Backtracking Algorithms
⏱ Estimated reading time: 2 min
Backtracking Algorithms
Backtracking is a systematic way of trying out different sequences of decisions until you find one that "works". It is used to solve problems that require exploring all possible configurations.
Key Idea
Build the solution incrementally and abandon a path ("backtrack") as soon as it is determined that it cannot lead to a valid solution.
Steps in Backtracking
- Choose – Make a choice at each step.
- Explore – Recur to explore further choices.
- Unchoose – If the choice leads to failure, undo it and try another.
Examples of Backtracking Problems
1. N-Queens Problem
Place N queens on an N×N chessboard so that no two queens attack each other.
2. Sudoku Solver
Fill a 9×9 Sudoku grid so that each row, column, and subgrid contains digits 1–9 exactly once.
3. Rat in a Maze
Find a path from the start to the destination in a maze.
4. Subset Sum Problem
Find all subsets of a given set that sum up to a specific value.
5. Hamiltonian Path / Graph Coloring
Used in graph traversal and optimization problems.
Advantages
- Finds all possible solutions, not just one.
- Elegant recursive approach.
Disadvantages
- High time complexity (exponential).
- May require pruning to optimize.
Example (Pseudo Code – N Queens)
def solveNQueens(board, row):
if row == N:
print(board)
return
for col in range(N):
if isSafe(board, row, col):
board[row][col] = 1
solveNQueens(board, row + 1)
board[row][col] = 0 # backtrack
Conclusion
Backtracking is a powerful strategy for constraint satisfaction problems. With proper pruning (like using heuristics), it can efficiently find optimal or valid solutions.
Register Now
Share this Post
← Back to Tutorials