Backtracking Algorithm

The backtracking algorithm is a powerful technique used to solve problems that involve exploring a search space to find a solution. It is particularly useful for solving problems with constraints, such as puzzles like Sudoku or problems involving finding a valid configuration for a set of elements.

The key idea behind backtracking is to build a solution step by step and check if the current path can lead to a valid solution. If the current path is not promising, the algorithm undoes the last choice and tries a different option.

Here are the general steps involved in solving a problem using the backtracking algorithm:

1. Define the problem as a search space, where each node in the search space represents a potential solution.

2. Define the search space using a recursive function that explores each potential solution.

3. Implement the base case that defines when a potential solution is valid or not.

4. Implement the recursive case that explores the search space by making choices and checking if each choice leads to a valid solution.

5. Implement the backtracking step that undoes the last choice and tries a different option if the current path is not promising.

Now that we have a basic understanding of the backtracking algorithm, let's apply it to solve the Sudoku puzzle.

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#include <iostream>

using namespace std;

int main() {

  // Backtracking algorithm

​

  // Backtracking is a problem-solving technique that involves moving

  // backward in the search space to find a solution. It is based on

  // exhaustive searching and backtracking to explore all possible

  // solutions until a satisfactory solution is found or all possible

  // options have been exhausted.

​

  // The key idea behind backtracking is to build a solution one step

  // at a time and check if the current path can lead to a solution.

  // If the current path is not promising, the algorithm undoes the

  // last choice and tries a different option.

​

  // Backtracking is particularly useful for solving problems with

  // constraints, such as finding a solution to a Sudoku puzzle or

  // placing N queens on an N x N chessboard without any two queens

  // threatening each other.

​

  // The general steps in a backtracking algorithm are as follows:

​

  // 1. Define the problem as a search space, where each node in the

  //    search space represents a potential solution.

​

  // 2. Define the search space using a recursive function that

  //    explores each potential solution.

​