Write an algorithm to print all ways of arranging eight queens on an 8*8 chess board so that none of them share the same row, column or diagonal.
思路：
本质上是DFS, 从第一行开始一行行地放棋子，每次放棋子之前根据当前的棋盘检查一下约束。
Code (from book)：
void placeQueen(int row, Integer[] columns, ArrayList<Integer[]> result){
if(row == GRID_SIZE){
result.add(columns.clone());
return;
}
for(int col = 0; col < GRID_SIZE; ++col){
if(checkValid(row, col, columns)){
columns[row] = col;
placeQueen(row + 1, columns, result);
}
}
}
// No need to check the same row because the program
// proceeds one row at a time
boolean checkValid(int row, int column, Integer[] columns){
for(int i = 0; i < row; ++i){
int j = columns[i];
// check the same column
if(column == j){
return false;
}
// check same diagonal
if(Math.abs(row - i) == Math.abs(column - j)){
return false;
}
}
return true;
}