How to Solve Complex Problems Step-by-Step (Backtracking Explained)

#algorithms #java #recursion #datastructures

Ever faced a problem where you need to try all possible solutions… but don’t know how?

That’s where Backtracking comes in.

What is Backtracking?

Backtracking is a technique where you:

Try a solution
If it fails → go back
Try another path

It’s like solving a maze:

Take a path
Hit a dead end
Go back and try another route

Where is Backtracking Used?

N-Queens problem
Sudoku solver
Generating subsets
Permutations & combinations
Rat in a maze

General Backtracking Template

void backtrack(parameters) {
if (solution found) {
process solution;
return;
}

for (int candidate : candidates) {
    if (isValid(candidate)) {
        makeChoice(candidate);

        backtrack(updatedParameters);

        undoChoice(candidate); // backtrack
    }
}

}

Example: Generate All Subsets

void subsets(int[] nums, int index, List current, List> result) {
result.add(new ArrayList<>(current));

for (int i = index; i < nums.length; i++) {
    current.add(nums[i]);

    subsets(nums, i + 1, current, result);

    current.remove(current.size() - 1); // backtrack
}

}

Key Idea

Backtracking works in 3 steps: