結果

問題 No.551 夏休みの思い出（２）
コンテスト
ユーザー 37zigen
提出日時 2017-07-29 01:16:59
言語 Java
(openjdk 23)
結果
AC  
実行時間 908 ms / 4,000 ms
コード長 4,275 bytes
コンパイル時間 2,652 ms
コンパイル使用メモリ 81,844 KB
実行使用メモリ 51,176 KB
最終ジャッジ日時 2024-10-10 18:21:03
合計ジャッジ時間 25,596 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge3
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
sample AC * 2
other AC * 47
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 # 

import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		new Main().run();
	}

	static long time = 0;

	public void run() {
		Scanner sc = new Scanner(System.in);
		int P = sc.nextInt();
		int R = sc.nextInt();
		int N = sc.nextInt();
		long[] A = new long[N];
		long[] B = new long[N];
		long[] C = new long[N];
		PrintWriter pw = new PrintWriter(System.out);
		long inv2 = inv(2, P);
		for (int i = 0; i < N; ++i) {
			A[i] = sc.nextInt();
			B[i] = sc.nextInt();
			C[i] = sc.nextInt();
			long invA = inv(A[i], P);
			B[i] = invA * B[i] % P;
			C[i] = invA * C[i] % P;
			A[i] = 1;
			long v = B[i] * B[i] - 4 * C[i];
			v %= P;
			while (v < 0)
				v += P;
			if (v == 0 || pow(v, (P - 1) / 2, P) == 1) {
				v = calc(v, P);
				long[] ans = { inv2 * (-B[i] + v), inv2 * (-B[i] + P - v) };
				for (int j = 0; j < ans.length; ++j) {
					ans[j] %= P;
					while (ans[j] < 0)
						ans[j] += P;
				}
				if (ans[0] > ans[1]) {
					long tmp = ans[0];
					ans[0] = ans[1];
					ans[1] = tmp;
				}
				if (ans[0] == ans[1]) {
					pw.println(ans[0]);
				} else {
					pw.println(ans[0] + " " + ans[1]);
				}
			} else {
				pw.println(-1);
			}
		}
		pw.close();
	}

	// x^2=aとなるxを探す

	static long calc(long a, long mod) {
		for (int b = 0; b < 100; ++b) {
			Poly p1 = new Poly(mod);
			Poly p2 = new Poly(mod);// (x-b)^2-a=0 mod p
			p2.add(2, 1);
			p2.add(1, -2 * b);
			p2.add(0, b * b - a);
			p1.add(1, 1);
			p1 = p1.pow((mod - 1) / 2, p2);
			p1.add(0, -1);
			Poly gcd = p1.gcd(p2);
			if (gcd.deg() == 1) {
				long ans = (-b - inv(gcd.val[1], mod) * gcd.val[0]) % mod;
				while (ans < 0)
					ans += mod;
				return ans;
			}
		}
		throw new AssertionError();
	}

	static class Poly {
		long[] val = new long[3];
		long mod;

		public Poly(long mod) {
			this.mod = mod;
		}

		void add(int deg, long v) {
			val[deg] += v;
			while (val[deg] < 0)
				val[deg] += mod;
			val[deg] %= mod;
		}

		int deg() {
			int deg = val.length - 1;
			while (deg > 0 && val[deg] == 0)
				--deg;
			return deg;
		}

		Poly mul(Poly p) {
			Poly ret = new Poly(mod);
			for (int i = 0; i < this.val.length; ++i) {
				if (val[i] == 0)
					continue;
				for (int j = 0; j < p.val.length; ++j) {
					if (p.val[j] == 0)
						continue;
					ret.add(i + j, this.val[i] * p.val[j]);
				}
			}
			return ret;
		}

		Poly mod(Poly p) {
			Poly ret = new Poly(mod);
			Poly modPoly = new Poly(mod);
			for (int i = 0; i < val.length; ++i) {
				ret.add(i, val[i]);
			}
			int max = p.deg();
			if (max == 0 && p.val[max] == 0)
				return new Poly(mod);
			long rev = (long) inv(p.val[max], mod);
			for (int i = 0; i < p.val.length; ++i) {
				modPoly.add(i, p.val[i] * rev);
			}
			for (int i = ret.val.length - 1; i >= max; --i) {
				if (ret.val[i] == 0)
					continue;
				long tmp = ret.val[i];
				for (int j = 0; j <= max; ++j) {
					ret.add(i - j, -tmp % mod * modPoly.val[max - j] % mod);
				}
			}
			return ret;
		}

		Poly gcd(Poly p) {
			int deg1 = this.deg();
			int deg2 = p.deg();
			if (deg1 > deg2) {
				return p.gcd(this);
			}
			if (deg1 == 0 && val[deg1] == 0)
				return p;
			return p.mod(this).gcd(this);
		}

		Poly pow(long n, Poly polyMod) {
			int deg = this.deg();
			if (val[deg] == 0)
				return new Poly(mod);
			Poly ret = new Poly(mod);
			ret.add(0, 1);
			Poly pow = new Poly(mod);
			for (int i = 0; i < val.length; ++i) {
				pow.add(i, val[i]);
			}
			for (; n > 0; n >>= 1, pow = pow.mul(pow), pow = pow.mod(polyMod)) {
				if (n % 2 == 1) {
					ret = ret.mul(pow);
					ret = ret.mod(polyMod);
				}
			}
			return ret;
		}
	}

	public static long inv(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;
	}

	// static long inv(long a, long mod) {
	// return pow(a, mod - 2, mod);
	// }

	static long pow(long a, long n, long mod) {
		long ret = 1;
		for (; n > 0; n >>= 1, a = (a * a) % mod) {
			if (n % 2 == 1) {
				ret = (ret * a) % mod;
			}
		}
		return ret;
	}

	static void tr(Object... objects) {
		System.out.println(Arrays.deepToString(objects));
	}
}
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