#51218 (Java21) No.283 スライドパズルと魔方陣

提出ソース

結果

問題	No.283 スライドパズルと魔方陣
ユーザー	uwi
提出日時	2015-09-26 18:37:47
言語	Java21 (openjdk 21)
結果	RE
実行時間	-
コード長	13,070 bytes
コンパイル時間	4,825 ms
コンパイル使用メモリ	90,004 KB
実行使用メモリ	51,188 KB
最終ジャッジ日時	2024-06-07 21:12:56
合計ジャッジ時間	10,490 ms
ジャッジサーバーID （参考情報）	judge1 / judge3

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	50 ms 50,304 KB
testcase_01	AC	52 ms 50,400 KB
testcase_02	AC	52 ms 50,312 KB
testcase_03	AC	54 ms 50,380 KB
testcase_04	AC	53 ms 50,012 KB
testcase_05	AC	54 ms 50,536 KB
testcase_06	AC	52 ms 50,116 KB
testcase_07	AC	52 ms 50,312 KB
testcase_08	AC	51 ms 50,024 KB
testcase_09	AC	56 ms 50,460 KB
testcase_10	RE	-
testcase_11	AC	53 ms 50,380 KB
testcase_12	AC	53 ms 50,148 KB
testcase_13	AC	55 ms 50,048 KB
testcase_14	AC	54 ms 50,552 KB
testcase_15	AC	55 ms 50,484 KB
testcase_16	AC	54 ms 50,228 KB
testcase_17	AC	56 ms 50,500 KB
testcase_18	AC	56 ms 50,512 KB
testcase_19	AC	55 ms 50,440 KB
testcase_20	AC	56 ms 50,540 KB
testcase_21	AC	58 ms 50,320 KB
testcase_22	AC	56 ms 50,520 KB
testcase_23	AC	62 ms 50,416 KB
testcase_24	AC	61 ms 50,640 KB
testcase_25	AC	57 ms 50,272 KB
testcase_26	AC	58 ms 50,508 KB
testcase_27	AC	78 ms 50,812 KB
testcase_28	AC	92 ms 51,188 KB
testcase_29	AC	81 ms 51,044 KB
testcase_30	AC	78 ms 50,784 KB
testcase_31	AC	85 ms 50,992 KB
testcase_32	AC	84 ms 51,068 KB
testcase_33	AC	87 ms 50,924 KB
testcase_34	AC	86 ms 51,148 KB
testcase_35	AC	85 ms 50,784 KB
testcase_36	AC	84 ms 51,056 KB
testcase_37	AC	88 ms 50,884 KB
testcase_38	AC	75 ms 51,008 KB

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ソースコード

raw source code

package q6xx;

import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.BitSet;
import java.util.InputMismatchException;

public class Q664_3 {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	
	void solve()
	{
//		for(int i = 1;i <= 12;i++){
//			tr(i);
//			int[][] tw = panmagicX4(i*4, 1);
////			tr(parity(tw));
//			tr(ismagic(tw));
//		}
//		if(true)return;
			
		int n = ni();
		int[] a = na(n*n);
		int x = 0;
		for(int i = 0;i < n*n;i++){
			if(a[i] == 0){
				a[i] = n*n;
				x ^= ((i/n)^(i%n))&1;
			}
		}
		int parity = parity(a)^x;
		
		if(n == 1){
			out.println("possible");
			out.println(1);
			return;
		}
		if(n == 2){
			out.println("impossible");
			return;
		}
//		if(n == 4 && parity == 0){
//			out.println("impossible");
//			return;
//		}
		out.println("possible");
		
		int[][] ms = null;
		if(n % 2 == 1){
			ms = what(n, parity);
		}else if(n % 4 == 2){
			ms = what2(n, parity);
		}else{
			ms = panmagicX4(n, parity);
		}
		if(!ismagic(ms) || ms.length != n){
			throw new RuntimeException();
		}
		int tp = parity(ms);
		for(int i = 0;i < n;i++){
			for(int j = 0;j < n;j++){
				if(ms[i][j] == n*n){
					tp ^= (i^j)&1;
				}
			}
		}
		if(tp != parity)throw new RuntimeException();
		
		for(int i = 0;i < n;i++){
			for(int j = 0;j < n;j++){
				if(j > 0)out.print(" ");
				out.print(ms[i][j]);
			}
			out.println();
		}
	}
	
	static int[][] what2(int n, int want)
	{
		n /= 2;
		int[] A = new int[n];
		for(int i = 0;i < n;i++)A[i] = i;
		int[] B = new int[n];
		for(int i = 0;i < n;i++)B[i] = i;
		do{
			int[][] a = new int[n][n];
			for(int i = 0;i < n;i++){
				for(int j = 0;j < n;j++){
					a[i][j] = A[(i+j+n-n/2)%n]*n+B[(i+n-j+n/2)%n]+1;
	//				a[i][j] = A[(i+j*0)%n];
	//				a[i][j] = B[(i+n-j+n/2)%n];
	//				a[i][j] = (i*(n-s)+j+2)%n;
				}
			}
			if(!ismagic(a))continue;
			a = constructByLUXMethod(a);
			if(!ismagic(a))throw new RuntimeException();
			int lp = -1;
			for(int i = 0;i < a.length;i++){
				for(int j = 0;j < a.length;j++){
					if(a[i][j] == 4*n*n)lp = (i^j)&1;
				}
			}
			if(lp == -1)throw new RuntimeException();
			if(parity(a) == (want^lp))return a;
		}while(nextPermutation(B));
		return null;
	}
	
	static int[][] what(int n, int want)
	{
		int[] A = new int[n];
		for(int i = 0;i < n;i++)A[i] = i;
		int[] B = new int[n];
		for(int i = 0;i < n;i++)B[i] = i;
		do{
			int[][] a = new int[n][n];
			int lp = -1;
			for(int i = 0;i < n;i++){
				for(int j = 0;j < n;j++){
					a[i][j] = A[(i+j+n-n/2)%n]*n+B[(i+n-j+n/2)%n]+1;
					if(a[i][j] == n*n)lp = (i^j)&1;
	//				a[i][j] = A[(i+j*0)%n];
	//				a[i][j] = B[(i+n-j+n/2)%n];
	//				a[i][j] = (i*(n-s)+j+2)%n;
				}
			}
			if(!ismagic(a))continue;
			if(lp == -1)throw new RuntimeException();
//			if(!ismagic(a))throw new RuntimeException();
			if(parity(a) == (want^lp))return a;
		}while(nextPermutation(B));
		return null;
	}
	
	public static boolean nextPermutation(int[] a) {
		int n = a.length;
		int i;
		for (i = n - 2; i >= 0 && a[i] >= a[i + 1]; i--)
			;
		if (i == -1)
			return false;
		int j;
		for (j = i + 1; j < n && a[i] < a[j]; j++)
			;
		int d = a[i];
		a[i] = a[j - 1];
		a[j - 1] = d;
		for (int p = i + 1, q = n - 1; p < q; p++, q--) {
			d = a[p];
			a[p] = a[q];
			a[q] = d;
		}
		return true;
	}
	
	static boolean ismagic(int[][] a)
	{
		int n = a.length;
		BitSet bs = new BitSet();
		for(int i = 0;i < n;i++){
			for(int j = 0;j < n;j++){
				if(a[i][j] <= 0 || a[i][j] > n*n)return false;
				bs.set(a[i][j]);
			}
		}
		if(bs.cardinality() != n*n)return false;
		
		// 1-base
		int S = n*(n*n+1)/2;
		for(int i = 0;i < n;i++){
			int ls = 0;
			for(int j = 0;j < n;j++)ls += a[i][j];
			if(ls != S)return false;
		}
		for(int i = 0;i < n;i++){
			int ls = 0;
			for(int j = 0;j < n;j++)ls += a[j][i];
			if(ls != S)return false;
		}
		{
			int ls = 0;
			for(int i = 0;i < n;i++)ls += a[i][i];
			if(ls != S)return false;
		}
		{
			int ls = 0;
			for(int i = 0;i < n;i++)ls += a[n-1-i][i];
			if(ls != S)return false;
		}
		return true;
	}
	
	static int parity(int[][] t)
	{
		int n = t.length;
		int[] u = new int[n*n];
		for(int i = 0;i < n;i++){
			for(int j = 0;j < n;j++){
				u[i*n+j] = t[i][j];
			}
		}
		return parity(u);
	}
	
	public static int[][] constructBySiameseMethod2(int n)
	{
		if(n <= 0 || n % 2 == 0)throw new RuntimeException();
		int[][] ret = new int[n][n];
		int r = n/2-1, c = n/2;
		for(int i = 1;i <= n*n;i++){
			ret[r][c] = i;
			int nr = r-1, nc = c+1;
			if(nr < 0)nr += n;
			if(nc >= n)nc -= n;
			if(ret[nr][nc] != 0){
				nr = r-2; nc = c;
				if(nr < 0)nr += n;
			}
			r = nr; c = nc;
		}
		return ret;
	}
	
	public static int parity(int[] a)
	{
		return (int)(inversion(a) % 2);
//		int[] b = Arrays.copyOf(a, a.length);
//		int x = 0;
//		int n = b.length;
//		for(int i = 0;i < n;i++){
//			if(i != b[i]-1){
//				int j = b[i]-1;
//				int d = b[i]; b[i] = b[j]; b[j] = d;
//				x ^= 1;
//			}
//		}
//		return x;
	}
	
	public static long inversion(int[] a)
	{
		int n = a.length;
		int[] ft = new int[n+2];
		long inv = 0;
		for(int i = n-1;i >= 0;i--){
			inv += sumFenwick(ft, a[i]);
			addFenwick(ft, a[i], 1);
		}
		return inv;
	}
	public static int sumFenwick(int[] ft, int i) {
		int sum = 0;
		for (i++; i > 0; i -= i & -i)
			sum += ft[i];
		return sum;
	}

	public static void addFenwick(int[] ft, int i, int v) {
		if (v == 0 || i < 0)
			return;
		int n = ft.length;
		for (i++; i < n; i += i & -i)
			ft[i] += v;
	}

	public static int findGFenwick(int[] ft, int v) {
		int i = 0;
		int n = ft.length;
		for (int b = Integer.highestOneBit(n); b != 0 && i < n; b >>= 1) {
			if (i + b < n) {
				int t = i + b;
				if (v >= ft[t]) {
					i = t;
					v -= ft[t];
				}
			}
		}
		return v != 0 ? -(i + 1) : i - 1;
	}

	public static int valFenwick(int[] ft, int i) {
		return sumFenwick(ft, i) - sumFenwick(ft, i - 1);
	}

	public static int[] restoreFenwick(int[] ft) {
		int n = ft.length - 1;
		int[] ret = new int[n];
		for (int i = 0; i < n; i++)
			ret[i] = sumFenwick(ft, i);
		for (int i = n - 1; i >= 1; i--)
			ret[i] -= ret[i - 1];
		return ret;
	}

	public static int before(int[] ft, int x) {
		int u = sumFenwick(ft, x - 1);
		if (u == 0)
			return -1;
		return findGFenwick(ft, u - 1) + 1;
	}

	public static int after(int[] ft, int x) {
		int u = sumFenwick(ft, x);
		int f = findGFenwick(ft, u);
		if (f + 1 >= ft.length - 1)
			return -1;
		return f + 1;
	}

	public static int[] buildFenwick(int[] a) {
		int n = a.length;
		int[] ft = new int[n + 1];
		System.arraycopy(a, 0, ft, 1, n);
		for (int k = 2, h = 1; k <= n; k *= 2, h *= 2) {
			for (int i = k; i <= n; i += k) {
				ft[i] += ft[i - h];
			}
		}
		return ft;
	}

	public static int[] buildFenwick(int n, int v) {
		int[] ft = new int[n + 1];
		Arrays.fill(ft, 1, n + 1, v);
		for (int k = 2, h = 1; k <= n; k *= 2, h *= 2) {
			for (int i = k; i <= n; i += k) {
				ft[i] += ft[i - h];
			}
		}
		return ft;
	}

	
	public static int[][] constructMagicSquare(int n)
	{
		if(n < 0)throw new RuntimeException();
		if(n % 4 == 0){
			// 4m
			return constructX4(n);
		}else if(n % 2 == 1){
			// 2m+1
			return constructBySiameseMethod(n);
		}else{
			// 4m+2
			return constructByLUXMethod(constructBySiameseMethod(n/2));
		}
	}
	
	public static int[][] panmagicX4(int n, int want)
	{
		int[][] ret = new int[n][n];
		for(int i = 0;i < n;i++){
			for(int j = 0;j < n;j++){
				int A = i%2 == 0 ? 
						(j < n/2 ? 1+j : n-(j-n/2)) :
						(j < n/2 ? n-j : 1+(j-n/2));
				int B = j%2 == 0 ? 
						(i < n/2 ? n/2+1+i : n/2-(i-n/2)) :
						(i < n/2 ? n/2-i : n/2+1+(i-n/2));
				ret[i][j] = A + n * B - n;
			}
		}
		int base = 0;
		for(int i = 0;i < n;i++){
			for(int j = 0;j < n;j++){
				if(ret[i][j] == n*n){
					base ^= (i^j)&1;
				}
			}
		}
		for(int j = 0;j < n;j++){
			for(int k = 0;k < n;k++){
				int[][] nret = new int[n][n];
				for(int i = 0;i < n;i++){
					for(int l = 0;l < n;l++){
						nret[(i+j)%n][(k+l)%n] = ret[i][l];
					}
				}
				if(!ismagic(nret))throw new RuntimeException();
				if(want == (parity(nret)^base^((j^k)&1))){
					return nret;
				}
			}
		}
		throw new RuntimeException();
	}
	
	public static int[][] constructX4(int n)
	{
		if(n < 0 || n % 4 != 0)throw new RuntimeException();
		int[][] ret = new int[n][n];
		for(int i = 0;i < n;i++){
			for(int j = 0;j < n;j++){
				int p = (i^j)&3;
				if(p == 0 || p == 3){
					ret[i][j] = i*n+j+1;
				}else{
					ret[i][j] = n*n-(i*n+j);
				}
			}
		}
		return ret;
	}
	
	public static int[][] constructByLUXMethod(int[][] a)
	{
		int n = a.length;
		if(n <= 0 || n % 2 == 0)throw new RuntimeException();
		int[][] ret = new int[2*n][2*n];
		for(int i = 0;i < n;i++){
			for(int j = 0;j < n;j++){
				int base = a[i][j]-1<<2;
				if(i > n/2+1){
					// X
					ret[i*2][j*2] = base + 1;
					ret[i*2][j*2+1] = base + 4;
					ret[i*2+1][j*2] = base + 3;
					ret[i*2+1][j*2+1] = base + 2;
				}else if(j != n/2 && i <= n/2 || j == n/2 && i <= n/2+1 && i != n/2){
					// L
					ret[i*2][j*2] = base + 4;
					ret[i*2][j*2+1] = base + 1;
					ret[i*2+1][j*2] = base + 2;
					ret[i*2+1][j*2+1] = base + 3;
				}else{
					// U
					ret[i*2][j*2] = base + 1;
					ret[i*2][j*2+1] = base + 4;
					ret[i*2+1][j*2] = base + 2;
					ret[i*2+1][j*2+1] = base + 3;
				}
			}
		}
		return ret;
	}
	
	// val(i,j)=n*((i+j+1+n/2))%n)+(i+2*j+1)%n+1 TODO
	public static int[][] constructBySiameseMethod(int n)
	{
		if(n <= 0 || n % 2 == 0)throw new RuntimeException();
		int[][] ret = new int[n][n];
		int r = 0, c = n/2;
		for(int i = 1;i <= n*n;i++){
			ret[r][c] = i;
			int nr = r-1, nc = c+1;
			if(nr < 0)nr += n;
			if(nc >= n)nc -= n;
			if(ret[nr][nc] != 0){
				nr = r+1; nc = c;
				if(nr >= n)nr -= n;
			}
			r = nr; c = nc;
		}
		return ret;
	}
	
	public static boolean check(int[][] a)
	{
		int n = a.length;
		int[] f = new int[n*n+1];
		for(int i = 0;i < n;i++){
			for(int j = 0;j < n;j++){
				if(a[i][j] < 0 || a[i][j] > n*n)return false;
				if(++f[a[i][j]] > 1)return false;
			}
		}
		int base = n*(n*n+1)/2;
		// row
		for(int i = 0;i < n;i++){
			int s = 0;
			for(int j = 0;j < n;j++)s += a[i][j];
			if(s != base)return false;
		}
		// col
		for(int i = 0;i < n;i++){
			int s = 0;
			for(int j = 0;j < n;j++)s += a[j][i];
			if(s != base)return false;
		}
		// diagonal
		{
			int s = 0;
			for(int j = 0;j < n;j++)s += a[j][j];
			if(s != base)return false;
		}
		{
			int s = 0;
			for(int j = 0;j < n;j++)s += a[n-1-j][j];
			if(s != base)return false;
		}
		return true;
	}
	
	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 Q664_3().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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結果

テストケース

ソースコード