#663802 (Java21) No.1533 Don't be Negative!

提出ソース

結果

問題	No.1533 Don't be Negative!
ユーザー	uwi
提出日時	2021-06-04 22:34:53
言語	Java21 (openjdk 21)
結果	AC
実行時間	324 ms / 8,000 ms
コード長	16,608 bytes
コンパイル時間	5,224 ms
コンパイル使用メモリ	93,512 KB
実行使用メモリ	58,084 KB
最終ジャッジ日時	2024-04-30 09:52:45
合計ジャッジ時間	19,554 ms
ジャッジサーバーID （参考情報）	judge3 / judge5

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	174 ms 55,980 KB
testcase_01	AC	188 ms 55,896 KB
testcase_02	AC	209 ms 56,188 KB
testcase_03	AC	216 ms 56,360 KB
testcase_04	AC	159 ms 56,296 KB
testcase_05	AC	188 ms 58,084 KB
testcase_06	AC	189 ms 56,344 KB
testcase_07	AC	166 ms 56,000 KB
testcase_08	AC	154 ms 56,296 KB
testcase_09	AC	200 ms 56,268 KB
testcase_10	AC	183 ms 56,304 KB
testcase_11	AC	257 ms 56,632 KB
testcase_12	AC	200 ms 56,700 KB
testcase_13	AC	177 ms 56,472 KB
testcase_14	AC	206 ms 56,908 KB
testcase_15	AC	213 ms 56,652 KB
testcase_16	AC	251 ms 56,556 KB
testcase_17	AC	176 ms 56,272 KB
testcase_18	AC	222 ms 56,420 KB
testcase_19	AC	246 ms 56,144 KB
testcase_20	AC	191 ms 56,440 KB
testcase_21	AC	250 ms 56,340 KB
testcase_22	AC	225 ms 56,592 KB
testcase_23	AC	149 ms 55,512 KB
testcase_24	AC	227 ms 56,652 KB
testcase_25	AC	252 ms 56,620 KB
testcase_26	AC	211 ms 56,308 KB
testcase_27	AC	205 ms 56,888 KB
testcase_28	AC	252 ms 56,432 KB
testcase_29	AC	252 ms 56,588 KB
testcase_30	AC	299 ms 56,620 KB
testcase_31	AC	214 ms 55,900 KB
testcase_32	AC	257 ms 56,232 KB
testcase_33	AC	270 ms 56,636 KB
testcase_34	AC	164 ms 56,256 KB
testcase_35	AC	151 ms 55,836 KB
testcase_36	AC	280 ms 56,496 KB
testcase_37	AC	250 ms 56,300 KB
testcase_38	AC	278 ms 56,808 KB
testcase_39	AC	255 ms 56,720 KB
testcase_40	AC	276 ms 56,508 KB
testcase_41	AC	233 ms 56,640 KB
testcase_42	AC	266 ms 56,688 KB
testcase_43	AC	256 ms 56,512 KB
testcase_44	AC	250 ms 56,556 KB
testcase_45	AC	264 ms 56,632 KB
testcase_46	AC	264 ms 56,272 KB
testcase_47	AC	295 ms 56,804 KB
testcase_48	AC	271 ms 56,580 KB
testcase_49	AC	239 ms 56,448 KB
testcase_50	AC	319 ms 56,728 KB
testcase_51	AC	307 ms 56,644 KB
testcase_52	AC	313 ms 56,696 KB
testcase_53	AC	320 ms 56,572 KB
testcase_54	AC	324 ms 56,644 KB
testcase_55	AC	296 ms 56,748 KB
testcase_56	AC	267 ms 56,540 KB

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ソースコード

raw source code

package contest210604;
import java.io.*;
import java.util.ArrayDeque;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.Queue;
import java.util.function.IntUnaryOperator;
import java.util.function.LongUnaryOperator;

public class G {
	InputStream is;
	FastWriter out;

	String INPUT = "";

	public void solve()
	{
		int n = ni(), M = ni(), K = ni();
		final int mod = 998244353;

		long[] dp = new long[2000];
		int o = 1000;
		dp[o] = 1;
		long[] a = new long[200];
		for(int i = 1;i <= 199;i++){
			long[] ndp = new long[2000];
			for(int j = 0;j < 2000;j++){
				if(dp[j] == 0)continue;
				for(int l = -M;l <= M;l++){
					if(l == -K || l == K)continue;
					ndp[j+l] += dp[j];
				}
			}
			for(int j = 0;j < 2000;j++){
				ndp[j] %= mod;
			}
			for(int j = 0;j < o;j++){
				a[i] += ndp[j];
			}
			a[i] %= mod;
			dp = ndp;
		}
		long[] hey = interpolate(n+1, mod, a);
		long ans = 0;
		int kk = 2*M+1 - (K == 0 ? 1 : 2);
		for(int len = 1;len <= n;len++){
			ans += hey[len] * (n-len+1) % mod * pow(kk, n-len, mod);
			ans %= mod;
		}
		out.println(ans);
	}

	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[] interpolate(int n, int mod, long... base)
	{
		int m = base.length;
		long[][] res = guessLeaned(mod, base);
		return interpolate(res, Arrays.copyOf(base, n+1), m, n+1, mod);
	}

	public static long[][] guessLeaned(int mod, long... a)
	{
		int n = a.length;

		// #formula >= #variable
		// n-r+2 >= r(r+1)/2
		for(int r = n;r >= 1;r--){
			if(n-r+2 < r*(r+1)/2)continue;
			int[][] M = new int[n-r+2][r*(r+1)/2];
			for(int i = 0;i < n-r+1;i++){
				int p = 0;
				for(int j = 0;j < r;j++){
					long prod = 1;
					for(int k = 0;k <= r-j-1;k++){
						M[i][p++] = (int)(prod*a[i+j]%mod);
						prod = prod * i % mod;
					}
				}
			}
			M[n-r+1][0] = 1;

			int[] v = new int[n-r+2];
			v[n-r+1] = 1;

			Result res = gaussElimination(M, v, mod);
			if(res.exists){
				long[][] ret = new long[r][];
				int p = 0;
				for(int i = 0;i < r;i++){
					ret[i] = new long[r-i];
					for(int j = 0;j < r-i;j++){
						ret[i][j] = res.sol[p++];
					}
				}

				// reformat
				int ilast = r;
				for(int i = r-1;i >= 0;i--){
					int last = ret[i].length;
					while(last > 0 && ret[i][last-1] == 0)last--;
					ret[i] = Arrays.copyOf(ret[i], last);
					if(last == 0 && i+1 == ilast){
						ilast--;
					}
				}
				ret = Arrays.copyOf(ret, ilast);

				return ret;
			}
		}
		return null;
	}

	public static Result gaussElimination(int[][] M, int[] v, int mod)
	{
		int n = M.length, m = M[0].length;
		int[] head = new int[n];

		// if not needed, comment out.
		for(int[] row : M){
			for(int i = 0;i < row.length;i++){
				row[i] %= mod;
				if(row[i] < 0)row[i] += mod;
			}
		}

		// Forward Elimination
		int row = 0;
		for(int col = 0;col < m;col++){
			// select pivot
			boolean pivotFound = false;
			out:
			for(int prow = row;prow < n;prow++){
				if(M[prow][col] != 0){
					// pivot found
					if(prow != row){
						// swap rows
						for(int k = 0;k < m;k++){
							int u = M[prow][k]; M[prow][k] = M[row][k]; M[row][k] = u;
						}
						int dum = v[prow]; v[prow] = v[row]; v[row] = dum;
					}
					pivotFound = true;
					break out;
				}
			}
			if(!pivotFound)continue;
			head[row] = col;

			// diag to 1
			long imul = invl(M[row][col], mod);
			for(int k = 0;k < m;k++){
				M[row][k] = (int)(M[row][k] * imul % mod);
			}
			v[row] = (int)(v[row] * imul % mod);

			for(int j = row+1;j < n;j++){
				if(M[j][col] != 0){
					long mul = mod-M[j][col];
					for(int k = col;k < m;k++){
						M[j][k] = (int)((M[j][k] + M[row][k] * mul) % mod);
					}
					v[j] = (int)((v[j] + v[row] * mul) % mod);
				}
			}
			row++;
		}

		Result ret = new Result();
		ret.mat = M;
		for(int i = row;i < n;i++){
			if(v[i] != 0){
				ret.rank = row;
				ret.exists = false;
				return ret;
			}
		}

		for(int i = row-1;i >= 0;i--){
			for(int j = i-1;j >= 0;j--){
				if(M[j][head[i]] != 0){
					long mul = mod-M[j][head[i]];
					for(int k = head[i];k < m;k++){
						M[j][k] = (int)((M[j][k] + M[i][k] * mul) % mod);
					}
					v[j] = (int)((v[j] + v[i] * mul) % mod);
				}
			}
		}

		int[] retv = new int[m];
		for(int i = 0;i < row;i++){
			retv[head[i]] = v[i];
		}

		ret.sol = retv;
		ret.rank = row;
		ret.exists = true;
		return ret;
	}

	public static class Result
	{
		public int[][] mat;
		public int[] sol;
		public int rank;
		public boolean exists;
	}


	/**
	 * vals[0,x-1]の情報を利用してvals[x]を埋める
	 * @param ged
	 * @param vals
	 * @param x
	 * @param mod
	 */
	public static long[] interpolate(long[][] ged, long[] vals, int l, int r, int mod)
	{
		int n = ged.length;

		for(int x = l, xx = x-(n-1);x < r;x++, xx++){
			int pos = x;

			long s = 0;
			long tar = 0;
			for(int i = 0;i < n;i++){
				long co = 0;
				for(int j = ged[i].length-1;j >= 0;j--){
					co = (co * xx + ged[i][j]) % mod;
				}
				if(i < n-1){
					s += co * vals[i+xx];
					s %= mod;
				}else{
					tar = co;
				}
			}

			long ret = (mod-invl(tar, mod)) * s % mod;
			vals[pos] = ret;
		}
		return vals;
	}

	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