結果

問題 No.301 サイコロで確率問題 (1)
ユーザー uwiuwi
提出日時 2015-11-13 22:59:16
言語 Java21
(openjdk 21)
結果
AC  
実行時間 456 ms / 1,000 ms
コード長 4,725 bytes
コンパイル時間 4,222 ms
コンパイル使用メモリ 92,696 KB
実行使用メモリ 58,772 KB
最終ジャッジ日時 2024-09-13 15:01:51
合計ジャッジ時間 5,966 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge4
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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 373 ms
58,424 KB
testcase_01 AC 456 ms
58,772 KB
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ソースコード

diff # 

package contest;

import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;

public class Q189 {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	
	void solve()
	{
		double[][] M = new double[12][12];
		for(int i = 0;i < 6;i++){
			M[i][5] = 1./6;
			M[i+6][5+6] = 1./6;
			M[i+6][5] = 1./6;
		}
		for(int i = 0;i < 5;i++){
			M[i+1][i] = 1;
			M[i+1+6][i+6] = 1;
		}
		
		double[][][] p2 = generateP2(M, 61);
		
		double[] v = new double[12];
		v[5] = 1;
		for(int T = ni();T > 0;T--){
			long n = nl();
			double[] w = pow(p2, v, n);
			double p = w[5];
			double elast = w[11];
			double eloop = w[6]+w[7]+w[8]+w[9]+w[10];
			out.printf("%.14f\n", eloop/p + elast/p);
		}
	}
	
	public static double[][][] generateP2(double[][] A, int n)
	{
		double[][][] ret = new double[n+1][][];
		ret[0] = A;
		for(int i = 1;i <= n;i++)ret[i] = p2(ret[i-1]);
		return ret;
	}
	
	// A[0]^e*v
	// A[n]=A[0]^(2^n)
	public static double[] pow(double[][][] A, double[] v, long e)
	{
		for(int i = 0;e > 0;e>>>=1,i++) {
			if((e&1)==1)v = mul(A[i], v);
		}
		return v;
	}

	
	// double行列*ベクトル
	public static double[] mul(double[][] A, double[] v)
	{
		int m = A.length;
		int n = v.length;
		double[] w = new double[m];
		for(int i = 0;i < m;i++){
			double sum = 0;
			for(int k = 0;k < n;k++){
				sum += A[i][k] * v[k];
			}
			w[i] = sum;
		}
		return w;
	}
	
	// double行列の2乗
	public static double[][] p2(double[][] A)
	{
		int n = A.length;
		double[][] C = new double[n][n];
		for(int i = 0;i < n;i++){
			for(int k = 0;k < n;k++){
				for(int j = 0;j < n;j++){
					C[i][j] += A[i][k] * A[k][j];
				}
			}
		}
		return C;
	}
	
	// A^e*v
	public static double[] pow(double[][] A, double[] v, long m)
	{
		double[][] mu = A;
		double[] r = v;
		for(;m > 0;m>>>=1){
			if((m&1)==1)r = mul(mu, r);
			mu = p2(mu);
		}
		return r;
	}

	
	void run() throws Exception
	{
//		int n = 10000, m = 99999;
//		Random gen = new Random();
//		StringBuilder sb = new StringBuilder();
//		sb.append(n + " ");
//		for (int i = 0; i < n; i++) {
//			sb.append(Math.abs(gen.nextLong() % 1000000000000000000L) + " ");
//		}
//		INPUT = sb.toString();
		
		is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		long s = System.currentTimeMillis();
		solve();
		out.flush();
		if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");
	}
	
	public static void main(String[] args) throws Exception { new Q189().run(); }
	
	private byte[] inbuf = new byte[1024];
	private int lenbuf = 0, ptrbuf = 0;
	
	private int readByte()
	{
		if(lenbuf == -1)throw new InputMismatchException();
		if(ptrbuf >= lenbuf){
			ptrbuf = 0;
			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
			if(lenbuf <= 0)return -1;
		}
		return inbuf[ptrbuf++];
	}
	
	private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
	private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private double nd() { return Double.parseDouble(ns()); }
	private char nc() { return (char)skip(); }
	
	private String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private char[] ns(int n)
	{
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while(p < n && !(isSpaceChar(b))){
			buf[p++] = (char)b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}
	
	private char[][] nm(int n, int m)
	{
		char[][] map = new char[n][];
		for(int i = 0;i < n;i++)map[i] = ns(m);
		return map;
	}
	
	private int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	
	private int ni()
	{
		int num = 0, b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private long nl()
	{
		long num = 0;
		int b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private static void tr(Object... o) { System.out.println(Arrays.deepToString(o)); }
}
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