0/1 knapsack

Items are (positive weight, nonnegative value); capacity is nonnegative. Return max value with each item used at most once. Duplicate tuples are separate items. Invalid weight/value/capacity throws invalid_argument. Prototype enumerate subsets; final descending-capacity O(nC) DP/O(C) space. Preserve input.

Public signatures:

Int prototype(const Vec<std::pair<Int,Int>>& items,const Int& capacity);
Int solve(const Vec<std::pair<Int,Int>>& items,const Int& capacity);

Compile and run from this directory:

c++ -std=c++20 -O2 -Wall -Wextra -pedantic -pthread main.cpp -o practice
./practice --stage prototype
./practice --stage final

Edit exercise.hpp. Both stages start unfinished and must report failures until implemented. Keep main.cpp as the executable contract. The runner returns nonzero for a failed check, an unexpected exception, an invalid stage, or an empty suite. C++20 and only the standard library are required.