#412023 (Java21) No.950 行列累乗

提出ソース

結果

問題	No.950 行列累乗
ユーザー	uwi
提出日時	2019-12-26 00:00:58
言語	Java21 (openjdk 21)
結果	WA
実行時間	-
コード長	9,750 bytes
コンパイル時間	5,755 ms
コンパイル使用メモリ	90,372 KB
実行使用メモリ	63,816 KB
最終ジャッジ日時	2024-04-08 21:55:28
合計ジャッジ時間	15,819 ms
ジャッジサーバーID （参考情報）	judge13 / judge14

このコードへのチャレンジ
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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	100 ms 56,368 KB
testcase_01	AC	112 ms 56,516 KB
testcase_02	WA	-
testcase_03	AC	55 ms 54,000 KB
testcase_04	AC	54 ms 54,020 KB
testcase_05	WA	-
testcase_06	WA	-
testcase_07	WA	-
testcase_08	WA	-
testcase_09	WA	-
testcase_10	WA	-
testcase_11	WA	-
testcase_12	WA	-
testcase_13	WA	-
testcase_14	WA	-
testcase_15	WA	-
testcase_16	WA	-
testcase_17	WA	-
testcase_18	AC	56 ms 53,992 KB
testcase_19	WA	-
testcase_20	WA	-
testcase_21	WA	-
testcase_22	WA	-
testcase_23	WA	-
testcase_24	WA	-
testcase_25	WA	-
testcase_26	WA	-
testcase_27	WA	-
testcase_28	WA	-
testcase_29	WA	-
testcase_30	WA	-
testcase_31	WA	-
testcase_32	WA	-
testcase_33	WA	-
testcase_34	WA	-
testcase_35	WA	-
testcase_36	AC	109 ms 56,548 KB
testcase_37	WA	-
testcase_38	WA	-
testcase_39	AC	95 ms 56,044 KB
testcase_40	WA	-
testcase_41	WA	-
testcase_42	WA	-
testcase_43	WA	-
testcase_44	WA	-
testcase_45	WA	-
testcase_46	WA	-
testcase_47	WA	-
testcase_48	WA	-
testcase_49	WA	-
testcase_50	WA	-
testcase_51	WA	-
testcase_52	WA	-
testcase_53	WA	-
testcase_54	AC	57 ms 53,984 KB
testcase_55	AC	54 ms 53,884 KB
testcase_56	AC	116 ms 56,552 KB
testcase_57	AC	54 ms 53,960 KB
testcase_58	WA	-
testcase_59	AC	58 ms 54,012 KB
testcase_60	AC	57 ms 53,988 KB

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ソースコード

raw source code

package adv2019;
import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.HashMap;
import java.util.InputMismatchException;
import java.util.Map;

public class D21X {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	
	void solve()
	{
		int P = ni();
		int[][] a = new int[2][];
		for(int i = 0;i < 2;i++) a[i] = na(2);
		int[][] b = new int[2][];
		for(int i = 0;i < 2;i++) b[i] = na(2);
		long da = (long)a[0][0] * a[1][1] - (long)a[0][1] * a[1][0];
		long db = (long)b[0][0] * b[1][1] - (long)b[0][1] * b[1][0];
		da %= P;
		if(da < 0)da += P;
		db %= P;
		if(db < 0)db += P;
		
		{
			boolean ok = true;
			for(int i = 0;i < 2;i++) {
				for(int j = 0;j < 2;j++) {
					if(a[i][j] != b[i][j])ok = false;
				}
			}
			if(ok) {
				out.println(1);
				return;
			}
		}
		
		if(da == 0) {
			if(db != 0) {
				out.println(-1);
				return;
			}else {
				long tra = a[0][0] + a[1][1];
				long trb = b[0][0] + b[1][1];
				tra %= P;
				trb %= P;
				if(tra != 0) {
					long e = bsgs(tra, trb, P);
					if(e == -1) {
						out.println(-1);
						return;
					}else {
						for(int k = 0;k < 2;k++) {
							for(int l = 0;l < 2;l++) {
								if(pow(a[k][l], e, P) != b[k][l]) {
									out.println(-1); return;
								}
							}
						}
						out.println(e == 0 ? order((int)tra, P) : e);
						return;
					}
				}else {
					boolean ok = true;
					for(int i = 0;i < 2;i++) {
						for(int j = 0;j < 2;j++) {
							if(b[i][j] != 0) {
								ok = false;
							}
						}
					}
					if(ok) {
						out.println(2);
					}else {
						out.println(-1);
					}
					return;
				}
			}
		}
		
		long e = bsgs(da, db, P);
		tr(e);
		if(e == -1) {
			out.println(-1);
			return;
		}
		long m = order((int)da, P);
		int[][] am = pow(a, m, P);
		int[][] br = mul(b, pow(inv(a, P), e, P), P);
		long ans = bsgs(am, br, P, e == 0);
		if(ans == -1) {
			out.println(-1);
		}else {	
			out.println(ans*m+e);
		}
	}
	
	static int[][] inv(int[][] a, int p)
	{
		long D = (long)a[0][0] * a[1][1] - (long)a[1][0] * a[0][1];
		D %= p;
		if(D < 0)D += p;
		D = invl(D, p);
		return new int[][] {
			{(int)(a[1][1] * D % p), (int)((p-a[0][1]) * D % p)},
			{(int)((p-a[1][0]) * D % p), (int)(a[0][0] * D % p)}
		};
	}
	
	public static long bsgs(int[][] alpha, int[][] beta, int p, boolean shift)
	{
		int m = (int)Math.sqrt(p)+1;
		Map<Long, Integer> table = new HashMap<Long, Integer>();
		int[][] E = shift ? alpha : new int[][]{{1, 0}, {0, 1}};
		for(int j = 0;j < m;j++){
			long code = 0;
			for(int k = 0;k < 2;k++) {
				for(int l = 0;l < 2;l++) {
					code = code * 1000000009 + E[k][l];
				}
			}
			table.putIfAbsent(code, j);
			E = mul(E, alpha, p);
		}
		int[][] ie = inv(E, p);
		
		int[][] g = beta;
		for(int i = 0;i < m;i++){
			long code = 0;
			for(int k = 0;k < 2;k++) {
				for(int l = 0;l < 2;l++) {
					code = code * 1000000009 + beta[k][l];
				}
			}
			if(table.containsKey(code)) {
				return i*m+table.get(code) + (shift ? 1 : 0);
			}
			
			g = mul(g, ie, p);
		}
		return -1;
	}
	
	
	
	public static int[] pow(int[][] A, int[] v, long e, int mod)
	{
		int[][] MUL = A;
		for(int i = 0;i < v.length;i++)v[i] %= mod;
		for(;e > 0;e>>>=1) {
			if((e&1)==1)v = mul(MUL, v, mod);
			MUL = p2(MUL, mod);
		}
		return v;
	}
	
	
	// int matrix * int vector
	public static int[] mul(int[][] A, int[] v, int mod)
	{
		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];
				sum %= mod;
			}
			w[i] = (int)sum;
		}
		return w;
	}
	
	// int matrix^2 (cannot ensure negative values)
	public static int[][] p2(int[][] A, int mod)
	{
		int n = A.length;
		int[][] C = new int[n][n];
		for(int i = 0;i < n;i++){
			for(int j = 0;j < n;j++){
				long sum = 0;
				for(int k = 0;k < n;k++){
					sum += (long)A[i][k] * A[k][j];
					sum %= mod;
				}
				C[i][j] = (int)sum;
			}
		}
		return C;
	}
	
	// 普通の累乗計算セット ここまで
	
	// ret[n]=A^(2^n)
	public static int[][][] generateP2(int[][] A, int n, int mod)
	{
		int[][][] ret = new int[n+1][][];
		ret[0] = A;
		for(int i = 1;i <= n;i++)ret[i] = p2(ret[i-1], mod);
		return ret;
	}
	
	// A[0]^e*v
	// A[n]=A[0]^(2^n)
	public static int[] pow(int[][][] A, int[] v, long e, int mod)
	{
		for(int i = 0;e > 0;e>>>=1,i++) {
			if((e&1)==1)v = mul(A[i], v, mod);
		}
		return v;
	}
	
	public static int[][] mul(int mod, int[][]... a)
	{
		int[][] base = a[0];
		for(int i = 1;i < a.length;i++){
			base = mul(base, a[i], mod);
		}
		return base;
	}
	
	// メモ累乗計算セット ここまで
	
	// int行列の和
	public static int[][] add(int[][] A, int[][] B, int mod)
	{
		int m = A.length;
		int n = A[0].length;
		int[][] C = new int[m][n];
		for(int i = 0;i < m;i++){
			for(int j = 0;j < n;j++){
				C[i][j] = (A[i][j] + B[i][j]) % mod;
			}
		}
		return C;
	}
	
	public static int[] add(int[] A, int[] B, int mod)
	{
		int n = A.length;
		int[] C = new int[n];
		for(int i = 0;i < n;i++){
			C[i] = (A[i] + B[i]) % mod;
		}
		return C;
	}
	
	// A^e
	// O(N^3log N)
	public static int[][] pow(int[][] A, long e, int mod)
	{
		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, mod);
			MUL = p2(MUL, mod);
		}
		return C;
	}
	
	public static int[][] mul(int[][] A, int[][] B, int mod)
	{
		assert A[0].length == B.length;
		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++){
			for(int j = 0;j < o;j++){
				long sum = 0;
				for(int k = 0;k < n;k++){
					sum += (long)A[i][k] * B[k][j];
					sum %= mod;
				}
				C[i][j] = (int)sum;
			}
		}
		return C;
	}


	
	public static int order(int a, int p)
	{
		int q = p-1;
		for(int i = 2;i*i <= q;i++) {
			while(q % i == 0 && pow(a, q/i, p) == 1) {
				q /= i;
			}
		}
		return q;
	}
	
	public static long pow(long a, long n, long mod) {
		//		a %= mod;
		long ret = 1;
		int x = 63 - Long.numberOfLeadingZeros(n);
		for (; x >= 0; x--) {
			ret = ret * ret % mod;
			if (n << 63 - x < 0)
				ret = ret * a % mod;
		}
		return ret;
	}

	
	public static long bsgs(long alpha, long beta, int p)
	{
		int m = (int)Math.sqrt(p)+1;
		long[] table = new long[m];
		long val = 1;
		for(int j = 0;j < m;j++){
			table[j] = val<<32|j;
			val = val * alpha % p;
		}
		Arrays.sort(table);
		long ainvm = invl(val, p);
		
		long g = beta;
		for(int i = 0;i < m;i++){
			int ind = Arrays.binarySearch(table, g<<32);
			if(ind < 0)ind = -ind-1;
			if(ind < m && table[ind]>>>32 == g){
				return i*m+(int)table[ind];
			}
			g = g * ainvm % p;
		}
		return -1;
	}
	
	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;
	}


	
	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 D21X().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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結果

テストケース

ソースコード