結果

問題 No.463 魔法使いのすごろく🎲
ユーザー vjudge1
提出日時 2025-06-20 18:09:27
言語 C++11(廃止可能性あり)
(gcc 13.3.0)
結果
AC  
実行時間 3 ms / 2,000 ms
コード長 2,649 bytes
コンパイル時間 1,538 ms
コンパイル使用メモリ 159,772 KB
実行使用メモリ 7,844 KB
最終ジャッジ日時 2025-06-20 18:09:30
合計ジャッジ時間 2,941 ms
ジャッジサーバーID
(参考情報)
judge4 / judge3
このコードへのチャレンジ
(要ログイン)
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 <bits/stdc++.h>
using namespace std;

#define int long long

const int NN = 105;
const double eps = 1e-12;

int n, m;
double c[NN];
double cost[NN];
double g[NN], G[NN], M[NN];
double A[NN][NN], rhs[NN], h[NN];

inline int ne(int x, int k) 
{
    if (n == 1) return 1;
    if (n == 2) return ((x - 1 + k) & 1) + 1;
    int len = n - 1;
    int q = (x - 1 + k) % (2 * len);
    return (q < len) ? (q + 1) : (2 * len - q + 1);
}

void gauss(int N, double A[][NN], double b[], double x[]) 
{
    for (int i = 0; i < N; i ++ )
    {
        int piv = i;
        for (int r = i + 1; r < N; r ++ )
            if (fabs(A[r][i]) > fabs(A[piv][i])) piv = r;
        if (piv != i)
        {
            for (int c = i; c < N; c ++ ) swap(A[i][c], A[piv][c]);
            swap(b[i], b[piv]);
        }
        double div = A[i][i];
        for (int c = i; c < N; c ++ ) A[i][c] /= div;
        b[i] /= div;
        for (int r = 0; r < N; r ++ )
            if (r != i && fabs(A[r][i]) > 0)
            {
                double mul = A[r][i];
                for (int c = i; c < N; c ++ ) A[r][c] -= mul * A[i][c];
                b[r] -= mul * b[i];
            }
    }
    for (int i = 0; i < N; i ++ ) x[i] = b[i];
}

signed main() 
{
    cin >> n >> m;
    for (int i = 2; i < n; i ++ ) cin >> c[i];
    c[1] = c[n] = 0;
    for (int i = 1; i <= n; i ++ ) cost[i] = c[i];

    int N = n - 1;
    for (int i = 0; i < N; i ++ ) 
    {
        for (int j = 0; j < N; j ++ ) A[i][j] = 0;
        A[i][i] = 1;
        double SS = 0;
        int x = i + 1;
        for (int k = 1; k <= m; k ++ ) 
        {
            int y = ne(x, k);
            SS += cost[y] / m;
            if (y != n) A[i][y - 1] -= 1.0 / m;
        }
        rhs[i] = SS;
    }
    gauss(N, A, rhs, h);
    h[n - 1] = 0;

    for (int x = 1; x < n; x ++ ) 
    {
        double res = 1e18;
        for (int k = 1; k <= m; k ++ ) 
        {
            int y = ne(x, k);
            double v = cost[y] + (y == n ? 0 : h[y - 1]);
            res = min(res, v);
        }
        M[x] = res;
    }

    
    for (int x = 1; x <= n; x ++ ) g[x] = (x < n ? M[x] : 0);

    while (1) 
    {
        double diff = 0;
        for (int x = 1; x < n; x ++ ) 
        {
            double R = 0;
            for (int k = 1; k <= m; k ++ ) 
            {
                int y = ne(x, k);
                R += (cost[y] + g[y]) / m;
            }
            G[x] = min(R, M[x]);
            diff = max(diff, fabs(G[x] - g[x]));
        }
        for (int x = 1; x < n; x ++ ) g[x] = G[x];
        if (diff < eps) break;
    }

    cout << fixed << setprecision(10) << g[1];
    return 0;
}
0