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175 lines (151 loc) · 4.63 KB
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#ifndef CPP_ALGORITHM_ROD_CUTTING_H
#define CPP_ALGORITHM_ROD_CUTTING_H
#include <algorithm>
#include <limits>
#include <map>
#include <vector>
namespace RodCutting
{
/**
* \brief Rod cutting algorithm to call recursively.
* \param price prices for rod length
* \param length length of a rod
* \return the maximum revenue
*/
int CutRod(
const std::map<int, int>& price,
int length);
/**
* \brief Rod cutting algorithm with memoization that use top-down approach.
* \param price prices for rod length
* \param length length of a rod
* \return the maximum revenue
*/
int MemoizedCutRod(
const std::map<int, int>& price,
int length);
/**
* \brief Sub procedure for rod cutting algorithm with memoization.
* This use auxiliary array for memoization.
* \param price prices for rod length
* \param length length of a rod
* \param memo memoized results
* \return the maximum revenue
*/
int MemoizedCutRodAux(
const std::map<int, int>& price,
int length,
std::vector<int>& memo);
/**
* \brief Rod cutting algorithm that use bottom-up approach.
* \param price prices for rod length
* \param length length of a rod
* \return the maximum revenue
*/
int BottomUpCutRod(
const std::map<int, int>& price,
int length);
/**
* \brief Rod cutting algorithm that computes the maximum revenue and the optimal size of the first piece for given
* rod length.
* \param price prices for rod length
* \param length length of a rod
* \return the maximum revenue and the optimal size of the first piece
*/
std::tuple<int, int> ExtendedBottomUpCutRod(
const std::map<int, int>& price,
int length);
}
// ----------------------------------------------------------------------------
inline int RodCutting::CutRod(
const std::map<int, int>& price,
const int length)
{
if (length == 0)
{
return 0;
}
int max_revenue = std::numeric_limits<int>::min();
for (int i = 1; i <= length; ++i)
{
max_revenue = std::max(max_revenue, price.at(i) + CutRod(price, length - i));
}
return max_revenue;
}
// ----------------------------------------------------------------------------
inline int RodCutting::MemoizedCutRod(
const std::map<int, int>& price,
const int length)
{
std::vector<int> memo(static_cast<int>(price.size()) + 1, -1);
return MemoizedCutRodAux(price, length, memo);
}
// ----------------------------------------------------------------------------
inline int RodCutting::MemoizedCutRodAux(
const std::map<int, int>& price,
const int length,
std::vector<int>& memo)
{
int max_revenue = std::numeric_limits<int>::min();
if (memo[length] >= 0)
{
return memo[length];
}
if (length == 0)
{
max_revenue = 0;
}
else
{
for (int i = 1; i <= length; ++i)
{
max_revenue = std::max(max_revenue, price.at(i) + MemoizedCutRodAux(price, length - i, memo));
}
}
memo[length] = max_revenue;
return max_revenue;
}
// ----------------------------------------------------------------------------
inline int RodCutting::BottomUpCutRod(
const std::map<int, int>& price,
const int length)
{
std::vector<int> memo(static_cast<int>(price.size()) + 1, -1);
memo[0] = 0;
for (int i = 1; i <= length; ++i)
{
int max_revenue = std::numeric_limits<int>::min();
for (int j = 1; j <= i; ++j)
{
max_revenue = std::max(max_revenue, price.at(j) + memo[i - j]);
}
memo[i] = max_revenue;
}
return memo[length];
}
// ----------------------------------------------------------------------------
inline std::tuple<int, int> RodCutting::ExtendedBottomUpCutRod(
const std::map<int, int>& price,
const int length)
{
// the memoization of the max revenue
std::vector<int> memo(static_cast<int>(price.size()) + 1, -1);
memo[0] = 0;
// the optimal size of the first piece to cut off
std::vector<int> optimal_first_piece(static_cast<int>(price.size()) + 1, -1);
for (int i = 1; i <= length; ++i)
{
int max_revenue = std::numeric_limits<int>::min();
for (int j = 1; j <= i; ++j)
{
if (max_revenue < price.at(j) + memo[i - j])
{
max_revenue = price.at(j) + memo[i - j];
optimal_first_piece[i] = j;
}
}
memo[i] = max_revenue;
}
return std::make_tuple(memo[length], optimal_first_piece[length]);
}
#endif