Cracking the Coding Interview, 4 Edition - 150 Programming Interview Questions and Solutions

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
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 }
1 7 7
Cracking the Coding Interview | Concepts and Algorithms