#689283 (Java21) No.1648 Sum of Powers

提出ソース

結果

問題	No.1648 Sum of Powers
ユーザー	uwi
提出日時	2021-08-13 22:24:11
言語	Java21 (openjdk 21)
結果	AC
実行時間	224 ms / 2,000 ms
コード長	14,374 bytes
コンパイル時間	4,763 ms
コンパイル使用メモリ	92,864 KB
実行使用メモリ	62,096 KB
最終ジャッジ日時	2024-10-03 19:59:10
合計ジャッジ時間	17,007 ms
ジャッジサーバーID （参考情報）	judge4 / judge1

このコードへのチャレンジ
（要ログイン）

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	206 ms 61,656 KB
testcase_01	AC	118 ms 54,252 KB
testcase_02	AC	114 ms 52,956 KB
testcase_03	AC	110 ms 52,916 KB
testcase_04	AC	137 ms 53,188 KB
testcase_05	AC	116 ms 52,784 KB
testcase_06	AC	131 ms 53,120 KB
testcase_07	AC	133 ms 53,056 KB
testcase_08	AC	141 ms 53,544 KB
testcase_09	AC	130 ms 52,904 KB
testcase_10	AC	132 ms 53,124 KB
testcase_11	AC	125 ms 53,208 KB
testcase_12	AC	124 ms 52,764 KB
testcase_13	AC	125 ms 52,880 KB
testcase_14	AC	112 ms 52,752 KB
testcase_15	AC	131 ms 53,028 KB
testcase_16	AC	129 ms 53,192 KB
testcase_17	AC	140 ms 53,304 KB
testcase_18	AC	122 ms 53,244 KB
testcase_19	AC	134 ms 53,024 KB
testcase_20	AC	111 ms 52,592 KB
testcase_21	AC	131 ms 53,164 KB
testcase_22	AC	193 ms 61,712 KB
testcase_23	AC	197 ms 61,244 KB
testcase_24	AC	202 ms 61,372 KB
testcase_25	AC	195 ms 61,592 KB
testcase_26	AC	200 ms 61,424 KB
testcase_27	AC	202 ms 61,760 KB
testcase_28	AC	204 ms 61,684 KB
testcase_29	AC	205 ms 61,932 KB
testcase_30	AC	195 ms 61,528 KB
testcase_31	AC	200 ms 61,712 KB
testcase_32	AC	196 ms 61,396 KB
testcase_33	AC	195 ms 61,388 KB
testcase_34	AC	205 ms 61,432 KB
testcase_35	AC	191 ms 61,764 KB
testcase_36	AC	198 ms 61,852 KB
testcase_37	AC	221 ms 61,672 KB
testcase_38	AC	218 ms 61,768 KB
testcase_39	AC	210 ms 61,636 KB
testcase_40	AC	224 ms 61,352 KB
testcase_41	AC	214 ms 61,536 KB
testcase_42	AC	200 ms 61,532 KB
testcase_43	AC	202 ms 61,724 KB
testcase_44	AC	208 ms 62,096 KB
testcase_45	AC	203 ms 61,708 KB
testcase_46	AC	198 ms 61,648 KB
testcase_47	AC	144 ms 53,592 KB
testcase_48	AC	119 ms 54,120 KB
testcase_49	AC	136 ms 52,976 KB
testcase_50	AC	139 ms 53,132 KB
testcase_51	AC	75 ms 50,832 KB
testcase_52	AC	201 ms 61,580 KB
testcase_53	AC	202 ms 61,572 KB
testcase_54	AC	201 ms 61,424 KB
testcase_55	AC	197 ms 61,532 KB
testcase_56	AC	215 ms 61,396 KB
testcase_57	AC	72 ms 51,052 KB

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

raw source code

package contest210813;
import java.io.*;
import java.util.*;
import java.util.function.IntUnaryOperator;
import java.util.function.LongUnaryOperator;

public class G {
	InputStream is;
	FastWriter out;

	String INPUT = "";


	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 void solve()
	{
		// Q*A = P + XY^(N-1) + X^(N-1)Y = P + BR
		// P = QA - BR
		final int mod = 998244353;
		int A = ni(), B = ni(), P = ni(), Q = ni();

		if(B == 0 && A == 0){
			out.println(2);
			return;
		}

		if(B == 0){
			// X=0, Y=A
			long hit = bsgs(A, Q*invl(A, mod) % mod, mod);
			out.println(hit+2);
			return;
		}

		int[][] M = {
				{A, mod-B},
				{1, 0}
		};
		// [[0,1],[-1/B, A/B]]
		int ib = (int)invl(B, mod);
		int[][] IM = {
				{0, 1},
				{mod-ib, (int)((long)A*ib%mod)}
		};

		// M^kS*v = M^-l*(p q)

		final int S = 100000;

		Map<Long, Integer> map = new HashMap<>();
		int[] v = {P, Q};
		for(int i = 0;i < S;i++){
			long h = (long)v[0]<<32|v[1];
			map.put(h, i);
			v = mul(IM, v, mod);
		}

		int[][] MS = pow(M, S, mod);
		int[] w = mul(M, new int[]{A, 2}, mod);
		long offset = 2;
		for(;;){
			long h = (long)w[0]<<32|w[1];
			if(map.containsKey(h)){
				int ind = map.get(h);
				out.println(offset + ind);
				return;
			}
			w = mul(MS, w, mod);
			offset += S;
		}
	}

	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[][] 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;
	}


	// int行列の積
	// O(N^3)
	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[] 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;
	}


	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 void main(String[] args) {
		new G().run();
	}

	public void run()
	{
		long S = System.currentTimeMillis();
		is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new FastWriter(System.out);

		solve();
		out.flush();
		long G = System.currentTimeMillis();
		tr(G-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();
	}

	private 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 final 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 boolean isSpaceChar(int c) { return !(c >= 32 && 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))){
			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 long[] nal(int n)
	{
		long[] a = new long[n];
		for(int i = 0;i < n;i++)a[i] = nl();
		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();
		}
	}

	public static class FastWriter
	{
		private static final int BUF_SIZE = 1<<13;
		private final byte[] buf = new byte[BUF_SIZE];
		private final OutputStream out;
		private int ptr = 0;

		private FastWriter(){out = null;}

		public FastWriter(OutputStream os)
		{
			this.out = os;
		}

		public FastWriter(String path)
		{
			try {
				this.out = new FileOutputStream(path);
			} catch (FileNotFoundException e) {
				throw new RuntimeException("FastWriter");
			}
		}

		public FastWriter write(byte b)
		{
			buf[ptr++] = b;
			if(ptr == BUF_SIZE)innerflush();
			return this;
		}

		public FastWriter write(char c)
		{
			return write((byte)c);
		}

		public FastWriter write(char[] s)
		{
			for(char c : s){
				buf[ptr++] = (byte)c;
				if(ptr == BUF_SIZE)innerflush();
			}
			return this;
		}

		public FastWriter write(String s)
		{
			s.chars().forEach(c -> {
				buf[ptr++] = (byte)c;
				if(ptr == BUF_SIZE)innerflush();
			});
			return this;
		}

		private static int countDigits(int l) {
			if (l >= 1000000000) return 10;
			if (l >= 100000000) return 9;
			if (l >= 10000000) return 8;
			if (l >= 1000000) return 7;
			if (l >= 100000) return 6;
			if (l >= 10000) return 5;
			if (l >= 1000) return 4;
			if (l >= 100) return 3;
			if (l >= 10) return 2;
			return 1;
		}

		public FastWriter write(int x)
		{
			if(x == Integer.MIN_VALUE){
				return write((long)x);
			}
			if(ptr + 12 >= BUF_SIZE)innerflush();
			if(x < 0){
				write((byte)'-');
				x = -x;
			}
			int d = countDigits(x);
			for(int i = ptr + d - 1;i >= ptr;i--){
				buf[i] = (byte)('0'+x%10);
				x /= 10;
			}
			ptr += d;
			return this;
		}

		private static int countDigits(long l) {
			if (l >= 1000000000000000000L) return 19;
			if (l >= 100000000000000000L) return 18;
			if (l >= 10000000000000000L) return 17;
			if (l >= 1000000000000000L) return 16;
			if (l >= 100000000000000L) return 15;
			if (l >= 10000000000000L) return 14;
			if (l >= 1000000000000L) return 13;
			if (l >= 100000000000L) return 12;
			if (l >= 10000000000L) return 11;
			if (l >= 1000000000L) return 10;
			if (l >= 100000000L) return 9;
			if (l >= 10000000L) return 8;
			if (l >= 1000000L) return 7;
			if (l >= 100000L) return 6;
			if (l >= 10000L) return 5;
			if (l >= 1000L) return 4;
			if (l >= 100L) return 3;
			if (l >= 10L) return 2;
			return 1;
		}

		public FastWriter write(long x)
		{
			if(x == Long.MIN_VALUE){
				return write("" + x);
			}
			if(ptr + 21 >= BUF_SIZE)innerflush();
			if(x < 0){
				write((byte)'-');
				x = -x;
			}
			int d = countDigits(x);
			for(int i = ptr + d - 1;i >= ptr;i--){
				buf[i] = (byte)('0'+x%10);
				x /= 10;
			}
			ptr += d;
			return this;
		}

		public FastWriter write(double x, int precision)
		{
			if(x < 0){
				write('-');
				x = -x;
			}
			x += Math.pow(10, -precision)/2;
			//		if(x < 0){ x = 0; }
			write((long)x).write(".");
			x -= (long)x;
			for(int i = 0;i < precision;i++){
				x *= 10;
				write((char)('0'+(int)x));
				x -= (int)x;
			}
			return this;
		}

		public FastWriter writeln(char c){ return write(c).writeln(); }
		public FastWriter writeln(int x){ return write(x).writeln(); }
		public FastWriter writeln(long x){ return write(x).writeln(); }
		public FastWriter writeln(double x, int precision){ return write(x, precision).writeln(); }

		public FastWriter write(int... xs)
		{
			boolean first = true;
			for(int x : xs) {
				if (!first) write(' ');
				first = false;
				write(x);
			}
			return this;
		}

		public FastWriter write(long... xs)
		{
			boolean first = true;
			for(long x : xs) {
				if (!first) write(' ');
				first = false;
				write(x);
			}
			return this;
		}

		public FastWriter write(IntUnaryOperator f, int... xs)
		{
			boolean first = true;
			for(int x : xs) {
				if (!first) write(' ');
				first = false;
				write(f.applyAsInt(x));
			}
			return this;
		}

		public FastWriter write(LongUnaryOperator f, long... xs)
		{
			boolean first = true;
			for(long x : xs) {
				if (!first) write(' ');
				first = false;
				write(f.applyAsLong(x));
			}
			return this;
		}

		public FastWriter writeln()
		{
			return write((byte)'\n');
		}

		public FastWriter writeln(int... xs) { return write(xs).writeln(); }
		public FastWriter writeln(long... xs) { return write(xs).writeln(); }
		public FastWriter writeln(IntUnaryOperator f, int... xs) { return write(f, xs).writeln(); }
		public FastWriter writeln(LongUnaryOperator f, long... xs) { return write(f, xs).writeln(); }
		public FastWriter writeln(char[] line) { return write(line).writeln(); }
		public FastWriter writeln(char[]... map) { for(char[] line : map)write(line).writeln();return this; }
		public FastWriter writeln(String s) { return write(s).writeln(); }

		private void innerflush()
		{
			try {
				out.write(buf, 0, ptr);
				ptr = 0;
			} catch (IOException e) {
				throw new RuntimeException("innerflush");
			}
		}

		public void flush()
		{
			innerflush();
			try {
				out.flush();
			} catch (IOException e) {
				throw new RuntimeException("flush");
			}
		}

		public FastWriter print(byte b) { return write(b); }
		public FastWriter print(char c) { return write(c); }
		public FastWriter print(char[] s) { return write(s); }
		public FastWriter print(String s) { return write(s); }
		public FastWriter print(int x) { return write(x); }
		public FastWriter print(long x) { return write(x); }
		public FastWriter print(double x, int precision) { return write(x, precision); }
		public FastWriter println(char c){ return writeln(c); }
		public FastWriter println(int x){ return writeln(x); }
		public FastWriter println(long x){ return writeln(x); }
		public FastWriter println(double x, int precision){ return writeln(x, precision); }
		public FastWriter print(int... xs) { return write(xs); }
		public FastWriter print(long... xs) { return write(xs); }
		public FastWriter print(IntUnaryOperator f, int... xs) { return write(f, xs); }
		public FastWriter print(LongUnaryOperator f, long... xs) { return write(f, xs); }
		public FastWriter println(int... xs) { return writeln(xs); }
		public FastWriter println(long... xs) { return writeln(xs); }
		public FastWriter println(IntUnaryOperator f, int... xs) { return writeln(f, xs); }
		public FastWriter println(LongUnaryOperator f, long... xs) { return writeln(f, xs); }
		public FastWriter println(char[] line) { return writeln(line); }
		public FastWriter println(char[]... map) { return writeln(map); }
		public FastWriter println(String s) { return writeln(s); }
		public FastWriter println() { return writeln(); }
	}

	public static void trnz(int... o)
	{
		for(int i = 0;i < o.length;i++)if(o[i] != 0)System.out.print(i+":"+o[i]+" ");
		System.out.println();
	}

	// print ids which are 1
	public static void trt(long... o)
	{
		Queue<Integer> stands = new ArrayDeque<>();
		for(int i = 0;i < o.length;i++){
			for(long x = o[i];x != 0;x &= x-1)stands.add(i<<6|Long.numberOfTrailingZeros(x));
		}
		System.out.println(stands);
	}

	public static void tf(boolean... r)
	{
		for(boolean x : r)System.out.print(x?'#':'.');
		System.out.println();
	}

	public static void tf(boolean[]... b)
	{
		for(boolean[] r : b) {
			for(boolean x : r)System.out.print(x?'#':'.');
			System.out.println();
		}
		System.out.println();
	}

	public void tf(long[]... b)
	{
		if(INPUT.length() != 0) {
			for (long[] r : b) {
				for (long x : r) {
					for (int i = 0; i < 64; i++) {
						System.out.print(x << ~i < 0 ? '#' : '.');
					}
				}
				System.out.println();
			}
			System.out.println();
		}
	}

	public void tf(long... b)
	{
		if(INPUT.length() != 0) {
			for (long x : b) {
				for (int i = 0; i < 64; i++) {
					System.out.print(x << ~i < 0 ? '#' : '.');
				}
			}
			System.out.println();
		}
	}

	private void tr(Object... o) { if(INPUT.length() != 0)System.out.println(Arrays.deepToString(o)); }
}

yukicoder

結果

テストケース

ソースコード