Backtracking is called so because it involves exploring possible solutions to a problem by incrementally building candidates and abandoning them ("backtracking") as soon as it is determined that they cannot lead to a valid solution. This method is akin to navigating a maze: you move forward along a path until you hit a dead end, at which point you backtrack to the previous decision point and try a different path.
Here are the key points that explain why it is called backtracking:
Incremental Solution Building: The algorithm builds a solution step by step, adding one piece at a time. If at any point it becomes clear that the current path cannot lead to a valid solution, the algorithm abandons that path and backtracks to the previous step to try a different option[1][2][5].
Recursive Nature: Backtracking algorithms typically use recursion to explore all possible solutions. When a partial solution is found to be invalid, the recursive call returns, effectively backtracking to the previous state[1][3][6].
State-Space Tree: The process can be visualized using a state-space tree, where each node represents a partial solution. The algorithm traverses this tree in a depth-first manner, backtracking whenever it encounters a node that cannot lead to a valid solution[1][4][7].
Constraint Satisfaction: Backtracking is particularly useful for problems with constraints, such as the N-Queens...
