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 04:23:46 |
| 言語 | Java (openjdk 23) |
| 結果 |
WA
|
| 実行時間 | - |
| コード長 | 8,617 bytes |
| コンパイル時間 | 4,431 ms |
| コンパイル使用メモリ | 88,872 KB |
| 実行使用メモリ | 51,292 KB |
| 最終ジャッジ日時 | 2024-12-26 06:28:06 |
| 合計ジャッジ時間 | 10,462 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge2 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | AC * 17 WA * 11 RE * 11 |
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;
}
assert !(n % 2 == 0 && parity == 1);
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][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)); }
}