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<title>Backtracking Algorithm</title>
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<h1>Backtracking Algorithm</h1>
<p class="editor-contents__short-description">In this tutorial, you will learn what a backtracking algorithm is. Also, you will find an example of a backtracking approach.</p>
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<p id="definition">A backtracking algorithm is a problem-solving algorithm that uses a <strong>brute force approach</strong> for finding the desired output.</p>
<p class="note-tip">The Brute force approach tries out all the possible solutions and chooses the desired/best solutions.</p>
<p>The term backtracking suggests that if the current solution is not suitable, then backtrack and try other solutions. Thus, recursion is used in this approach.</p>
<p>This approach is used to solve problems that have multiple solutions. If you want an optimal solution, you must go for <a href="/dsa/dynamic-programming.html">dynamic programming</a>.</p>
<hr><h2 id="tree">State Space Tree</h2>
<p>A space state tree is a tree representing all the possible states (solution or nonsolution) of the problem from the root as an initial state to the leaf as a terminal state.</p>
<figure><img alt="State Space Tree" src="//cdn.programiz.com/sites/tutorial2program/files/ba-state-space-tree.png" title="State Space Tree" width="422" height="263"><figcaption>State Space Tree</figcaption></figure><hr><h2 id="algorithm">Backtracking Algorithm</h2>
<pre>Backtrack(x)
if x is not a solution
return false
if x is a new solution
add to list of solutions
backtrack(expand x)</pre>
<hr><h2 id="example">Example Backtracking Approach</h2>
<p>Problem: You want to find all the possible ways of arranging 2 boys and 1 girl on 3 benches. Constraint: Girl should not be on the middle bench.</p>
<p></p><div class="clearfix"></div><p>Solution: There are a total of 3! = 6 possibilities. We will try all the possibilities and get the possible solutions. We recursively try all the possibilities.</p>
<p>All the possibilities are:</p>
<figure><img alt="All the possibilities" src="//cdn.programiz.com/sites/tutorial2program/files/ba-possibilities.png" title="All possibilities" width="312" height="184"><figcaption>All the possibilities</figcaption></figure><p>The following <a href="http://None">state space tree</a> shows the possible solutions.</p>
<figure><img alt="State state tree" src="//cdn.programiz.com/sites/tutorial2program/files/ba-state-state-tree-example.png" title="State state tree" width="213" height="281"><figcaption>State tree with all the solutions</figcaption></figure><hr><h2 id="applications">Backtracking Algorithm Applications</h2>
<ol><li>To find all <a href="https://en.wikipedia.org/wiki/Hamiltonian_path_problem" target="_blank">Hamiltonian Paths</a> present in a graph.</li>
<li>To solve the <a href="https://en.wikipedia.org/wiki/Eight_queens_puzzle" target="_blank">N Queen problem</a>.</li>
<li><a href="https://en.wikipedia.org/wiki/Maze_solving_algorithm" target="_blank">Maze solving problem</a>.</li>
<li><a href="https://en.wikipedia.org/wiki/Knight%27s_tour" target="_blank">The Knight's tour problem</a>.</li>
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<li><a href="#tree">State Space Tree</a></li>
<li><a href="#algorithm">Backtracking Algorithm</a></li>
<li><a href="#example">Example Backtracking Approach</a></li>
<li><a href="#applications">Backtracking Algorithm Applications</a></li>
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