Find a solution to the problem of the 8 queens that is different from that given in Figure 12.9

Find a solution to the problem of the 8 queens that is...

Key Concepts

Backtracking Algorithm

The backtracking algorithm is a systematic method for exploring all possible configurations of a problem by incrementally building candidates to the solutions and abandoning a candidate as soon as it is determined that it cannot lead to a valid solution. This approach is particularly useful for problems like the N-Queens Problem, where it efficiently navigates the search space by recursively placing queens and retracting placements when a conflict is detected.

Constraint Satisfaction

Constraint satisfaction involves solving problems by ensuring that a set of conditions or constraints is met. In the context of the N-Queens Problem, each queen must be placed in such a way that it satisfies the constraints of not being able to share a row, column, or diagonal with another queen. This concept is fundamental in fields such as artificial intelligence and operations research.

N-Queens Problem

The N-Queens Problem is a classic combinatorial puzzle that involves placing N queens on an N×N chessboard so that no two queens threaten each other. This means that no two queens share the same row, column, or diagonal. It serves as an important example in the study of recursion, backtracking, and constraint satisfaction problems in computer science and mathematics.

Transcript

0:00 Hello.

00:02 For problem 20, you're asked to write a program that will display all of the solutions to the eight queens puzzle.

00:13 So if you solved exercise 18, you found one solution.

00:19 And depending on how you wrote your program for problem 18, you might have to make some modifications.

00:25 I know i did.

00:27 So we'll start with defining an implementation.

00:30 List here of results which will hold all of the results.

00:35 We of course need to determine whether or not a queen can be placed in any given place.

00:42 So i've started by writing a function here called attack that determines if a queen placed on the board is in danger of attack.

00:51 We first checked vertically and horizontally to see if there are other queens on the board either in the vertical or horizontal direction.

01:02 And if there are, then you return true.

01:06 So it's true that you're in danger of attack.

01:10 And we'll do the same diagonally.

01:12 So we'll check the diagonals and see if there is a queen.

01:17 If there is a queen, we will again return.

01:20 That means that that location on the board is equal to one.

01:23 We'll return true.

01:25 If nothing is true, then we'll return false.

01:29 Indicating that the queen is not in danger of attack.

01:34 For solving the puzzle itself, we want to use a backtracking type method.

01:42 So for our given board, we will place a queen in a column and then we'll try all of the rows...

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