Cracking the Coding Interview - Fooo

Solutions to Chapter 8 | Recursion
8 8 Write an algorithm to print all ways of arranging eight queens on a chess board so
that none of them share the same row, column or diagonal
SOLUTION
1 7 7
Cracking the Coding Interview | Concepts and Algorithms
pg 64
We will use a backtracking algorithm For each row, the column where we want to put the
queen is based on checking that it does not violate the required condition
1 For this, we need to store the column of the queen in each row as soon as we have finalized
it Let ColumnForRow[] be the array which stores the column number for each row
2 The checks that are required for the three given conditions are:
» On same Column : ColumnForRow[i] == ColumnForRow[j]
» On same Diagonal: (ColumnForRow[i] - ColumnForRow[j] ) == ( i- j) or
(ColumnForRow[j] - ColumnForRow[i]) == (i - j)
1 int columnForRow[] = new int [8];
2 boolean check(int row) {
3 for (int i = 0; i < row; i++) {
4 int diff = Math.abs(columnForRow[i] - columnForRow[row]);
5 if (diff == 0 || diff == row - i) return false;
6 }
7 return true;
8 }
9
10 void PlaceQueen(int row){
11 if (row == 8) {
12 printBoard();
13 return;
14 }
15 for (int i = 0; i < 8; i++) {
16 columnForRow[row]=i;
17 if(check(row)){
18 PlaceQueen(row+1);
19 }
20 }
21 }