Backtracking algorithms are like problem-solving strategies that help explore different options to find the best solution. They work by trying out different paths and if one doesn’t work, they backtrack and try another until they find the right one. It’s like solving a puzzle by testing different pieces until they fit together perfectly.

Backtracking

What is Backtracking Algorithm?

Backtracking is a problem-solving algorithmic technique that involves finding a solution incrementally by trying different options and undoing them if they lead to a dead end.

It is commonly used in situations where you need to explore multiple possibilities to solve a problem, like searching for a path in a maze or solving puzzles like Sudoku. When a dead end is reached, the algorithm backtracks to the previous decision point and explores a different path until a solution is found or all possibilities have been exhausted.

How Does a Backtracking Algorithm Work?

A backtracking algorithm works by recursively exploring all possible solutions to a problem. It starts by choosing an initial solution, and then it explores all possible extensions of that solution. If an extension leads to a solution, the algorithm returns that solution. If an extension does not lead to a solution, the algorithm backtracks to the previous solution and tries a different extension.

The following is a general outline of how a backtracking algorithm works:

1. Choose an initial solution.
2. Explore all possible extensions of the current solution.
3. If an extension leads to a solution, return that solution.
4. If an extension does not lead to a solution, backtrack to the previous solution and try a different extension.
5. Repeat steps 2-4 until all possible solutions have been explored.

Example of Backtracking Algorithm

Example: Finding the shortest path through a maze

Input: A maze represented as a 2D array, where 0 represents an open space and 1 represents a wall.

Algorithm:

1. Start at the starting point.
2. For each of the four possible directions (up, down, left, right), try moving in that direction.
3. If moving in that direction leads to the ending point, return the path taken.
4. If moving in that direction does not lead to the ending point, backtrack to the previous position and try a different direction.
5. Repeat steps 2-4 until the ending point is reached or all possible paths have been explored.

When to Use a Backtracking Algorithm?

Backtracking algorithms are best used to solve problems that have the following characteristics:

• There are multiple possible solutions to the problem.
• The problem can be broken down into smaller subproblems.
• The subproblems can be solved independently.

Applications of Backtracking Algorithm

Backtracking algorithms are used in a wide variety of applications, including:

• Solving puzzles (e.g., Sudoku, crossword puzzles)
• Finding the shortest path through a maze
• Scheduling problems
• Resource allocation problems
• Network optimization problems

Basic of Backtracking Algorithm:

• Introduction to Backtracking – Data Structure and Algorithm Tutorials
• Difference between Backtracking and Branch-N-Bound technique
• What is the difference between Backtracking and Recursion?

Standard Problems on Backtracking Algorithm:

• The Knight’s tour problem
• Rat in a Maze
• N Queen Problem | Backtracking-3
• Subset Sum problem
• m Coloring Problem
• Hamiltonian Cycle
• Sudoku | Backtracking-7
• Magnet Puzzle
• Remove Invalid Parentheses
• A backtracking approach to generate n bit Gray Codes
• Write a program to print all permutations of a given string

Easy Problems on Backtracking Algorithm:

• Backtracking to find all subsets
• Check if a given string is sum-string
• Count all possible paths between two vertices
• Find all distinct subsets of a given set
• Find if there is a path of more than k length from a source
• Print all paths from a given source to a destination
• Print all possible strings that can be made by placing spaces

Medium Problems on Backtracking Algorithm:

• Tug of War
• 8 queen problem
• Combinational Sum
• Warnsdorff’s algorithm for Knight’s tour problem
• Find paths from corner cell to middle cell in maze
• Find Maximum number possible by doing at-most K swaps
• Rat in a Maze with multiple steps or jump allowed
• N Queen in O(n) space

Hard Problems on Backtracking Algorithm:

• Power Set in Lexicographic order
• Word Break Problem using Backtracking
• Partition of a set into K subsets with equal sum
• Longest Possible Route in a Matrix with Hurdles
• Find shortest safe route in a path with landmines
• Print all palindromic partitions of a string
• Printing all solutions in N-Queen Problem
• Print all longest common sub-sequences in lexicographical order

Quick Links :

• Learn Data Structure and Algorithms | DSA Tutorial
• Top 20 Backtracking Algorithm Interview Questions
• ‘Practice Problems’ on Backtracking
• ‘Quiz’ on Backtracking
• ‘Videos’ on Backtracking