結果

問題 No.42 貯金箱の溜息
コンテスト
ユーザー uwi
提出日時 2014-10-28 19:31:09
言語 Java
(openjdk 23)
結果
AC  
実行時間 183 ms / 5,000 ms
コード長 5,322 bytes
コンパイル時間 3,522 ms
コンパイル使用メモリ 81,108 KB
実行使用メモリ 40,772 KB
最終ジャッジ日時 2024-12-30 14:07:13
合計ジャッジ時間 4,755 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge4
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
other AC * 3
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 #
raw source code 

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 Main {
	static InputStream is;
	static PrintWriter out;
	static String INPUT = "";
	
	static int mod = 1000000009;
	
	static void solve()
	{
		int u = 10005;
		long[][] f = new long[6][u];
		Arrays.fill(f[0], 1);
		int[] Q = {1, 5, 10, 50, 100, 500};
		
		for(int k = 1;k < 6;k++){
			for(int i = 0;i < u;i++){
				f[k][i] = f[k-1][i];
				if(i-Q[k] >= 0)f[k][i] += f[k][i-Q[k]];
				if(f[k][i] >= mod)f[k][i] -= mod;
			}
		}
		long[][] co = new long[500][];
		for(int k = 0;k < 500;k++){
			long[][] xv = new long[10][];
			for(int i = 0;i < 10;i++){
				xv[i] = new long[]{k+i*500, f[5][k+i*500]};
			}
			co[k] = guess(1000000009, xv);
		}
		
		for(int T = ni();T >= 1;T--){
			long n = nl();
			out.println(apply(co[(int)(n%500)], n, mod));
		}
	}
	
	public static long apply(long[] co, long x, long mod)
	{
		x %= mod;
		long ret = 0;
		for(int i = co.length-1;i >= 0;i--){
			ret = (ret * x + co[i]) % mod;
		}
		return ret;
	}
	
	public static long invl(long a, long mod) {
		long b = mod;
		long p = 1, q = 0;
		while (b > 0) {
			long c = a / b;
			long d;
			d = a;
			a = b;
			b = d % b;
			d = p;
			p = q;
			q = d - c * q;
		}
		return p < 0 ? p + mod : p;
	}
	
	public static long[] guess(long mod, long[][] co)
	{
		int n = co.length;
		long[] dp = new long[n+1];
		dp[0] = 1;
		// (x-x0)(x-x1)...(x-x{n-1})
		for(int i = 0;i < n;i++){
			for(int j = i;j >= 0;j--){
				dp[j+1] += dp[j];
				if(dp[j+1] >= mod)dp[j+1] -= mod;
				dp[j] = dp[j]*-co[i][0]%mod;
				if(dp[j]<0)dp[j] += mod;
			}
		}
		
		long[] ret = new long[n];
		for(int i = 0;i < n;i++){
			long den = 1;
			for(int j = 0;j < n;j++){
				if(i != j){
					den *= co[i][0]-co[j][0];
					den %= mod;
				}
			}
			if(den < 0)den += mod;
			long iden = invl(den, mod);
			iden = iden*co[i][1]%mod;
			
			long minus = 0;
			for(int j = n-1;j >= 0;j--){
				minus = (dp[j+1] + minus * co[i][0]) % mod;
				ret[j] = (ret[j] + minus*iden) % mod;
			}
		}
		return ret;
	}

	
	public static void main(String[] args) throws Exception
	{
		long S = System.currentTimeMillis();
		is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		solve();
		out.flush();
		long G = System.currentTimeMillis();
		tr(G-S+"ms");
	}
	
	private static boolean eof()
	{
		if(lenbuf == -1)return true;
		int lptr = ptrbuf;
		while(lptr < lenbuf)if(!isSpaceChar(inbuf[lptr++]))return false;
		
		try {
			is.mark(1000);
			while(true){
				int b = is.read();
				if(b == -1){
					is.reset();
					return true;
				}else if(!isSpaceChar(b)){
					is.reset();
					return false;
				}
			}
		} catch (IOException e) {
			return true;
		}
	}
	
	private static byte[] inbuf = new byte[1024];
	static int lenbuf = 0, ptrbuf = 0;
	
	private static 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 static boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
	private static int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private static double nd() { return Double.parseDouble(ns()); }
	private static char nc() { return (char)skip(); }
	
	private static 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 static 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 static 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 static int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	
	private static 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 static 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) { if(INPUT.length() != 0)System.out.println(Arrays.deepToString(o)); }
}
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