Backtracking Basics
Backtracking is a systematic way to explore all possible configurations of a problem, using recursion. It's like solving a maze: you try a path, if it leads to a dead end, you go back and try another path.
Backtracking is used to solve problems like:
- N-Queens problem
- Sudoku solver
- Generating all 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 of a set.
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);
}
}
Two Minute Drill
- Backtracking explores all possibilities using recursion.
- Useful for constraint satisfaction and combinatorial problems.
- Template: check base, loop candidates, make choice, recurse, undo choice.
- Complexity often exponential, but pruning can help.
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