Backtracking Technique in DSA

What is the Backtracking Technique?

Backtracking is a recursive technique for solving problems incrementally, one piece at a time, and removing those solutions that fail to satisfy the problem's constraints as soon as possible. It is often used for constraint satisfaction problems like N-Queens, Sudoku Solver, Subset Sum, and Permutation Generation.

The basic idea is to build a solution step-by-step and go back ("backtrack") as soon as we determine that the current path cannot lead to a valid solution. It is essentially a depth-first search with pruning.

Key Characteristics of Backtracking

• Solves problems by exploring all potential candidates.
• Abandons a path as soon as it is determined to be invalid (pruning).
• Usually implemented recursively using DFS-style exploration.

General Backtracking Pseudocode

// Function to try all possible options
function backtrack(state):
    if isSolution(state):
        output(state)
        return

    for option in getOptions(state):
        if isValid(option, state):
            applyOption(state, option)
            backtrack(state)
            undoOption(state, option)

Explanation of Steps

• isSolution(state) — Check if the current state is a complete/valid solution.
• getOptions(state) — Generate all possible choices/options from the current state.
• isValid(option, state) — Check if the option is valid in the current state.
• applyOption(state, option) — Make the move (update state).
• undoOption(state, option) — Undo the move (backtrack to previous state).

Where is Backtracking Used?

• N-Queens Problem
• Sudoku Solver
• Generate All Subsets / Permutations
• Word Search in Grid
• Maze Path Finding
• Graph Coloring

Backtracking is powerful for problems with complex constraints and multiple solution paths. It’s particularly effective when combined with pruning techniques to skip unnecessary branches in the solution space.