Backtracking is a technique used to explore all possible solutions by trying one possibility at a time and undoing the last choice if it leads to a dead end. It's useful for constraint-satisfaction problems.

Backtracking is a fundamental technique in competitive programming for solving constraint-satisfaction problems, such as generating permutations, solving mazes, or finding solutions to the N-queens problem. The basic idea behind backtracking is to explore possible solutions incrementally, one step at a time, and to backtrack as soon as you realize that the current solution cannot lead to a valid or optimal answer. For example, in the N-queens problem, you place queens on a chessboard one by one. If placing a queen in a particular position leads to a conflict with previously placed queens, you backtrack by removing the last queen and trying the next possible position. The key to backtracking is identifying when you have made a wrong choice early so that you can avoid exploring invalid paths further. This pruning of the search space makes backtracking more efficient than brute force in many cases. However, backtracking can still be slow if there are many possibilities to explore, so it's important to combine it with other optimization techniques, such as memoization, when possible. Backtracking is particularly useful in problems where the solution space is large but can be efficiently pruned by discarding partial solutions that are not feasible, like in constraint satisfaction, combinatorial generation, and puzzle-solving problems.