Discrete Structures

A collection of C++ console programs written for CS 131: Discrete Structures.
Each file builds into its own executable and demonstrates a core concept from the course: logic, sets, functions, recursion, permutations, and probability.

Tooling: CMake creates one executable per *.cpp (named after the file). The project targets C++20.

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📁 Project Layout

discrete-structures/
├─ CMakeLists.txt
├─ README.md
├─ AsymptoticComplexity.cpp   # O(n), O(log n), O(n^2) growth demo
├─ BoolLogic.cpp              # Boolean function evaluator f(x,y,z)
├─ DeMorgansLaws.cpp          # Verify De Morgan’s Laws
├─ DirectProofs.cpp           # Direct proof with perfect squares
├─ FloorCeilRounding.cpp      # Floor and ceiling of real numbers
├─ nPrPermutations.cpp        # Recursive factorial for permutations
├─ QuantsContas.cpp           # Quantifiers and contrapositives
├─ RandomProbability.cpp      # Probability of random matches
├─ RecursiveCounter.cpp       # Recursively count digits of a number
└─ SetOperations.cpp          # Union and intersection of sets

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🛠️ Prerequisites

• CMake ≥ 3.25
• A C++20 compiler
  • Windows: MSVC (Visual Studio 2022)
  • macOS: Apple Clang (Xcode tools)
  • Linux: GCC 12+ or Clang 15+

No third-party libraries are required.

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🚀 Build Once, Run Any Program

From the repository root:

Windows (Visual Studio generator)

cmake -S . -B build -G "Visual Studio 17 2022"
cmake --build build --config Release
# Run executables:
.\build\Release\DeMorgansLaws.exe
.\build\Release\QuantsContas.exe
.\build\Release\SetOperations.exe
# ... etc.

macOS / Linux (default Makefiles or Ninja)

cmake -S . -B build
cmake --build build -j
# Run executables:
./build/DeMorgansLaws
./build/QuantsContas
./build/SetOperations
# ... etc.

💡 Add a new Foo.cpp and rerun the two CMake commands above—CMake will generate a Foo executable automatically.

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📚 Program Index

Executable (target)	What it does	Core topics	Typical interaction
DeMorgansLaws	Demonstrates De Morgan’s laws with integer predicates.	Boolean algebra, logic laws	Prompts for 4 integers (x,y,i,j)
QuantsContas	Tests universal quantifiers and contrapositives (odd/even).	Quantifiers, logic	Prompts for integer n
DirectProofs	Proves that product of two perfect squares is a square.	Direct proof, square roots	Prompts for integers m, n
SetOperations	Computes union & intersection of two sets (size 4 each).	Sets, algorithms	Prompts for elements of two sets
FloorCeilRounding	Displays floor and ceiling of real numbers.	Floor/ceil functions	Prompts for 4 doubles
BoolLogic	Evaluates a custom Boolean function f(x,y,z).	Boolean functions	Prompts for true/false inputs
AsymptoticComplexity	Shows examples of O(n), O(log n), and O(n^2).	Asymptotic growth	Prompts for integer n
RecursiveCounter	Recursively counts the digits of a number.	Recursion	Prompts for an integer
nPrPermutations	Computes permutations P(n,r) with recursion.	Factorial, recursion	Prompts for n and r
RandomProbability	Generates 3 random numbers and computes match probability.	Probability, random	Prompts for lower/upper bounds

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🔧 Building Tips

• If you add new .cpp files at the top level, CMake will automatically create a new executable for each on the next configure/generate step.
• On Windows, the built executables live under build\{Debug|Release}\ when using Visual Studio generators.
• If a program appears to “hang,” it’s usually waiting for input—check the “Typical interaction” column above.

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✅ License / Usage

These are educational lab exercises; feel free to use, modify, and extend for learning purposes.