#190944 (C++11) No.75 回数の期待値の問題

提出ソース

結果

問題	No.75 回数の期待値の問題
ユーザー	kopricky
提出日時	2017-07-23 17:56:48
言語	C++11 (gcc 11.4.0)
結果	WA
実行時間	-
コード長	8,600 bytes
コンパイル時間	1,490 ms
コンパイル使用メモリ	166,960 KB
実行使用メモリ	6,824 KB
最終ジャッジ日時	2024-10-09 11:01:52
合計ジャッジ時間	2,264 ms
ジャッジサーバーID （参考情報）	judge1 / judge4

このコードへのチャレンジ
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テストケース

テストケース表示

入力	結果	実行時間実行使用メモリ
testcase_00	AC	2 ms 6,816 KB
testcase_01	AC	2 ms 6,816 KB
testcase_02	AC	1 ms 6,820 KB
testcase_03	AC	2 ms 6,816 KB
testcase_04	AC	1 ms 6,816 KB
testcase_05	AC	2 ms 6,816 KB
testcase_06	AC	2 ms 6,816 KB
testcase_07	WA	-
testcase_08	WA	-
testcase_09	WA	-
testcase_10	WA	-
testcase_11	WA	-
testcase_12	WA	-
testcase_13	WA	-
testcase_14	WA	-
testcase_15	WA	-
testcase_16	WA	-
testcase_17	WA	-
testcase_18	WA	-
testcase_19	WA	-

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ソースコード

raw source code

#include <bits/stdc++.h>
#define ll long long
#define INF 1000000005
#define MOD 1000000007
#define EPS 1e-10
#define rep(i,n) for(int i=0;i<(int)n;++i)
#define each(a, b) for(auto (a): (b))
#define all(v) (v).begin(),(v).end()
#define fi first
#define se second
#define pb push_back
#define show(x) cout <<#x<<" = "<<(x)<<endl
#define spair(p) cout <<#p<<": "<<p.fi<<" "<<p.se<<endl
#define svec(v) cout<<#v<<":";rep(kbrni,v.size())cout<<" "<<v[kbrni];cout<<endl
#define sset(s) cout<<#s<<":";each(kbrni,s)cout <<" "<<kbrni;cout<<endl

using namespace std;

typedef pair<int,int>P;

const int MAX_N = 100005;

template<typename T> class mat : public vector<vector<T> > {
private:
    int r,c;    //行,列
    int mat_rank;
    T mat_det;
public:
    int row() const {
        return r;
    }
    int column() const {
        return c;
    }
    mat(int n,int m,T val = 0){
        mat_rank = INF,mat_det = INF;
        this->r = n,this->c = m;
        rep(i,n){
            this->push_back(vector<T>(m,val));
        }
    }
    mat operator+(const mat& another){
        if(this->r != another.r && this->c != another.c){
            cout << "足し算失敗(サイズ不一致)" << endl;
            exit(1);
        }
        mat<T> X(this->r,this->c);
        rep(i,this->r){
            rep(j,this->c){
                X[i][j] = (*this)[i][j] + another[i][j];
            }
        }
        return X;
    }
    mat operator+(const T val){
        mat<T> X(this->r,this->c);
        rep(i,this->r){
            rep(j,this->c){
                X[i][j] = (*this)[i][j] + val;
            }
        }
        return X;
    }
    mat operator-(const mat& another){
        if(this->r != another.r && this->c != another.c){
            cout << "引き算失敗(サイズ不一致)" << endl;
            exit(1);
        }
        mat<T> X(this->r,this->c);
        rep(i,this->r){
            rep(j,this->c){
                X[i][j] = (*this)[i][j] - another[i][j];
            }
        }
        return X;
    }
    mat operator-(const T val){
        mat<T> X(this->r,this->c);
        rep(i,this->r){
            rep(j,this->c){
                X[i][j] = (*this)[i][j] - val;
            }
        }
        return X;
    }
    vector<T> operator*(const vector<T>& another){
        if(this->c != another.size()){
            cout << "掛け算失敗(サイズ不一致)" << endl;
            exit(1);
        }
        vector<T> vec(this->r,0);
        rep(i,this->r){
            rep(j,this->c){
                vec[i] += (*this)[i][j] * another[j];
            }
        }
        return vec;
    }
    mat operator*(const mat& another){
        if(this->c != another.r){
            cout << "掛け算失敗(サイズ不一致)" << endl;
            exit(1);
        }
        mat<T> X(this->r,another.c);
        rep(i,this->r){
            rep(k,this->c){
                rep(j,another.c){
                    X[i][j] += (*this)[i][k]*another[k][j];
                }
            }
        }
        return X;
    }
    mat operator-(){
        mat<T> X(this->r,this->c);
        rep(i,this->r){
            rep(j,this->c){
                X[i][j] = -(*this)[i][j];
            }
        }
        return X;
    }
    int rank(){
        if(this->mat_rank <= min(this->r,this->c)){
            return this->mat_rank;
        }
        int n = this->r;
        T D = 1;
        mat B(n,n);
        rep(i,n){
            rep(j,n){
                B[i][j] = (*this)[i][j];
            }
        }
        rep(i,n){
            int pivot = i;
            for(int j=i;j<n;j++){
                if(abs(B[j][i]) > abs(B[pivot][i])){
                    pivot = j;
                }
            }
            if(abs(B[pivot][i]) < EPS){
                this->mat_rank = i;
                this->mat_det = 0;
                return i;
            }
            swap(B[i],B[pivot]);
            D *= B[i][i];
            for(int j=i+1;j<n;j++){
                B[i][j] /= B[i][i];
            }
            for(int j=i+1;j<n;j++){
                for(int k=i+1;k<n;k++){
                    B[j][k] -= B[j][i] * B[i][k];
                }
            }
        }
        this->mat_rank = n;
        this->mat_det = D;
        return n;
    }
    T det(){
        if(this->r != this->c){
            cout << "正方行列でない(行列式定義不可)" << endl;
            exit(1);
        }
        if(this->mat_rank <= this->r){
            return this->mat_det;
        }
        int res = rank();
        return this->mat_det;
    }
    mat inverse(){
        if(this->r != this->c){
            cout << "正方行列でない(逆行列定義不可)" << endl;
            exit(1);
        }
        if(this->mat_rank < this->r){
            cout << "ランク落ち(逆行列が存在しない)" << endl;
            exit(1);
        }
        int n = this->r;
        T D = 1;
        mat B(n,2*n);
        rep(i,n){
            rep(j,n){
                B[i][j] = (*this)[i][j];
            }
        }
        rep(i,n){
            B[i][n+i] = 1;
        }
        rep(i,n){
            int pivot = i;
            for(int j=i;j<n;j++){
                if(abs(B[j][i]) > abs(B[pivot][i])){
                    pivot = j;
                }
            }
            if(abs(B[pivot][i]) < EPS){
                cout << "解なしor不定" << endl;
                exit(1);
            }
            swap(B[i],B[pivot]);
            D *= B[i][i];
            for(int j=i+1;j<=2*n;j++){
                B[i][j] /= B[i][i];
            }
            rep(j,n){
                if(i != j){
                    for(int k=i+1;k<=2*n;k++){
                        B[j][k] -= B[j][i] * B[i][k];
                    }
                }
            }
        }
        this->mat_rank = n;
        this->mat_det = D;
        mat res(n,n);
        rep(i,n){
            rep(j,n){
                res[i][j] = B[i][n+j];
            }
        }
        return res;
    }
    void print(){
        rep(i,this->r){
            rep(j,(this->c)-1){
                cout << (*this)[i][j] << ",";
            }
            cout << (*this)[i][(this->c)-1] << endl;
        }
    }
};

template<typename T> vector<T> eq_solve(const mat<T>& A,const vector<T>& b){
    if(A.row() != A.column()){
        cout << "正方行列でない(解なしor不定)" << endl;
        exit(1);
    }
    int n = A.row();
    mat<T> B(n,n+1);
    rep(i,n){
        rep(j,n){
            B[i][j] = A[i][j];
        }
    }
    rep(i,n){
        B[i][n] = b[i];
    }
    rep(i,n){
        int pivot = i;
        for(int j=i;j<n;j++){
            if(abs(B[j][i]) > abs(B[pivot][i])){
                pivot = j;
            }
        }
        if(abs(B[pivot][i]) < EPS){
            cout << "解なしor不定" << endl;
            exit(1);
        }
        swap(B[i],B[pivot]);
        for(int j=i+1;j<=n;j++){
            B[i][j] /= B[i][i];
        }
        rep(j,n){
            if(i != j){
                for(int k=i+1;k<=n;k++){
                    B[j][k] -= B[j][i] * B[i][k];
                }
            }
        }
    }
    vector<T> res(n);
    rep(i,n){
        res[i] = B[i][n];
    }
    return res;
}

template<typename T> mat<T> pow(mat<T> A,ll cnt)
{
    if(A.row() != A.column()){
        cout << "累乗不可" << endl;
    }
    int n = A.row();
	mat<T> B(n,n);
	rep(i,n){
		B[i][i] = 1;
	}
	while(cnt>0){
		if(cnt & 1){
			B = B*A;
		}
		A = A*A;
		cnt >>= 1;
	}
	return B;
}

template<typename T> mat<T> mod_mul(mat<T>& A,mat<T>& B,ll mod)
{
    if(A.column() != B.row()){
        cout << "掛け算失敗(サイズ不一致)" << endl;
        exit(1);
    }
    mat<T> X(A.row(),B.column());
    rep(i,A.row()){
        rep(k,A.column()){
            rep(j,B.column()){
                X[i][j] = (X[i][j] + A[i][k]*B[k][j]) % mod;
            }
        }
    }
    return X;
}

template<typename T> mat<T> pow(mat<T> A,ll cnt,ll mod)
{
    if(A.row() != A.column()){
        cout << "累乗不可" << endl;
    }
    int n = A.row();
	mat<T> B(n,n);
	rep(i,n){
		B[i][i] = 1;
	}
	while(cnt>0){
		if(cnt & 1){
			B = mod_mul(B,A,mod);
		}
		A = mod_mul(A,A,mod);
		cnt >>= 1;
	}
	return B;
}

int main()
{
    int K;
    cin >> K;
    mat<double> ex(K+1,K+1);
    rep(i,K){
        ex[i][i] += 1;
        for(int j=1;i+j<=K;j++){
            ex[i][i+j] -= 1 / 6.0;
        }
    }
    for(int i=max(K-5,0);i<K;i++){
        ex[i][0] -= (6-K+i) / 6.0;
    }
    ex[K][K] += 1;
    vector<double> b(K+1,1);
    b[K] = 0;
    vector<double> res = eq_solve(ex,b);
    printf("%.10f\n",res[0]);
    return 0;
}

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結果

テストケース

ソースコード