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Lesson 6 of 8

Generate combinations and permutations

Encode whether order matters, and avoid equivalent duplicate-value branches.

Understand the idea

A combination uses strictly increasing chosen indices so the same group is not generated in different orders. A permutation fills ordered positions using any unused input index. Mark an index before recursion and unmark it on return.

Trace a small example

Choosing two of A, B, C gives combinations AB, AC, BC. Ordered selections also include BA, CA, CB. For a sorted multiset [1, 1, 2], unique permutation generation skips an equal candidate when the previous equal index is not already used on the current path.

Conditions and cost

Distinct full permutations number n!, and output costs O(n × n!). Duplicate skipping applies at one decision depth, not by forbidding equal values everywhere. A used table tracks input positions, not numeric values.

Pause & predict

How many length-2 combinations of three distinct items exist?

Choose an answer
Try it yourself

Turn the idea into code

List the unique full permutations of [1, 1, 2].

Give me a hint

Equal copies may not create duplicate sibling choices.

Show the explained solution

112, 121, and 211. There are 3 unique results, although the two labelled copies would create 6 positional permutations.

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.