# Backtracking

##### What is Backtracking?

Recur­sion is the key in back­track­ing pro­gram­ming. As the name sug­gests we back­track to find the solution. In backtracking, we start with one possible option out of many available options and try to solve the problem if we are able to solve the problem with the selected move then we will print the solution else we will backtrack and select some other option and try to solve it and so on. If none if the options work out we will claim that there is no solution for the problem.

Backtracking is a form of recursion. The usual scenario is that you are faced with a number of options, and you must choose one of these. After you make your choice you will get a new set of options; just what set of options you get depends on what choice you made. This procedure is repeated over and over until you reach a final state. If you made a good sequence of choices, your final state is a goal state; if you didn’t, it isn’t.

Backtracking can be thought of as a selective tree/graph traversal method. The tree is a way of representing some initial starting position (the root node) and a final goal state (one of the leaves). Backtracking allows us to deal with situations in which a raw brute-force approach would explode into an impossible number of options to consider. Backtracking is a sort of refined brute force. At each node, we eliminate choices that are obviously not possible and proceed to recursively check only those that have potential.

###### Example Algorithms of Backtracking
1. N Queens Problem
2. Sudoku
3. The Knapsack Problem
4. Graph Coloring Problem
5. Hamiltonian Cycles.
Backtracking

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