# Understanding Backtracking

Backtracking is a general algorithmic technique that involves exploring all possible solutions by incrementally building candidates and abandoning a candidate ("backtracking") as soon as it determines that the candidate cannot lead to a valid solution. This technique is particularly useful for solving problems that involve searching for a combination or permutation of elements, such as puzzles, constraint satisfaction problems, and combinatorial optimization problems.

**Process**

**Initialization**: Start by defining the problem space and initializing the candidate solution.**Recursive Exploration**: Recursively explore each possible choice or move that can be made from the current state.**Constraint Checking**: At each step, check if the current candidate satisfies all the problem constraints. If it does, continue exploring further choices.**Backtracking**: If the current candidate does not satisfy the constraints or leads to an invalid solution, backtrack to the previous state and explore other possible choices.**Termination**: The process terminates when all possible solutions have been explored or when a valid solution is found.

### When to Use

**Combinatorial Problems**: To solve problems that involve finding combinations or permutations of elements.**Constraint Satisfaction Problems**: To solve problems where the goal is to find a solution that satisfies a set of constraints.**Puzzles and Games**: Solve puzzles like Sudoku, N-Queens, and the Knight's Tour.

### How Does It Reduce Time Complexity?

**Prune Invalid Paths**: By abandoning invalid candidates early, backtracking reduces the number of unnecessary computations, effectively pruning the search space.**Exhaustive Search**: Despite being an exhaustive search technique, backtracking can be more efficient than brute force methods by avoiding exploring paths that cannot lead to a solution.

### Example problems for better understanding

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