# Basic CS-Data Structures [Redpine Infotech Placement]: Sample Questions 3 - 3 of 4

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## Question 3

Data Structures

### Explanation

- 8 queen problem can solved by using back tracking method.
- Back tracking is used to solving the problems like puzzles.
- Search path is followed and the algorithm backtracks at a particular point in the path.
- The backtracking happens when algorithm realizes path will not lead to a valid solution and then it follows another path starting from a previous decision point.

## Ex. Of 8 Queen Problem

- Eight queen puzzle is the problem of placing eight chess queens on an chessboard.
- A solution required that no two queen share the same row, column, or diagonal.
- Strategy: the rows and columns are numbered through 1 to 8.
- Each queen is put on a different row without loss, we assume queen i is to be placed on row i.
- 8 tuple () , where is the column queen i is placed.

## Implicit Constraints Are

- No two can be the same that is, all queens must be on different column.
- No two queens can be on the same diagonal.
- Reduce the size of space from 8- tuples.
- First solution is (4, 6 , 8 , 2, 7,6, 3,5)

- Second solution is (3, 7, 1, 5, 8,2, 4,6)