結果
| 問題 |
No.283 スライドパズルと魔方陣
|
| コンテスト | |
| ユーザー |
 uwi
|
| 提出日時 | 2015-09-26 18:37:47 |
| 言語 | Java (openjdk 23) |
| 結果 |
RE
|
| 実行時間 | - |
| コード長 | 13,070 bytes |
| コンパイル時間 | 4,716 ms |
| コンパイル使用メモリ | 89,576 KB |
| 実行使用メモリ | 37,984 KB |
| 最終ジャッジ日時 | 2024-12-26 06:34:01 |
| 合計ジャッジ時間 | 11,175 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge2 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | AC * 38 RE * 1 |
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.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)); }
}