import java.awt.*;
import java.util.*;
import javax.swing.JButton;

/**
 * @author rpj
 * @version 14iii09
 *
 */
public class PartialSquare  {
        // size and numCells need to be static so the extensions know the dimensions
        private static int size;  // size of magic square. 
        private static int numCells; // number of cells in magic square (size*size)
        private Vector<Integer> myNums;
        public PartialSquare(int theSize) {
                // create an empty partial square 
                size = theSize;
                numCells = size * size;
                myNums = new Vector<Integer>();
        }
        private PartialSquare(Vector<Integer> itsNums) {
                // create a partial square from an existing vector
                // Note: this constructor cannot be called from outside!
                myNums = new Vector<Integer>();
                for (int i:itsNums) extend(i);
        }
        public Vector<PartialSquare> successors() {
                Vector<PartialSquare> retValue = new Vector<PartialSquare>();
                if (myNums.size() != numCells)  { // generate all the successors
                        PartialSquare aCandidate;
                        for (int i=1; i<numCells+1; i++) {
                            aCandidate = new PartialSquare(myNums); // copy me
                            aCandidate.extend(i);
                            retValue.add(aCandidate);
                        }
                }
                return retValue;        
        }
        public boolean success() {
                if (myNums.size() < numCells) return false;

                if ((new TreeSet<Integer>(myNums)).size() < myNums.size()) return false;
                int firstRowSum = 0;
                for (int i = 0; i < size; i++) firstRowSum += myNums.elementAt(i);
                // check other rows
                int sum;
                for (int row = 1; row < size; row++) {
                        sum = 0;
                        for (int i = size*row; i < size*(row+1); i++) 
                                sum += myNums.elementAt(i);
                        if (sum != firstRowSum) return false;
                }
                // check columns

                for (int col = 0; col < size; col++) {
                        sum = 0;
                        for (int i = col; i < numCells; i+= size) 
                                sum += myNums.elementAt(i);
                        if (sum != firstRowSum) return false;
                }
                
                // check topleft-bottomright diagonal
                sum = 0;
                for (int i = 0; i < numCells; i += size+1) 
                        sum += myNums.elementAt(i);
                if (sum != firstRowSum) return false;
                
                // check other diagonal
                sum = 0;
                for (int i = size-1; i < numCells-size+1; i += size-1) 
                        sum += myNums.elementAt(i);
                if (sum != firstRowSum) return false;
                
                // all tests passed, so
                return true;
                
        }
        private void extend(int i) {  // Note private!
                myNums.add(i);  
        }
        
        public Vector<Integer> getNums() { // so the caller can display me
                return myNums;
        }
}