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/* The Computer Language Shootout
http://shootout.alioth.debian.org/
benchmark implementation (not optimized)
JRE 1.5 only
contributed by Josh Goldfoot */
import java.io.*;
import java.lang.*;
import java.util.*;
public class magicsquares {
static int n;
static int mn;
public static class FfmResult {
public int x;
public int y;
public int[] moves;
public FfmResult(int ix, int iy, int[] imoves) {
x = ix;
y = iy;
moves = (int[]) imoves.clone();
}
}
public static class PQNode implements Comparable {
public int [] grid;
boolean priorityCalculated;
private int priority;
private FfmResult ffm;
public PQNode() {
grid = new int [n * n];
int i;
for (i = 0; i < n * n; i++)
grid[i] = 0;
priorityCalculated = false;
ffm = null;
}
public PQNode(PQNode other) {
grid = (int[]) other.grid.clone();
priorityCalculated = false;
}
public int[] gridRow(int y) {
int[] r = new int[n];
int x;
for (x = 0; x < n; x++)
r[x] = grid[x + y * n];
return r;
}
public int[] gridCol(int x) {
int[] r = new int[n];
int y;
for (y = 0; y < n; y++)
r[y] = grid[x + y * n];
return r;
}
public int[] diagonal(int q) {
int[] r = new int[n];
int i;
for (i = 0; i < n; i++) {
if (q == 1)
r[i] = grid[i + i * n];
else if (q == 2) {
r[i] = grid[i + (n - 1 - i) * n];
}
}
return r;
}
public int[] possibleMoves(int x, int y) {
int zerocount, sum, highest, j, i;
if (grid[x + y * n] != 0)
return ( new int [] { });
ArrayList<int[]> cellGroups = new ArrayList<int[]>();
cellGroups.add(gridCol(x));
cellGroups.add(gridRow(y));
if (x == y)
cellGroups.add(diagonal(1));
if (x + y == n - 1)
cellGroups.add(diagonal(2));
HashSet<Integer> usedNumbers = new HashSet<Integer>();
for (i = 0; i < grid.length; i++)
usedNumbers.add(new Integer(grid[i]));
HashSet<Integer> onePossible = new HashSet<Integer>();
highest = n * n;
for (int[] group: cellGroups) {
zerocount = 0;
sum = 0;
for (int num: group) {
if (num == 0)
zerocount++;
sum += num;
}
if (zerocount == 1)
onePossible.add(new Integer(mn - sum));
if (mn - sum < highest)
highest = mn - sum;
}
if (onePossible.size() == 1) {
Integer onlyPossibleMove = (Integer) onePossible.iterator().next();
int opmint = onlyPossibleMove.intValue();
if (opmint >= 1 &&
opmint <= n * n &&
! usedNumbers.contains(onlyPossibleMove))
return (new int[] { opmint });
else
return ( new int [] { });
} else if (onePossible.size() > 1)
return ( new int [] { });
ArrayList<Integer> moves = new ArrayList<Integer>();
for (i = 1; i <= highest; i++) {
Integer ii = new Integer(i);
if (! usedNumbers.contains(ii))
moves.add(ii);
}
int[] r = new int[moves.size()];
i = 0;
for (Integer move: moves) {
r[i++] = move.intValue();
}
return r;
}
public FfmResult findFewestMoves() {
if (ffm != null)
return ffm;
int x, y, mx, my, ind;
int[] minmoves = (new int[] { });
int[] moves;
mx = my = -1;
for (y = 0; y < n; y++)
for (x = 0; x < n; x++) {
ind = x + y * n;
if (grid[ind] == 0) {
moves = possibleMoves(x,y);
if (mx == -1 || moves.length < minmoves.length) {
mx = x;
my = y;
minmoves = (int[]) moves.clone();
}
}
}
ffm = new FfmResult(mx, my, minmoves);
return ffm;
}
public void calculatePriority()
{
int i, zerocount;
zerocount = 0;
for (int cell: grid)
if (cell == 0)
zerocount++;
priority = zerocount + findFewestMoves().moves.length;
priorityCalculated = true;
}
public int getPriority()
{
if (priorityCalculated)
return priority;
else {
calculatePriority();
return priority;
}
}
public int compareTo(Object anotherMSquare) throws ClassCastException {
if (!(anotherMSquare instanceof PQNode))
throw new ClassCastException();
PQNode other = (PQNode) anotherMSquare;
int c = getPriority() - other.getPriority();
if (c == 0) {
int i = 0;
while (c == 0 && i < n * n) {
c = grid[i] - other.grid[i];
i++;
}
}
return c;
}
public String toString() {
StringBuilder sb = new StringBuilder();
int y, x;
for (y = 0; y < n; y++) {
for (x = 0; x < n; x++) {
sb.append(grid[x + y * n]);
if (x < n-1)
sb.append(' ');
}
if (y < n-1)
sb.append('\n');
}
return sb.toString();
}
}
public magicsquares() { }
public static void main(String[] args) {
n = 3;
if (args.length > 0)
n = Integer.parseInt(args[0]);
mn = n * (1 + n * n) / 2;
PriorityQueue<magicsquares.PQNode> pq = new PriorityQueue<magicsquares.PQNode>();
pq.offer(new magicsquares.PQNode() );
while (! pq.isEmpty()) {
PQNode topSquare = pq.poll();
if (topSquare.getPriority() == 0) {
System.out.println(topSquare);
break;
}
magicsquares.FfmResult result = topSquare.findFewestMoves();
int ind = result.x + result.y * n;
for (int move: result.moves) {
magicsquares.PQNode newSquare = new magicsquares.PQNode(topSquare);
newSquare.grid[ind] = move;
pq.offer(newSquare);
}
}
}
}
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