public Board(int[][] blocks) // construct a board from an N-by-N array of blocks

// (where blocks[i][j] = block in row i, column j)

public int dimension() // board dimension N

public int hamming() // number of blocks out of place

public int manhattan() // sum of Manhattan distances between blocks and goal

public boolean isGoal() // is this board the goal board?

public Board twin() // a board obtained by exchanging two adjacent blocks in the same row

public boolean equals(Object y) // does this board equal y?

public Iterable<Board> neighbors() // all neighboring boards

public String toString() // string representation of the board (in the output format specified below)

}