Subset_Sum.H File Reference

Subset sum algorithms: classical DP and meet-in-the-middle. More...

#include <algorithm>
#include <concepts>
#include <cstddef>
#include <cstdint>
#include <limits>
#include <type_traits>
#include <utility>
#include <ah-errors.H>
#include <tpl_array.H>
#include <tpl_sort_utils.H>

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Classes
struct	Aleph::Subset_Sum_Result< T >
	Result of a subset sum computation. More...

Namespaces
namespace	Aleph
	Main namespace for Aleph-w library functions.
namespace	Aleph::subset_sum_detail

Functions
template<std::integral T>
size_t	Aleph::subset_sum_detail::to_size_checked (const T value, const char *fn_name, const char *field_name)
template<std::integral T>
Array< size_t >	Aleph::subset_sum_detail::extract_values_checked (const Array< T > &values, const char *fn_name)
template<typename T >
Array< std::pair< long long, uint64_t > >	Aleph::subset_sum_detail::enumerate_sums (const Array< T > &arr, size_t start, size_t len)
template<std::integral T>
Subset_Sum_Result< T >	Aleph::subset_sum (const Array< T > &values, T target)
	Subset sum via classical DP with reconstruction.
template<std::integral T>
bool	Aleph::subset_sum_exists (const Array< T > &values, T target)
	Subset sum existence check (space-optimized).
template<std::integral T>
size_t	Aleph::subset_sum_count (const Array< T > &values, T target)
	Count the number of subsets summing to target.
template<std::integral T>
Subset_Sum_Result< T >	Aleph::subset_sum_mitm (const Array< T > &values, T target)
	Subset sum via meet-in-the-middle (MITM).

Detailed Description

Subset sum algorithms: classical DP and meet-in-the-middle.

Provides:

• Classical DP subset sum: O(n * target) for integral values
• Counting variant: number of subsets that sum to target
• Meet-in-the-middle (MITM): O(n * 2^(n/2)) for n <= ~40

Definition in file Subset_Sum.H.