Project: Arithmetic Expression Generator & Solver (C++ Implementation) Author: Semih Taha AKSOY (WlayerX) Version: 1.0.0 License: MIT License

ArithmoGen is a command-line utility designed to solve arithmetic puzzles by generating expression trees from a given set of integer inputs. The application utilizes a recursive backtracking algorithm optimized for performance, capable of handling standard arithmetic operations (+, -, *, /) as well as investigating permutations, concatenation, and unary negation options to reach a specified target value.

This project demonstrates modern C++17 standards, focusing on efficient memory management, thread-safe parallel processing for permutation sets, and strict type safety.

• Language Standard: C++17
• Build System: CMake (Version 3.10+)
• Concurrency: std::thread, std::async, std::mutex for parallelized search of unordered sets.
• Precision: Double-precision floating-point arithmetic with epsilon comparisons for equality checks.

The project uses CMake for build configuration. Ensure a compatible C++ compiler (GCC, Clang, or MSVC) is installed.

1. Navigate to the project root directory.
2. Create a build directory:

   mkdir build
   cd build

3. Configure the project:

   cmake ..

4. Compile the source code:

   make

The executable ArithmoGen will be generated in the build directory.

The tool accepts command-line arguments to define the input set, target value, and operational constraints.

./ArithmoGen --numbers <n1 n2 ...> --target <value> [options]

• --numbers, -n: Space-separated list of input integers.
• --target, -t: The target integer or floating-point value to compute.
• --ordered, -o: Restrict search to the given order of numbers (default behavior).
• --no-ordered: Enable permutation generation to search all possible orderings.
• --concat, -c: Allow concatenation of adjacent digits (e.g., 1 and 2 becoming 12).
• --unary, -u: Permit unary negation of input numbers.
• --all, -a: Continue search after finding the first valid solution to list all possibilities.

Standard Search (Ordered):

./ArithmoGen --numbers 1 2 3 4 --target 10 --ordered

Permutation Search (Unordered):

./ArithmoGen --numbers 1 5 7 2 --target 29 --no-ordered

Complex Operations (Concatenation & Unary):

./ArithmoGen --numbers 1 2 3 4 --target 120 --concat --unary

For small sets (N < 7), the solver operates nearly instantaneously. As N increases, the search space grows factorially. This implementation mitigates execution time by parallelizing the search across available CPU cores when the --no-ordered flag is active.

This software is provided "as is", without warranty of any kind. It is intended for educational and algorithmic demonstration purposes.