Learning pathOriginal reference
Lesson 4 of 8

Choose, explore, and undo

Generate decisions without letting one branch contaminate the next.

Understand the idea

Backtracking extends a partial candidate, explores its completions, and restores temporary state before trying a sibling. To generate subsets, make one take-or-skip decision per input position. To generate binary strings, append one symbol, recurse, then remove it.

Trace a small example

For [A, B], decisions produce {}, {B}, {A}, and {A, B}. These are subsets of positions: two equal input values can still represent different choices. A shared vector must lose the item added by a branch before that branch returns.

Conditions and cost

There are 2^n subsets. Copying or printing each may add O(n) work per result. Store only the current path unless all answers are required in memory. Do not stop a counting task merely because the current sum already matches a target.

Pause & predict

Why is pop_back needed after exploring an appended choice?

Choose an answer
Try it yourself

Turn the idea into code

List all index subsets of [5, 5].

Give me a hint

Name the two positions A and B even though their values match.

Show the explained solution

The four subsets are {}, {A}, {B}, and {A, B}. The two one-element subsets are distinct position choices.

Your notes

Ready for the next idea?

Mark complete when you can explain it yourself.

From a problem to a programIdentify the input, output, and constraints, then translate a small plan into C++.Variables, types, and remembered valuesChoose a representation, initialize it, and understand what assignment really changes.Arithmetic without surprisesPredict division and remainder, widen before multiplication, and format decimal answers.Conditions and logical decisionsBuild exclusive categories, combine comparisons, and protect operations with short-circuit logic.Optional: other ways to chooseRecognize switch for exact choices and the conditional operator for choosing a value.For loops: make repetition preciseTrace initialization, condition, body, and update—and avoid an extra iteration.While, do-while, and stopping rulesChoose a loop from its stopping condition and read the exact input format.Break, continue, and early answersDistinguish leaving a loop from skipping one iteration, without losing required input.Five patterns worth understandingUse sums, counts, best-so-far candidates, products, and flags to process a stream.Nested loops: rows and columnsTranslate a shape into two loop roles and count the total work.Take a number apart, one digit at a timeUse remainder and division to process decimal digits, including zero.Multiple cases and a debugging mindsetCombine the patterns, isolate each case, and test the boundaries that can break your idea.Arrays: give every value a placeUnderstand indices, initialization, capacity, active length, and the first safe array loop.Scan, count, search, and compareDistinguish values from positions and preserve the exact tie rule a problem asks for.Change a sequence without losing itUpdate, copy, compare, reverse, and inspect neighbours using the correct bounds.Matrices: think in two coordinatesTraverse tables, total rows and columns, inspect diagonals, and protect grid neighbours.Characters become stringsSeparate characters from numbers, then safely inspect and edit managed text.Read the text the problem actually givesChoose words or full lines, preserve empty cases, and reset only the state that needs it.Scan text: count, filter, transformBuild a result from matching characters without losing leading zeros or skipping shifted text.Join, compare, and find textLearn content comparison, lexicographical order, substring counts, and the not-found sentinel.