結果

問題 No.187 中華風 (Hard)
コンテスト
ユーザー uwi
提出日時 2015-04-22 14:04:48
言語 Java
(openjdk 23)
結果
WA  
実行時間 -
コード長 7,348 bytes
記録
記録タグの例:
初AC ショートコード 純ショートコード 純主流ショートコード 最速実行時間
コンパイル時間 4,026 ms
コンパイル使用メモリ 89,028 KB
実行使用メモリ 41,444 KB
最終ジャッジ日時 2024-07-05 00:13:14
合計ジャッジ時間 9,575 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge1
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 * 20 WA * 5
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 Q448_2 {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	
	boolean hasContradiction(int[] x, int[] y)
	{
		int n = x.length;
		for(int i = 0;i < n;i++){
			for(int j = i+1;j < n;j++){
				int g = gcd(y[i], y[j]);
				if((x[i] - y[i]) % g != 0)return true;
			}
		}
		return false;
	}
	
	public static int gcd(int a, int b) {
		while (b > 0) {
			int c = a;
			a = b;
			b = c % b;
		}
		return a;
	}
	
	
	void solve()
	{
//		long[] v = garner(new int[]{49, 76, 65}, new int[]{99, 97, 95});
//		long u = v[2];
//		u = u * 97 + v[1];
//		u = u * 99 + v[0];
//		tr(u);
//		tr(u%99);
//		tr(u%97);
//		tr(u%95);
		int n = ni();
		int[] x = new int[n];
		int[] y = new int[n];
		for(int i = 0;i < n;i++){
			x[i] = ni();
			y[i] = ni();
		}
		if(hasContradiction(x, y)){
			out.println(-1);
			return;
		}
		
		int[] primes = sieveEratosthenes(100000);
		int[][][] fs = new int[n][][];
		for(int i = 0;i < n;i++){
			fs[i] = factor(y[i], primes);
		}
		int[] ps = new int[n];
		
		int[] vals = new int[9*n];
		int[] mods = new int[9*n];
		int q = 0;
		while(true){
			int minp = Integer.MAX_VALUE;
			int maxe = 0;
			int argmax = -1;
			for(int i = 0;i < n;i++){
				if(ps[i] < fs[i].length && fs[i][ps[i]][0] <= minp){
					if(fs[i][ps[i]][0] < minp){
						minp = fs[i][ps[i]][0];
						maxe = 0;
					}
					if(fs[i][ps[i]][1] > maxe){
						maxe = fs[i][ps[i]][1];
						argmax = i;
					}
				}
			}
			if(minp == Integer.MAX_VALUE)break;
			
			mods[q] = (int)Math.pow(fs[argmax][ps[argmax]][0], fs[argmax][ps[argmax]][1]);
			vals[q] = x[argmax] % mods[q];
			q++;
			for(int i = 0;i < n;i++){
				if(ps[i] < fs[i].length && fs[i][ps[i]][0] == minp){
					ps[i]++;
				}
			}
		}
//		tr(vals);
//		tr(mods);
		long[] gs = garner(Arrays.copyOf(vals, q), Arrays.copyOf(mods, q));
//		tr(gs);
		long ret = 0;
		boolean zero = true;
		for(int i = gs.length-1;i >= 0;i--){
			ret = ret * mods[i] + gs[i];
			if(gs[i] > 0)zero = false;
			ret %= 1000000007;
		}
		if(zero){
			ret = 1;
			for(int i = 0;i < q;i++){
				ret = ret * mods[i] % 1000000007;
			}
		}
		out.println(ret);
	}
	
	public static long[] garner(int[] u, int[] m)
	{
		int n = u.length;
		assert n == m.length;
		if(n == 0)return new long[0];
		long[] gamma = new long[n];
		for(int k = 1;k < n;k++){
			long prod = 1;
			for(int i = 0;i < k;i++){
				prod = prod * m[i] % m[k];
			}
			gamma[k] = invl(prod, m[k]);
		}
		
		long[] v = new long[n];
		v[0] = u[0];
		for(int k = 1;k < n;k++){
			long temp = v[k-1];
			for(int j = k-2;j >= 0;j--){
				temp = (temp * m[j] + v[j]) % m[k];
			}
			v[k] = (u[k] - temp) * gamma[k] % m[k];
			if(v[k] < 0)v[k] += m[k];
		}
		return v;
	}
	
	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 int[][] factor(int n, int[] primes)
	{
		int[][] ret = new int[9][2];
		int rp = 0;
		for(int p : primes){
			if(p * p > n)break;
			int i;
			for(i = 0;n % p == 0;n /= p, i++);
			if(i > 0){
				ret[rp][0] = p;
				ret[rp][1] = i;
				rp++;
			}
		}
		if(n != 1){
			ret[rp][0] = n;
			ret[rp][1] = 1;
			rp++;
		}
		return Arrays.copyOf(ret, rp);
	}
	
	public static int[] sieveEratosthenes(int n) {
		if (n <= 32) {
			int[] primes = { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31 };
			for (int i = 0; i < primes.length; i++) {
				if (n < primes[i]) {
					return Arrays.copyOf(primes, i);
				}
			}
			return primes;
		}

		int u = n + 32;
		double lu = Math.log(u);
		int[] ret = new int[(int) (u / lu + u / lu / lu * 1.5)];
		ret[0] = 2;
		int pos = 1;

		int[] isnp = new int[(n + 1) / 32 / 2 + 1];
		int sup = (n + 1) / 32 / 2 + 1;

		int[] tprimes = { 3, 5, 7, 11, 13, 17, 19, 23, 29, 31 };
		for (int tp : tprimes) {
			ret[pos++] = tp;
			int[] ptn = new int[tp];
			for (int i = (tp - 3) / 2; i < tp << 5; i += tp)
				ptn[i >> 5] |= 1 << (i & 31);
			for (int j = 0; j < sup; j += tp) {
				for (int i = 0; i < tp && i + j < sup; i++) {
					isnp[j + i] |= ptn[i];
				}
			}
		}

		// 3,5,7
		// 2x+3=n
		int[] magic = { 0, 1, 23, 2, 29, 24, 19, 3, 30, 27, 25, 11, 20, 8, 4,
				13, 31, 22, 28, 18, 26, 10, 7, 12, 21, 17, 9, 6, 16, 5, 15, 14 };
		int h = n / 2;
		for (int i = 0; i < sup; i++) {
			for (int j = ~isnp[i]; j != 0; j &= j - 1) {
				int pp = i << 5 | magic[(j & -j) * 0x076be629 >>> 27];
				int p = 2 * pp + 3;
				if (p > n)
					break;
				ret[pos++] = p;
				if ((long) p * p > n)
					continue;
				for (int q = (p * p - 3) / 2; q <= h; q += p)
					isnp[q >> 5] |= 1 << q;
			}
		}

		return Arrays.copyOf(ret, pos);
	}
	
	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");
	}
	
	public static void main(String[] args) throws Exception { new Q448_2().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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