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algorithm-examples/cpp-algorithm/src/dp/rod_cutting.cpp at main · codejsha/algorithm-examples · GitHub
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rod_cutting.cpp
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algorithm-examples
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rod_cutting.cpp
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#
include
"
rod_cutting.h
"
#
include
<
algorithm
>
#
include
<
limits
>
auto
RodCutting::CutRod
(
const
std::map<
int
,
int
>& price,
const
int
length) -> int
{
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;
}
auto
RodCutting::MemoizedCutRod
(
const
std::map<
int
,
int
>& price,
const
int
length) -> int
{
std::vector<
int
>
memo
(
static_cast
<
int
>(price.
size
()) +
1
, -
1
);
return
MemoizedCutRodAux
(price, length, memo);
}
auto
RodCutting::MemoizedCutRodAux
(
const
std::map<
int
,
int
>& price,
const
int
length, std::vector<
int
>& memo) -> int
{
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;
}
auto
RodCutting::BottomUpCutRod
(
const
std::map<
int
,
int
>& price,
const
int
length) -> int
{
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];
}
auto
RodCutting::ExtendedBottomUpCutRod
(
const
std::map<
int
,
int
>& price,
const
int
length) -> std::tuple<int, int>
{
//
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]);
}
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