Computer Science
Grade 11
20 min
Backtracking
Backtracking
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Define backtracking as a problem-solving technique.
Identify problems that are suitable for a backtracking approach, such as constraint satisfaction and pathfinding problems.
Visualize the problem-solving process as a state-space tree.
Implement a recursive backtracking algorithm using the 'choose, explore, un-choose' pattern.
Trace the execution of a backtracking algorithm on a small-scale problem like the N-Queens problem or generating permutations.
Explain how pruning the state-space tree improves the efficiency of a backtracking algorithm.
Ever tried to solve a Sudoku or a maze and hit a dead end? 🤔 Backtracking is how a computer can intelligently 'undo' its last move and try another path until it finds the solution!
This tutoria...
2
Key Concepts & Vocabulary
TermDefinitionExample
BacktrackingAn algorithmic technique for solving problems recursively by trying to build a solution piece by piece, abandoning a path as soon as it is determined that it cannot possibly lead to a valid solution.In a Sudoku solver, if placing a '5' in a cell leads to a state where another cell has no valid numbers, the algorithm backtracks by removing the '5' and trying the next possible number in the original cell.
State-Space TreeA conceptual tree representing all possible states or configurations of a problem. The root is the initial state, and each path from the root to a leaf represents a potential solution sequence.For generating permutations of {A, B}, the root is an empty set. The first level has nodes for 'A' and 'B'. F...
3
Core Syntax & Patterns
The Backtracking Algorithm Template
function backtrack(candidate_solution):
if is_a_solution(candidate_solution):
process_solution(candidate_solution)
return
for next_choice in list_of_choices:
if is_valid(next_choice):
place(next_choice) // Choose
backtrack(new_candidate) // Explore
remove(next_choice) // Un-choose
This pseudocode represents the fundamental structure of most backtracking algorithms. It checks for a solution, then iterates through valid choices, recursively explores each one, and crucially, undoes the choice to allow exploration of other paths.
Choose, Explore, Un-choose Pattern
1. Make a choice.
2. Recurse (explore).
3. Undo the choice (backtrack).
This is the core mantra of backtracking. You must always undo your choice a...
4 more steps in this tutorial
Sign up free to access the complete tutorial with worked examples and practice.
Sign Up Free to ContinueSample Practice Questions
Challenging
You need to modify the standard backtracking template to find only the *first* solution to a problem and then stop immediately. How should the template be changed?
A.The function should return a boolean. It returns `true` after processing a solution, and this return value is checked after each recursive call to stop the loops.
B.Add a global counter that is incremented when a solution is found, and add `if (counter > 0) return;` at the start of the function.
C.Remove the `is_valid` check to make the algorithm run faster.
D.Change the `for` loop to a `while` loop.
Challenging
A student implements the 4-Queens solver, but their `is_valid` check only verifies that no two queens are in the same row or column; it completely forgets to check diagonals. Which of the following invalid arrangements might their program output as a 'solution'?
A.Queens at (0,0), (1,1), (2,2), (3,3)
B.Queens at (0,1), (1,3), (2,0), (3,2)
C.Queens at (0,0), (0,1), (0,2), (0,3)
D.Queens at (0,0), (1,0), (2,0), (3,0)
Challenging
When generating permutations of N unique items, what is the most efficient way to implement the constraint check (i.e., to see if an item has already been used in the current permutation)?
A.Before adding an item, iterate through the entire current permutation list to see if the item exists.
B.Maintain a separate boolean array or hash set to track used items, allowing for an O(1) lookup.
C.After adding an item, check for duplicates and then remove it if the check fails.
D.Generate all possible permutations first, then filter out the ones with duplicate items.
Want to practice and check your answers?
Sign up to access all questions with instant feedback, explanations, and progress tracking.
Start Practicing Free