(auto a:ss){if(a!=ss.begin())os<<" "; os<<a;}return os;}
template<typename T1,typename T2> ostream& operator << (ostream& os, const pair<T1,T2>& p){return os<<p.first<<" "<<p.second;}
template<typename K,typename V> ostream& operator << (ostream& os, const map<K,V>& m){bool isF=true;for(auto& p:m){if(!isF)os<<endl;os<<p;isF=false;}return os;}
template<typename T1> ostream& operator << (ostream& os, const tuple<T1>& t){return os << get<0>(t);}
template<typename T1,typename T2> ostream& operator << (ostream& os, const tuple<T1,T2>& t){return os << get<0>(t)<<" "<<get<1>(t);}
template<typename T1,typename T2,typename T3> ostream& operator << (ostream& os, const tuple<T1,T2,T3>& t){return os << get<0>(t)<<" "<<get<1>(t)<<" "<<get<2>(t);}
template<typename T1,typename T2,typename T3,typename T4> ostream& operator << (ostream& os, const tuple<T1,T2,T3,T4>& t){return os << get<0>(t)<<" "<<get<1>(t)<<" "<<get<2>(t)<<" "<<get<3>(t);}
template<typename T> ostream& operator << (ostream& os, const vector<T>& as){for(int i:range(as.size())){if(i!=0)os<<" "; os<<as[i];}return os;}
template<typename T> ostream& operator << (ostream& os, const vector<vector<T>>& as){for(int i:range(as.size())){if(i!=0)os<<endl; os<<as[i];}return os;}

// values
template<typename T> inline T INF(){assert(false);};
template<> inline int INF<int>(){return 1<<28;};
template<> inline ll INF<ll>(){return 1LL<<60;};
template<> inline double INF<double>(){return 1e16;};
template<> inline long double INF<long double>(){return 1e16;};

template<class T> inline T EPS(){assert(false);};
template<> inline int EPS<int>(){return 1;};
template<> inline ll EPS<ll>(){return 1LL;};
template<> inline double EPS<double>(){return 1e-12;};
template<> inline long double EPS<long double>(){return 1e-12;};

// min{2^r | n < 2^r}
template<typename T> inline T upper_pow2(T n){ T res=1;while(res<n)res<<=1;return res;}
// max{d | 2^d  <= n}
template<typename T> inline T msb(T n){ int d=62;while((1LL<<d)>n)d--;return d;}

template<typename T,typename U> T pmod(T v,U M){return (v%M+M)%M;}

namespace Matrix{

	class Inconsistent{};//none
	class Ambiguous{};//many
	class NoSolution{};

	template <typename T> class Mat :public vector<vector<T>>{
		public:
		const int H,W;
		Mat(int H,int W):vector<vector<T>>(H,vector<T>(W)),H(H),W(W){
			for(int y:range(H))for(int x:range(W)) (*this)[y][x] = ve;
		}
		const T ve = 0.0;
		inline T vc(T a,T b){return a+b;}
		inline T vinv(T a){return -a;}
		const T vme = 1.0;
		inline T vmc(T a,T b){return a*b;}
		inline T vminv(T a){return 1/a;}
		inline T sig(T a,T b = 0){return a-b>EPS<T>()?+1:a-b<-EPS<T>()?-1:0;}

		const inline Mat e(){
			return vector<vector<T>>(H,vector<T>(W,ve));
		}
		inline Mat c(Mat a,Mat b){return a+b;}
		inline Mat<T> inv(Mat<T> a){return -a;}
		const inline Mat me(){
			static Mat A(H,W);
			for(int y:range(H))for(int x:range(W))A[y][x]= ve;
			for(int i:range(min(H,W)))A[i][i]= vme;
			return A;
		}
		inline Mat<T> mc(Mat<T> a,Mat<T> b){return a*b;}

		//O(n^2)
		Mat operator+(const Mat& r){
			const Mat& l=*this;
			Mat res(l.H,r.W);
			for(int y:range(l.H))for(int x:range(r.W)) res[y][x]= c(l[y][x],r[y][x]);
			return res;
		}

		//O(n^2)
		Mat operator-(){
			Mat res=*this;
			for(int y:range(res.H))for(int x:range(res.W)) res[y][x] = inv(res[y][x]);
			return res;
		}
		Mat operator-(const Mat& r){ return (*this) + (-r); }

		//O(n^3)
		Mat operator*(const Mat& r){
			const Mat& l=*this;
			Mat res(l.H,r.W);

			for(int y:range(l.H))for(int x:range(r.W))for(int k:range(r.H))
				res[y][x] = c(res[y][x], mc(l[y][k],r[k][x]));
			return res;
		}
		//O(n^2)
		vector<T> operator*(const vector<T>& r){
			const Mat& l=*this;
			vector<T> res(r.size());
			for(int y:range(l.H))for(int x:range(l.W))
				res[y] = c(res[y],mc(l[y][x],r[x]));
			return res;
		}

		// O(n^3*log(d))
		// Mat x must be n*n size
		//:TODO abstraction
		Mat pow(ll d){
			Mat x=*this,res=e();
			while(d!=0){
				if(d%2)res=res*x;
				x=x*x;
				d/=2;
			}
			return res;
		}

		//O(n^3)
		//Ax = b
		void gauss(vector<T>& b){
			Mat A=*this;
			int py =0,px = 0;
			while(py < H && px < W){
				for(int y=py+1;y<H;y++){ // pivot
					if(sig(abs(A[y][px]),abs(A[py][px])) > 0){
						swap(A[y],A[py]);swap(b[y],b[py]);
					}
				}
				if(sig(A[py][px]) != 0){
					T d = vminv(A[py][px]);
					for(int x=0;x<W;x++) A[py][x] = vmc(A[py][x],d);
					b[py] = vmc(b[py],d);
					for(int y=py+1;y<H;y++){
						T k = A[y][px];
						for(int x=0;x<W;x++) A[y][x] = vc(A[y][x],vinv(vmc(k,A[py][x])));
						b[y] = vc(b[y],vinv(vmc(k,b[py])));
					}
					py++;
				}
				px++;
			}
			for(int y=py;y<H;y++)if(sig(b[y]) != 0)throw NoSolution();
			if(py < W || px < W)throw Ambiguous();

			for(int x=W-1;x>=0;x--)for(int y=0;y<x;y++){
				b[y] = vc(b[y],vinv(vmc(b[x],A[y][x])));
			}
		}
	};
}
using namespace Matrix;

class Main{
	public:
	void run(){
		int n,m;cin >> n >> m;
		vector<ld> cs(n);
		for(int i:range(1,n-1)){
			ld v;cin >> v;cs[i] = v;
		}
		Mat<ld> mat(n,n);
		vector<ld> bs(n);
		for(int s:range(n-m-1)) mat[s][s] = 1;
		for(int s:range(n-m-1,n)){
			bs[s] = m*cs[s];
			mat[s][s] = m;
			if(s < n-1){
				for(int e:range(1,m+1)){
					if(s+e < n){
						mat[s][(s+e)] -= 1.0;
					}else{
						mat[s][n-1 - (s+e - (n-1))] -= 1.0;
					}
				}
			}
		}
		mat.gauss(bs);
		vector<vector<ld>> dp(n,vector<ld>(2,INF<ld>()));
		for(int i:rrange(n-m-1,n)){
			dp[i][0] = bs[i] - cs[i]; dp[i][1] = 0;
		}
		for(int i:rrange(0,n-m-1)){
			for(int x:range(2)){
				ld sum = 0;
				for(int d:range(1,m+1)) sum += (cs[i+d]+dp[i+d][x])/m;
				dp[i][x]  = min(dp[i][x],sum);
			}
			for(int d:range(1,m+1)) dp[i][1] = min(dp[i][1],cs[i+d]+dp[i+d][0]);
		}
		// cerr << dp << endl;
		cout << dp[0][1] << endl;
	}
};

int main(){
	cout <<fixed<<setprecision(20);
	cin.tie(0);
	ios::sync_with_stdio(false);
	Main().run();
	return 0;
}
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