#51108 (Java21) No.283 スライドパズルと魔方陣

• 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 04:37:00
• 言語: Java21 (openjdk 21)
• 結果: WA
• 実行時間: -
• コード長: 8,660 bytes
• コンパイル時間: 4,133 ms
• コンパイル使用メモリ: 89,436 KB
• 実行使用メモリ: 52,616 KB
• 最終ジャッジ日時: 2024-06-07 21:08:45
• 合計ジャッジ時間: 9,707 ms
• ジャッジサーバーID （参考情報）: judge3 / judge4

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	53 ms; 50,508 KB
testcase_01	AC	52 ms; 50,528 KB
testcase_02	AC	53 ms; 50,464 KB
testcase_03	WA	-
testcase_04	WA	-
testcase_05	AC	53 ms; 50,280 KB
testcase_06	WA	-
testcase_07	WA	-
testcase_08	WA	-
testcase_09	AC	51 ms; 50,336 KB
testcase_10	WA	-
testcase_11	AC	53 ms; 50,552 KB
testcase_12	WA	-
testcase_13	AC	51 ms; 50,516 KB
testcase_14	WA	-
testcase_15	AC	53 ms; 50,448 KB
testcase_16	AC	52 ms; 50,248 KB
testcase_17	WA	-
testcase_18	WA	-
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	AC	80 ms; 51,016 KB
testcase_33	WA	-
testcase_34	AC	84 ms; 51,104 KB
testcase_35	WA	-
testcase_36	AC	84 ms; 51,304 KB
testcase_37	WA	-
testcase_38	WA	-

ソースコード

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.InputMismatchException;

public class Q664_2 {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	
	void solve()
	{
		int n = ni();
		int[] a = na(n*n);
		for(int i = 0;i < n*n;i++){
			if(a[i] == 0)a[i] = n*n;
		}
		long parity = inversion(a) % 2;
		
		if(n == 1){
			out.println("possible");
			out.println(1);
			return;
		}
		if(n == 2){
			out.println("impossible");
			return;
		}
		if(n % 4 != 3 && parity == 1){
			out.println("impossible");
			return;
		}
		out.println("possible");
		
		int[][] ms = constructMagicSquare(n);
		int[] b = new int[n*n];
		for(int i = 0;i < n;i++){
			for(int j = 0;j < n;j++){
				b[i*n+j] = ms[i][n-1-j];
			}
		}
		if(inversion(b) % 2 == parity){
			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();
			}
		}else{
			for(int i = 0;i < n;i++){
				for(int j = 0;j < n;j++){
					if(j > 0)out.print(" ");
					out.print(ms[i][n-1-j]);
				}
				out.println();
			}
		}
	}
	
	public static long inversion(int[] a)
	{
		int n = a.length;
		int[] b = shrink(a);
		int[] ft = new int[n+1];
		long inv = 0;
		for(int i = n-1;i >= 0;i--){
			inv += sumFenwick(ft, b[i]-1);
			addFenwick(ft, b[i], 1);
		}
		return inv;
	}
	
	public static int[] shrink(int[] a)
	{
		int n = a.length;
		long[] b = new long[n];
		for(int i = 0;i < n;i++)b[i] = (long)a[i]<<32|i;
		Arrays.sort(b);
		int[] ret = new int[n];
		int p = 0;
		for(int i = 0;i < n;i++) {
			if(i>0 && (b[i]^b[i-1])>>32!=0)p++;
			ret[(int)b[i]] = p;
		}
		return ret;
	}

	
	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[][] 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_2().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)); }
}