Learning pathOriginal reference
Lesson 2 of 8

Check, set, clear, and toggle

Choose a bitwise operation from its one-bit truth table.

Understand the idea

AND keeps a bit only if both operands have it; OR keeps a bit if either has it; XOR keeps a bit when they differ. For b = 1ULL << k, test (mask & b) != 0, set with mask |= b, clear with mask &= ~b, and toggle with mask ^= b.

Trace a small example

Starting at binary 1010, setting bit 0 gives 1011. Clearing bit 3 gives 0011, and toggling bit 1 gives 0001. Bitwise & examines all bits; logical && converts operands to truth values and short-circuits.

Conditions and cost

Use parentheses around bit tests in larger expressions. A complement flips every bit of the type, so intersect it with a universe mask when only the lowest n bits are meaningful. Do not compute (1ULL << n) when n equals the type width.

Prefix sum explorer

Query [l, r] is zero-based and inclusive. P[k] stores the total of the first k values; P[0] is zero.

Input array a

30
11
42
13
54
95

Prefix array P

00
31
42
83
94
145
236
P[5] − P[1] = 14 − (3) = 11

Preprocess once in O(n). Each range sum then takes O(1).

Guided simulation · Change the inputs to test your understanding.

Pause & predict

Which operation clears bit k while preserving the others?

Choose an answer
Try it yourself

Turn the idea into code

Start with mask 10. Set bit 0, then toggle bit 3. What value remains?

Give me a hint

10 is binary 1010.

Show the explained solution

Setting bit 0 gives 11 (1011); toggling bit 3 gives 3 (0011).

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.