#include<iostream>
#include<vector>
#include<cassert>
template<typename _Ty>
class subset
{
public:
using value_type = typename _Ty::const_iterator;
using container_type = std::vector<value_type>;
using iterator = typename container_type::iterator;
using const_iterator = typename container_type::const_iterator;
using reverse_iterator = typename container_type::reverse_iterator;
using const_reverse_iterator = typename container_type::const_reverse_iterator;
using size_type = typename container_type::size_type;
~subset (void) {};
explicit subset (const _Ty&);
subset (const subset&) = delete;
subset (subset&&) = delete;
subset& operator= (const subset&) = delete;
subset& operator= (subset&&) = delete;
const container_type& first (size_type);
const container_type& next (void);
private:
size_type m_size; // desired size of the subset
container_type m_set; // iterators to the full set
container_type m_subset; // subset of the full set of iterators
const_iterator find (const value_type&) const;
const bool get_next (const bool = true);
};
template<typename _Ty>
inline subset<_Ty>::subset (const _Ty& set):
m_size {set.size()}, m_set {}, m_subset {}
{
for (value_type it=set.begin(); it!=set.end(); ++it)
m_set.push_back (it);
m_set.shrink_to_fit();
}
template<typename _Ty>
inline typename subset<_Ty>::const_iterator subset<_Ty>::find (
const value_type& value) const
{
const_iterator it=m_set.begin();
while (it!=m_set.end() && *it!=value) ++it;
return it;
}
template<typename _Ty>
inline const typename subset<_Ty>::container_type& subset<_Ty>::first (
size_type count)
{
assert (count <= m_set.size());
m_size = count;
m_subset.clear();
for (const_iterator it=m_set.begin(); count--; ++it)
m_subset.push_back (*it);
return m_subset;
}
template<typename _Ty>
inline const bool subset<_Ty>::get_next (
const bool pop /* = true */)
{
const_reverse_iterator sub_it = m_subset.rbegin();
const_iterator set_it = find (*sub_it);
if (pop)
m_subset.pop_back();
if (++set_it != m_set.end())
m_subset.push_back (*set_it);
return m_subset.size() 1U)
return m_subset;
const value_type value = m_set.back();
m_set.pop_back();
--m_size;
next();
m_set.push_back (value);
if (m_size++ != m_subset.size())
return m_subset;
get_next (false);
return m_subset;
}
struct item
{
size_t value {0};
size_t weight {0};
item (size_t v=0, size_t w=0): value{v}, weight{w} {}
};
using vector = std::vector<item>;
item sum (vector& v)
{
item result;
for( auto i : v)
{
result.weight += i.weight;
result.value += i.value;
}
return result;
}
vector knapsack (vector items, size_t capacity)
{
vector v;
subset<vector> set {items};
for (size_t n=items.size(); n; --n)
{
subset<vector>::container_type selection {set.first (n)};
for (; selection.size(); selection=set.next())
{
vector t;
for (auto i : selection)
{
t.push_back (*i);
}
item s = sum (t);
if (s.weight <= capacity && sum(v).value < s.value)
v = t;
}
}
return v;
}
int main()
{
size_t capacity {4};
vector items {{1,8},{2,4},{3,1},{2,5},{2,3}};
vector rucksack = knapsack (items, capacity);
std::cout << "Items:\n" << std::endl;
for (auto i : items)
std::cout << '£' << i.value << '\t' << i.weight << "kg" << std::endl;
std::cout << std::endl;
std::cout << "Optimal selection for capacity " << capacity << "kg\n" << std::endl;
for (auto r : rucksack)
std::cout << '£' << r.value << '\t' << r.weight << "kg" << std::endl;
std::cout << std::endl;
item s = sum (rucksack);
std::cout << "Total value and weight:\n" << std::endl;
std::cout << '£' << s.value << '\t' << s.weight << "kg" << std::endl;
std::cout << std::endl;
}
pop push c++ programming
An Algorithm
Ronaldo! 'c' coding of Ricart-agarwala algorithm
Yes. More generally, every algorithm (defined as a sequence of finite steps to solve a problem that can be easily understood by a human) can be converted into machine code such that the algorithm can be understood by a machine. The C programming language is just one such method of converting algorithms into working machine code.
Complexity is a measure of how long an algorithm is expected to take and/or how much space is required to complete the task. It is not specific to C++ -- the language is immaterial -- it only applies to algorithms. Complexity is often expressed in big O notation, where O(1) is constant time (the best that can be expected of any algorithm).
pop push c++ programming
You don't write an algorithm for a C++ program, unless you are documenting the C++ program after-the-fact. The normal procedure is to write the algorithm first, in a language independent fashion, and then translate that stated algorithm into C++ code, or into whatever language you wish.
They are bosom-friends.
An Algorithm
A C++ implementation of the Binary GCD (Stern's) algorithm is shown in the Related Link below.
A manual check of the algorithm to ensure its correctness.
Use an SLR parser algorithm.
#define max (a, b) ((a) >= (b)) ? (a) : (b)
algorithm is a step by step procedure to solve a problem in c,
There is no specific Hard and Fast rule for writing algorithm. The normal method is the following: 1. get a problem 2. find or invent an algorithm to solve it 3. implement the algorithm in a programming language (C, for example)
The program itself is the solution. All programs are a solution to a given problem; that's the entire point of writing a program, to solve a problem. The program's algorithm specifies how the problem is solved and it's the programmer's job to convert that algorithm into working code.
Ronaldo! 'c' coding of Ricart-agarwala algorithm