結果

問題 No.42 貯金箱の溜息
ユーザー uwiuwi
提出日時 2017-06-01 02:43:42
言語 Java21
(openjdk 21)
結果
AC  
実行時間 139 ms / 5,000 ms
コード長 4,883 bytes
コンパイル時間 5,020 ms
コンパイル使用メモリ 88,064 KB
実行使用メモリ 41,372 KB
最終ジャッジ日時 2023-10-21 19:10:00
合計ジャッジ時間 6,052 ms
ジャッジサーバーID
（参考情報） 		judge11 / judge10
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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 128 ms
40,580 KB
testcase_01 AC 136 ms
41,372 KB
testcase_02 AC 139 ms
41,216 KB
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ソースコード

diff # 

package no0xx;
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 No42 {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	
	void solve()
	{
		int mod = 1000000009;
		int[] C = {1, 5, 10, 50, 100, 500};
		int Z = 3500;
		long[][] dp = new long[6][Z];
		Arrays.fill(dp[0], 1L);
		for(int i = 1;i < 6;i++){
			for(int j = 0;j < Z;j++){
				dp[i][j] = dp[i-1][j];
				if(j-C[i] >= 0)dp[i][j] += dp[i][j-C[i]];
				if(dp[i][j] >= mod)dp[i][j] -= mod;
			}
		}
		
		int[][] fif = enumFIF(Z/500, mod);
		for(int T = ni();T > 0;T--){
			long X = nl();
			long[] ys = new long[6];
			for(int i = 0;i < 6;i++){
				ys[i] = dp[5][(int)(X%500)+i*500];
			}
			long val = guessDirectly2(mod, X/500, fif, ys);
			out.println(val);
		}
	}
	
	public static int[][] enumFIF(int n, int mod) {
		int[] f = new int[n + 1];
		int[] invf = new int[n + 1];
		f[0] = 1;
		for (int i = 1; i <= n; i++) {
			f[i] = (int) ((long) f[i - 1] * i % mod);
		}
		long a = f[n];
		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;
		}
		invf[n] = (int) (p < 0 ? p + mod : p);
		for (int i = n - 1; i >= 0; i--) {
			invf[i] = (int) ((long) invf[i + 1] * (i + 1) % mod);
		}
		return new int[][] { f, invf };
	}

	
	public static long guessDirectly2(long mod, long x, int[][] fif, long... y)
	{
		int n = y.length;
		if(0 <= x && x < n){
			return y[(int)x];
		}else{
			x %= mod;
			long s = 0;
			long sig = 1;
			long big = 8L*mod*mod;
			long[] left = new long[n+1];
			long[] right = new long[n+1];
			left[0] = 1;
			for(int i = 0;i < n;i++){
				left[i+1] = left[i] * (x-i) % mod;
			}
			right[n] = 1;
			for(int i = n-1;i >= 0;i--){
				right[i] = right[i+1] * (x-i) % mod;
			}
			
			for(int i = n-1;i >= 0;i--){
				s += left[i] * right[i+1] % mod * fif[1][i] % mod * fif[1][n-1-i] % mod * y[i] * sig;
				if(s >= big)s -= big;
				if(s <= -big)s += big;
				sig = -sig;
			}
			s %= mod;
			if(s < 0)s += mod;
			return s;
		}
	}
	
	void run() throws Exception
	{
		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");
//		Thread t = new Thread(null, null, "~", Runtime.getRuntime().maxMemory()){
//			@Override
//			public void run() {
//				long s = System.currentTimeMillis();
//				solve();
//				out.flush();
//				if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");
//			}
//		};
//		t.start();
//		t.join();
	}
	
	public static void main(String[] args) throws Exception { new No42().run(); }
	
	private byte[] inbuf = new byte[1024];
	public 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 int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	
	private long[] nal(int n)
	{
		long[] a = new long[n];
		for(int i = 0;i < n;i++)a[i] = nl();
		return a;
	}
	
	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[][] nmi(int n, int m) {
		int[][] map = new int[n][];
		for(int i = 0;i < n;i++)map[i] = na(m);
		return map;
	}
	
	private int ni() { return (int)nl(); }
	
	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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