/**
 * Solve the Instant Insanity puzzle.  Four cubes have sides colored red, green,
 * blue, and white.  The object is to arrange them into a tower so that each side
 * of the tower has exactly one of each color.
 * 
 * This version prunes by testing each placement for validity before going on.
 * It also tests "buried" colors to make sure that a solution is still possible.
 * 
 * Based on an earlier C++ version that Scot Drysdale wrote for CS 15.
 * 
 * @author Scot Drysdale
 */
public class Insane3 {
  private static int numPlacements;
  private static int validityTests;
  
	/**
	 * Performs the backtracking by placing cube number "cubeNum" in all possible 
	 *   positions.  This version rejects a placement if it conflicts with earlier
	 *   cube placements or has too many of a given color buried (appearing on
	 *   the top or bottom face of a placed cube).
	 * @param cubes the stack of cubes to place in all positions
	 * @param cubeNo the cube currently being placed
	 */
	public static void PlaceCube(CubeTower cubes, int cubeNo) {
    numPlacements++;  // Count another cube placed
    
		if (cubeNo > CubeTower.NUMCUBES) {	// All cubes placed?
		  System.out.println(cubes);
		}
		else {
			for (int tips = 1; tips <= 3; tips++)	{	 // For each of three top-bottom pairs

				cubes.bury(cubeNo);		// Bury top and bottom colors of current cube
				
				if (cubes.buriedOK()) {
					if (cubeNo == 1) {			// First cube has 3 non-symetric positions
						validityTests++;
						if(cubes.isValid(cubeNo))
							PlaceCube(cubes, cubeNo+1);
					}
					else  {								// Other cubes have 24 possible positions
						for (int rot = 1; rot <= 4; rot++) {	// For each of 4 rotation positions
							validityTests++;
							if(cubes.isValid(cubeNo))
								PlaceCube(cubes, cubeNo+1);
							cubes.rotate(cubeNo);
						}

						cubes.flip(cubeNo);

						for (int rot = 1; rot <= 4; rot++) {	// For each of 4 rotation positions
							validityTests++;
							if(cubes.isValid(cubeNo))
								PlaceCube(cubes, cubeNo+1);
							cubes.rotate(cubeNo);
						}

						cubes.flip(cubeNo);				// Get back to original position
					}
				}

				cubes.unbury(cubeNo);				// Different set of faces will be buried
				cubes.rotate(cubeNo);
				cubes.tip(cubeNo);					// Get a different top-bottom pair
			}
		}
	}


	public static void main(String [] args) {
		CubeTower cubes = new CubeTower();	// Stack of cubes to place

    numPlacements = 0;							// Count nodes examined
    validityTests = 0;              // Count validity tests made

		PlaceCube(cubes, 1);
		
		System.out.println("Number of cube placements: " + numPlacements +
				"\nNumber of validity tests: " + validityTests);
	}
}