結果

問題 No.42 貯金箱の溜息
ユーザー uwiuwi
提出日時 2015-04-04 14:33:31
言語 Java21
(openjdk 21)
結果
AC  
実行時間 1,439 ms / 5,000 ms
コード長 6,439 bytes
コンパイル時間 4,363 ms
コンパイル使用メモリ 82,576 KB
実行使用メモリ 53,972 KB
最終ジャッジ日時 2024-07-04 01:49:28
合計ジャッジ時間 7,977 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge3
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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 553 ms
53,880 KB
testcase_01 AC 1,439 ms
53,852 KB
testcase_02 AC 1,363 ms
53,972 KB
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 # 

package q0xx;

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 Q22 {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	
	void solve()
	{
		final int[] len = {1, 2, 10, 20, 100};
		int[] offset = new int[6];
		for(int i = 1;i <= 5;i++){
			offset[i] = offset[i-1] + len[i-1];
		}
		int n = offset[5];
		int[][] M = new int[n+1][n+1];
		for(int i = 0;i < 5;i++){
			for(int j = 1;j < len[i];j++){
				M[offset[i]+j][offset[i]+j-1] = 1;
			}
			M[offset[i]][offset[i]+len[i]-1] = 1;
			if(i < 4)M[offset[i+1]][offset[i]] = 1;
		}
		M[offset[5]][offset[4]] = 1;
		M[n][n] = 1;
		
		int[][][] Ms = new int[61][][];
		Ms[0] = M;
		for(int i = 1;i <= 60;i++){
			Ms[i] = p2(Ms[i-1]);
		}
		int[][][] nz = new int[61][][];
		for(int i = 0;i <= 60;i++){
			int p = 0;
			for(int j = 0;j <= n;j++){
				for(int k = 0;k <= n;k++){
					if(Ms[i][j][k] != 0){
						p++;
					}
				}
			}
			nz[i] = new int[p][];
			p = 0;
			for(int j = 0;j <= n;j++){
				for(int k = 0;k <= n;k++){
					if(Ms[i][j][k] != 0){
						nz[i][p++] = new int[]{j, k, Ms[i][j][k]};
					}
				}
			}
		}
		
		for(int T = ni();T >= 1;T--){
			long m = nl()/5;
			int[] v = new int[n+1];
			v[0] = 1;
			m += 5;
			for(int j = 0;m > 0;m>>>=1,j++){
				if((m&1) == 1){
					v = mulsparse(nz[j], v);
				}
			}
			out.println(v[n]);
		}
	}
	
	///////// begin
	public static final int mod = 1000000009;
	public static final long m2 = (long)mod*mod;
	public static final long BIG = 8L*m2;
	
	// A^e*v
	public static int[] pow(int[][] A, int[] v, long e)
	{
		for(int i = 0;i < v.length;i++){
			if(v[i] >= mod)v[i] %= mod;
		}
		int[][] MUL = A;
		for(;e > 0;e>>>=1) {
			if((e&1)==1)v = mul(MUL, v);
			MUL = p2(MUL);
		}
		return v;
	}
	
	// int matrix*int vector
	public static int[] mul(int[][] A, int[] v)
	{
		int m = A.length;
		int n = v.length;
		int[] w = new int[m];
		for(int i = 0;i < m;i++){
			long sum = 0;
			for(int k = 0;k < n;k++){
				sum += (long)A[i][k] * v[k];
				if(sum >= BIG)sum -= BIG;
			}
			w[i] = (int)(sum % mod);
		}
		return w;
	}
	
	public static int[] mulsparse(int[][] A, int[] v)
	{
		int m = A.length;
		int[] w = new int[m];
		long sum = 0;
		for(int i = 0;i < A.length;i++){
			sum += (long)A[i][2] * v[A[i][1]];
			if(sum >= BIG)sum -= BIG;
			if(i+1 == A.length || A[i][0] != A[i+1][0]){
				w[A[i][0]] = (int)(sum % mod);
				sum = 0;
			}
		}
		return w;
	}
	
	// int matrix^2 (be careful about negative value)
	public static int[][] p2(int[][] A)
	{
		int n = A.length;
		int[][] C = new int[n][n];
		for(int i = 0;i < n;i++){
			long[] sum = new long[n];
			for(int k = 0;k < n;k++){
				for(int j = 0;j < n;j++){
					sum[j] += (long)A[i][k] * A[k][j];
					if(sum[j] >= BIG)sum[j] -= BIG;
				}
			}
			for(int j = 0;j < n;j++){
				C[i][j] = (int)(sum[j] % mod);
			}
		}
		return C;
	}
	
	//////////// end
	
	// A^e
	// O(N^3log N)
	public static int[][] pow(int[][] A, long e)
	{
		int[][] MUL = A;
		int n = A.length;
		int[][] C = new int[n][n];
		for(int i = 0;i < n;i++)C[i][i] = 1;
		for(;e > 0;e>>>=1) {
			if((e&1)==1)C = mul(C, MUL);
			MUL = p2(MUL);
		}
		return C;
	}
	
	public static int[][] mul(int[][] A, int[][] B)
	{
		int m = A.length;
		int n = A[0].length;
		int o = B[0].length;
		int[][] C = new int[m][o];
		for(int i = 0;i < m;i++){
			long[] sum = new long[n];
			for(int k = 0;k < n;k++){
				for(int j = 0;j < n;j++){
					sum[j] += (long)A[i][k] * B[k][j];
					if(sum[j] >= BIG)sum[j] -= BIG;
				}
			}
			for(int j = 0;j < n;j++){
				C[i][j] = (int)(sum[j] % mod);
			}
		}
		return C;
	}
	
	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 Q22().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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