Backtracking: A Problem Solving Approach for Programming (ChooseUnchoose pattern)
Backtracking is a powerful technique used in solving combinatorial problems like generating permutations, combinations, subsets, and solving constraint satisfaction problems such as the NQueens problem, Sudoku, and more. In this post, we’ll break down the “chooseunchoose” paradigm of backtracking, provide a template code, and explain it with an example.
What is Backtracking?
Backtracking is a depthfirst search approach for solving problems incrementally, where we build a solution step by step and backtrack when we realize that a certain path doesn’t lead to a valid solution. The idea is to explore all possible configurations and prune the paths that do not satisfy the constraints.
The ChooseUnchoose Paradigm
The “chooseunchoose” paradigm is a common pattern used in backtracking algorithms. It consists of three steps:
 Choose: Make a choice from the available options.
 Recurse: Proceed with the choice and recursively solve the remaining problem.
 Unchoose: Undo the choice (i.e., backtrack) and try another option.
This pattern ensures that all possible solutions are explored, and it backtracks when a dead end is reached.
Template Code for Backtracking
Below is a template for a typical backtracking solution using the “chooseunchoose” paradigm:
function backtrack(solution, choices) {
// Base case: If the solution is complete or meets the problem requirements
if (isSolution(solution)) {
// Process the complete solution
processSolution(solution);
return;
}
// Iterate through all possible choices
for (let i = 0; i < choices.length; i++) {
// Choose: Add the current choice to the solution
solution.push(choices[i]);
// Recurse: Continue building the solution
backtrack(solution, choices);
// Unchoose: Remove the current choice to explore the next option
solution.pop();
}
}
// Helper function to check if a solution is valid (problemspecific)
function isSolution(solution) {
// Define criteria for a valid solution
return true; // Placeholder
}
// Helper function to process a complete solution (problemspecific)
function processSolution(solution) {
console.log(solution);
}
Example: Generating All Subsets of a Set
Let’s apply this template to a concrete problem: generating all possible subsets of a given set of numbers. This problem is a classic example of backtracking because we explore all possible subsets (combinations of elements) by either including or excluding each element.
Problem Statement
Given a set of distinct integers, generate all possible subsets (the power set).
Example: Input: [1, 2, 3]
Output:
[[], [1], [2], [1, 2], [3], [1, 3], [2, 3], [1, 2, 3]]
Backtracking Approach with ChooseUnchoose
function subsets(nums) {
const result = []; // To store all subsets
function backtrack(start, currentSubset) {
// Add the current subset to the result (it's a valid subset)
result.push([...currentSubset]);
// Explore further choices
for (let i = start; i < nums.length; i++) {
// Choose: Include nums[i] in the current subset
currentSubset.push(nums[i]);
// Recurse: Move to the next element
backtrack(i + 1, currentSubset);
// Unchoose: Remove nums[i] from the current subset
currentSubset.pop();
}
}
backtrack(0, []); // Start with an empty subset
return result;
}
// Example usage:
const nums = [1, 2, 3];
console.log(subsets(nums));
// Output: [[], [1], [2], [1, 2], [3], [1, 3], [2, 3], [1, 2, 3]]
Explanation

Initialization:
 We initialize an empty array
result
to store all the subsets.
 We initialize an empty array

Recursive Backtracking Function (
backtrack
): The
backtrack
function takes two parameters:start
: The index to start from for the current recursive call.currentSubset
: The current subset being formed.
 The

Base Case:
 There isn’t a strict base case in this example because every subset (including the empty set) is a valid result. We add the
currentSubset
toresult
every time the function is called.
 There isn’t a strict base case in this example because every subset (including the empty set) is a valid result. We add the

ChooseUnchoose Steps:
 Choose: Include the element
nums[i]
in thecurrentSubset
.  Recurse: Call
backtrack(i + 1, currentSubset)
to proceed with the next elements.  Unchoose: Remove the element
nums[i]
fromcurrentSubset
to explore other possibilities without it.
 Choose: Include the element
Key Takeaways
 Backtracking explores all possible configurations by making choices, recursing with those choices, and undoing them to try new paths.
 The “chooseunchoose” pattern ensures that we explore all potential solutions and backtrack when a path doesn’t lead to a valid solution.
 This pattern is versatile and can be adapted to various combinatorial problems, from generating subsets and permutations to solving more complex problems like the NQueens problem.
Conclusion
Backtracking with the “chooseunchoose” pattern provides a structured approach to solving combinatorial problems. The template and example discussed in this post should give you a solid foundation to tackle similar problems. Try applying this approach to problems like generating permutations, solving Sudoku, or finding paths in a maze. Happy coding!