9.3 Backtracking
Backtracking is a very useful algorithmic technique that can solve a wide range of complex problems in a reasonable amount of time. It is commonly used in decision-making problems where the set of potential choices can be organized into a decision tree or graph.
The basic idea behind backtracking is to construct a solution one step at a time while checking to see if each step contributes to the overall solution. If a step does not contribute to the solution, it is removed, and the next step is attempted.
One great example of a problem that can be solved using backtracking is the N-Queens puzzle. This puzzle requires the placement of N queens on an NxN chessboard in such a way that no two queens threaten each other. This means that no two queens can be in the same row, column, or diagonal. By using backtracking, it is possible to find a solution to this problem.
Backtracking can also be used in other types of problems, such as finding the shortest path in a maze or...