// tile a defective chessboard

#include <iostream.h>
#include <iomanip.h>
#include <stdlib.h>

int Board[64][64], size, tile = 1;

void TileBoard(int tr, int tc, int dr, int dc, int size)
{// Tile a defective chessboard.
	if (size == 1) 
		return;
	int t = tile++,  // tile number to use
		s = size/2;  // quadrant size
	
	// tile top-left quadrant
	if (dr < tr + s && dc < tc + s)
		// defect is in this quadrant
		TileBoard(tr, tc, dr, dc, s);
	else 
	{// no defect in this quadrant
		// place tile t in bottom-right corner
		Board[tr + s - 1][tc + s - 1] = t;
		// tile the rest
		TileBoard(tr, tc, tr+s-1, tc+s-1, s);
	}
	
	// tile top-right quadrant
	if (dr < tr + s && dc >= tc + s)
		// defect is in this quadrant
		TileBoard(tr, tc+s, dr, dc, s);
	else 
	{// no defect in this quadrant
		// place tile t in bottom-left corner
		Board[tr + s - 1][tc + s] = t;
		// tile the rest
		TileBoard(tr, tc+s, tr+s-1, tc+s, s);
	}
	
	// tile bottom-left quadrant
	if (dr >= tr + s && dc < tc + s)
		// defect is in this quadrant
		TileBoard(tr+s, tc, dr, dc, s);
	else 
	{// place tile t in top-right corner
		Board[tr + s][tc + s - 1] = t;
		// tile the rest
		TileBoard(tr+s, tc, tr+s, tc+s-1, s);
	}
	
	// tile bottom-right quadrant
	if (dr >= tr + s && dc >= tc + s)
		// defect is in this quadrant
		TileBoard(tr+s, tc+s, dr, dc, s);
	else 
	{// place tile t in top-left corner
		Board[tr + s][tc + s] = t;
		// tile the rest
		TileBoard(tr+s, tc+s, tr+s, tc+s, s);
	}
}

void OutputBoard(int size)
{
	for (int i = 0; i < size; i++) 
	{
		for (int j = 0; j < size; j++)
			cout << setw (5) << Board[i][j];
		cout << endl;
	}
}

void main(void)
{
	int k, dr, dc;
	cout << "Enter k, board size is 2^k" << endl;
	cout << "k should be in the range 0 through 6" << endl;
	cin >> k;
	if (k < 0 || k > 6)
	{
		cerr << "k out of range" << endl;
		exit(1);
	}
	size = 1;
	for (int i = 1; i <= k; i++) size += size;
	cout << "Enter location of defect" << endl;
	cin >> dr >> dc;
	if (dr < 1 || dr > size || dc < 1 || dc >size) 
	{
		cerr << "Improper defect location" << endl;
		exit(1);
	}
	dr--; dc--;
	Board[dr][dc] = 0;
	TileBoard(0, 0, dr, dc, size);
	OutputBoard(size);
}