bump doxygen to latest version
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Laurent Perron
@@ -3,13 +3,13 @@
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<head>
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<meta charset="utf-8">
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<meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1" />
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<meta name="generator" content="pdoc 0.6.2" />
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<meta name="generator" content="pdoc 0.6.3" />
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<title>pywrapknapsack_solver API documentation</title>
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<meta name="description" content="" />
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<link href='https://cdnjs.cloudflare.com/ajax/libs/normalize/8.0.0/normalize.min.css' rel='stylesheet'>
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<link href='https://cdnjs.cloudflare.com/ajax/libs/10up-sanitize.css/8.0.0/sanitize.min.css' rel='stylesheet'>
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<link href="https://cdnjs.cloudflare.com/ajax/libs/highlight.js/9.12.0/styles/github.min.css" rel="stylesheet">
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<style>.flex{display:flex !important}body{line-height:1.5em}#content{padding:20px}#sidebar{padding:30px;overflow:hidden}.http-server-breadcrumbs{font-size:130%;margin:0 0 15px 0}#footer{font-size:.75em;padding:5px 30px;border-top:1px solid #ddd;text-align:right}#footer p{margin:0 0 0 1em;display:inline-block}#footer p:last-child{margin-right:30px}h1,h2,h3,h4,h5{font-weight:300}h1{font-size:2.5em;line-height:1.1em}h2{font-size:1.75em;margin:1em 0 .50em 0}h3{font-size:1.4em;margin:25px 0 10px 0}h4{margin:0;font-size:105%}a{color:#058;text-decoration:none;transition:color .3s ease-in-out}a:hover{color:#e82}.title code{font-weight:bold}h2[id^="header-"]{margin-top:2em}.ident{color:#900}pre code{background:#f8f8f8;font-size:.8em;line-height:1.4em}code{background:#f2f2f1;padding:1px 4px;overflow-wrap:break-word}h1 code{background:transparent}pre{background:#f8f8f8;border:0;border-top:1px solid #ccc;border-bottom:1px solid #ccc;margin:1em 0;padding:1ex}#http-server-module-list{display:flex;flex-flow:column}#http-server-module-list div{display:flex}#http-server-module-list dt{min-width:10%}#http-server-module-list p{margin-top:0}.toc ul,#index{list-style-type:none;margin:0;padding:0}#index code{background:transparent}#index h3{border-bottom:1px solid #ddd}#index ul{padding:0}#index h4{font-weight:bold}#index h4 + ul{margin-bottom:.6em}@media (min-width:200ex){#index .two-column{column-count:2}}@media (min-width:300ex){#index .two-column{column-count:3}}dl{margin-bottom:2em}dl dl:last-child{margin-bottom:4em}dd{margin:0 0 1em 3em}#header-classes + dl > dd{margin-bottom:3em}dd dd{margin-left:2em}dd p{margin:10px 0}.name{background:#eee;font-weight:bold;font-size:.85em;padding:5px 10px;display:inline-block;min-width:40%}.name:hover{background:#e0e0e0}.name > span:first-child{white-space:nowrap}.name.class > span:nth-child(2){margin-left:.4em}.inherited{color:#999;border-left:5px solid #eee;padding-left:1em}.inheritance em{font-style:normal;font-weight:bold}.desc h2{font-weight:400;font-size:1.25em}.desc h3{font-size:1em}.desc dt code{background:inherit}.source summary{color:#666;text-align:right;font-weight:400;font-size:.8em;text-transform:uppercase;cursor:pointer}.source pre{max-height:500px;overflow:auto;margin:0}.source pre code{font-size:12px;overflow:visible}.hlist{list-style:none}.hlist li{display:inline}.hlist li:after{content:',\2002'}.hlist li:last-child:after{content:none}.hlist .hlist{display:inline;padding-left:1em}img{max-width:100%}.admonition{padding:.1em .5em}.admonition-title{font-weight:bold}.admonition.note,.admonition.info,.admonition.important{background:#aef}.admonition.todo,.admonition.versionadded,.admonition.tip,.admonition.hint{background:#dfd}.admonition.warning,.admonition.versionchanged,.admonition.deprecated{background:#fd4}.admonition.error,.admonition.danger,.admonition.caution{background:lightpink}</style>
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<style>.flex{display:flex !important}body{line-height:1.5em}#content{padding:20px}#sidebar{padding:30px;overflow:hidden}.http-server-breadcrumbs{font-size:130%;margin:0 0 15px 0}#footer{font-size:.75em;padding:5px 30px;border-top:1px solid #ddd;text-align:right}#footer p{margin:0 0 0 1em;display:inline-block}#footer p:last-child{margin-right:30px}h1,h2,h3,h4,h5{font-weight:300}h1{font-size:2.5em;line-height:1.1em}h2{font-size:1.75em;margin:1em 0 .50em 0}h3{font-size:1.4em;margin:25px 0 10px 0}h4{margin:0;font-size:105%}a{color:#058;text-decoration:none;transition:color .3s ease-in-out}a:hover{color:#e82}.title code{font-weight:bold}h2[id^="header-"]{margin-top:2em}.ident{color:#900}pre code{background:#f8f8f8;font-size:.8em;line-height:1.4em}code{background:#f2f2f1;padding:1px 4px;overflow-wrap:break-word}h1 code{background:transparent}pre{background:#f8f8f8;border:0;border-top:1px solid #ccc;border-bottom:1px solid #ccc;margin:1em 0;padding:1ex}#http-server-module-list{display:flex;flex-flow:column}#http-server-module-list div{display:flex}#http-server-module-list dt{min-width:10%}#http-server-module-list p{margin-top:0}.toc ul,#index{list-style-type:none;margin:0;padding:0}#index code{background:transparent}#index h3{border-bottom:1px solid #ddd}#index ul{padding:0}#index h4{font-weight:bold}#index h4 + ul{margin-bottom:.6em}@media (min-width:200ex){#index .two-column{column-count:2}}@media (min-width:300ex){#index .two-column{column-count:3}}dl{margin-bottom:2em}dl dl:last-child{margin-bottom:4em}dd{margin:0 0 1em 3em}#header-classes + dl > dd{margin-bottom:3em}dd dd{margin-left:2em}dd p{margin:10px 0}.name{background:#eee;font-weight:bold;font-size:.85em;padding:5px 10px;display:inline-block;min-width:40%}.name:hover{background:#e0e0e0}.name > span:first-child{white-space:nowrap}.name.class > span:nth-child(2){margin-left:.4em}.inherited{color:#999;border-left:5px solid #eee;padding-left:1em}.inheritance em{font-style:normal;font-weight:bold}.desc h2{font-weight:400;font-size:1.25em}.desc h3{font-size:1em}.desc dt code{background:inherit}.source summary{color:#666;text-align:right;font-weight:400;font-size:.8em;text-transform:uppercase;cursor:pointer}.source pre{max-height:500px;overflow:auto;margin:0}.source pre code{font-size:12px;overflow:visible}.hlist{list-style:none}.hlist li{display:inline}.hlist li:after{content:',\2002'}.hlist li:last-child:after{content:none}.hlist .hlist{display:inline;padding-left:1em}img{max-width:100%}.admonition{padding:.1em .5em;margin-bottom:1em}.admonition-title{font-weight:bold}.admonition.note,.admonition.info,.admonition.important{background:#aef}.admonition.todo,.admonition.versionadded,.admonition.tip,.admonition.hint{background:#dfd}.admonition.warning,.admonition.versionchanged,.admonition.deprecated{background:#fd4}.admonition.error,.admonition.danger,.admonition.caution{background:lightpink}</style>
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<style media="print">@media print{#sidebar h1{page-break-before:always}.source{display:none}}@media print{*{background:transparent !important;color:#000 !important;box-shadow:none !important;text-shadow:none !important}a[href]:after{content:" (" attr(href) ")";font-size:90%}a[href][title]:after{content:none}abbr[title]:after{content:" (" attr(title) ")"}.ir a:after,a[href^="javascript:"]:after,a[href^="#"]:after{content:""}pre,blockquote{border:1px solid #999;page-break-inside:avoid}thead{display:table-header-group}tr,img{page-break-inside:avoid}img{max-width:100% !important}@page{margin:0.5cm}p,h2,h3{orphans:3;widows:3}h1,h2,h3,h4,h5,h6{page-break-after:avoid}}</style>
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<style type="text/css">
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@@ -28,17 +28,17 @@ a:link { color: #46641e; text-decoration: none}
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<details class="source">
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<summary>Source code</summary>
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<pre><code class="python"># This file was automatically generated by SWIG (http://www.swig.org).
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# Version 4.0.0
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# Version 4.0.1
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#
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# Do not make changes to this file unless you know what you are doing--modify
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# the SWIG interface file instead.
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from sys import version_info as _swig_python_version_info
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if _swig_python_version_info < (2, 7, 0):
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raise RuntimeError('Python 2.7 or later required')
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raise RuntimeError("Python 2.7 or later required")
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# Import the low-level C/C++ module
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if __package__ or '.' in __name__:
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if __package__ or "." in __name__:
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from . import _pywrapknapsack_solver
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else:
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import _pywrapknapsack_solver
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@@ -48,35 +48,6 @@ try:
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except ImportError:
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import __builtin__
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def _swig_setattr_nondynamic(self, class_type, name, value, static=1):
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if name == "thisown":
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return self.this.own(value)
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if name == "this":
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if type(value).__name__ == 'SwigPyObject':
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self.__dict__[name] = value
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return
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method = class_type.__swig_setmethods__.get(name, None)
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if method:
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return method(self, value)
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if not static:
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object.__setattr__(self, name, value)
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else:
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raise AttributeError("You cannot add attributes to %s" % self)
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def _swig_setattr(self, class_type, name, value):
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return _swig_setattr_nondynamic(self, class_type, name, value, 0)
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def _swig_getattr(self, class_type, name):
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if name == "thisown":
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return self.this.own()
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method = class_type.__swig_getmethods__.get(name, None)
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if method:
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return method(self)
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raise AttributeError("'%s' object has no attribute '%s'" % (class_type.__name__, name))
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def _swig_repr(self):
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try:
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strthis = "proxy of " + self.this.__repr__()
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@@ -120,180 +91,31 @@ class _SwigNonDynamicMeta(type):
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class KnapsackSolver(object):
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r"""
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This library solves knapsack problems.
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Problems the library solves include:
|
||||
- 0-1 knapsack problems,
|
||||
- Multi-dimensional knapsack problems,
|
||||
|
||||
Given n items, each with a profit and a weight, given a knapsack of
|
||||
capacity c, the goal is to find a subset of items which fits inside c
|
||||
and maximizes the total profit.
|
||||
The knapsack problem can easily be extended from 1 to d dimensions.
|
||||
As an example, this can be useful to constrain the maximum number of
|
||||
items inside the knapsack.
|
||||
Without loss of generality, profits and weights are assumed to be positive.
|
||||
|
||||
From a mathematical point of view, the multi-dimensional knapsack problem
|
||||
can be modeled by d linear constraints:
|
||||
|
||||
ForEach(j:1..d)(Sum(i:1..n)(weight_ij * item_i) <= c_j
|
||||
where item_i is a 0-1 integer variable.
|
||||
|
||||
Then the goal is to maximize:
|
||||
|
||||
Sum(i:1..n)(profit_i * item_i).
|
||||
|
||||
There are several ways to solve knapsack problems. One of the most
|
||||
efficient is based on dynamic programming (mainly when weights, profits
|
||||
and dimensions are small, and the algorithm runs in pseudo polynomial time).
|
||||
Unfortunately, when adding conflict constraints the problem becomes strongly
|
||||
NP-hard, i.e. there is no pseudo-polynomial algorithm to solve it.
|
||||
That's the reason why the most of the following code is based on branch and
|
||||
bound search.
|
||||
|
||||
For instance to solve a 2-dimensional knapsack problem with 9 items,
|
||||
one just has to feed a profit vector with the 9 profits, a vector of 2
|
||||
vectors for weights, and a vector of capacities.
|
||||
E.g.:
|
||||
|
||||
**Python**:
|
||||
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||||
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||||
.. code-block:: c++
|
||||
|
||||
|
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profits = [ 1, 2, 3, 4, 5, 6, 7, 8, 9 ]
|
||||
weights = [ [ 1, 2, 3, 4, 5, 6, 7, 8, 9 ],
|
||||
[ 1, 1, 1, 1, 1, 1, 1, 1, 1 ]
|
||||
]
|
||||
capacities = [ 34, 4 ]
|
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|
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solver = pywrapknapsack_solver.KnapsackSolver(
|
||||
pywrapknapsack_solver.KnapsackSolver
|
||||
.KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER,
|
||||
'Multi-dimensional solver')
|
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solver.Init(profits, weights, capacities)
|
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profit = solver.Solve()
|
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|
||||
|
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**C++**:
|
||||
|
||||
|
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.. code-block:: c++
|
||||
|
||||
|
||||
const std::vectorint64 profits = { 1, 2, 3, 4, 5, 6, 7, 8, 9 };
|
||||
const std::vectorstd::vector<int64 weights =
|
||||
{ { 1, 2, 3, 4, 5, 6, 7, 8, 9 },
|
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{ 1, 1, 1, 1, 1, 1, 1, 1, 1 } };
|
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const std::vectorint64 capacities = { 34, 4 };
|
||||
|
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KnapsackSolver solver(
|
||||
KnapsackSolver::KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER,
|
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"Multi-dimensional solver");
|
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solver.Init(profits, weights, capacities);
|
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const int64 profit = solver.Solve();
|
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**Java**:
|
||||
|
||||
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.. code-block:: c++
|
||||
|
||||
|
||||
final long[] profits = { 1, 2, 3, 4, 5, 6, 7, 8, 9 };
|
||||
final long[][] weights = { { 1, 2, 3, 4, 5, 6, 7, 8, 9 },
|
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{ 1, 1, 1, 1, 1, 1, 1, 1, 1 } };
|
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final long[] capacities = { 34, 4 };
|
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|
||||
KnapsackSolver solver = new KnapsackSolver(
|
||||
KnapsackSolver.SolverType.KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER,
|
||||
"Multi-dimensional solver");
|
||||
solver.init(profits, weights, capacities);
|
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final long profit = solver.solve();
|
||||
|
||||
|
||||
"""
|
||||
|
||||
thisown = property(lambda x: x.this.own(), lambda x, v: x.this.own(v), doc='The membership flag')
|
||||
thisown = property(lambda x: x.this.own(), lambda x, v: x.this.own(v), doc="The membership flag")
|
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__repr__ = _swig_repr
|
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KNAPSACK_BRUTE_FORCE_SOLVER = _pywrapknapsack_solver.KnapsackSolver_KNAPSACK_BRUTE_FORCE_SOLVER
|
||||
r"""
|
||||
Brute force method.
|
||||
|
||||
Limited to 30 items and one dimension, this
|
||||
solver uses a brute force algorithm, ie. explores all possible states.
|
||||
Experiments show competitive performance for instances with less than
|
||||
15 items.
|
||||
"""
|
||||
KNAPSACK_64ITEMS_SOLVER = _pywrapknapsack_solver.KnapsackSolver_KNAPSACK_64ITEMS_SOLVER
|
||||
r"""
|
||||
Optimized method for single dimension small problems
|
||||
|
||||
Limited to 64 items and one dimension, this
|
||||
solver uses a branch & bound algorithm. This solver is about 4 times
|
||||
faster than KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER.
|
||||
"""
|
||||
KNAPSACK_DYNAMIC_PROGRAMMING_SOLVER = _pywrapknapsack_solver.KnapsackSolver_KNAPSACK_DYNAMIC_PROGRAMMING_SOLVER
|
||||
r"""
|
||||
Dynamic Programming approach for single dimension problems
|
||||
|
||||
Limited to one dimension, this solver is based on a dynamic programming
|
||||
algorithm. The time and space complexity is O(capacity *
|
||||
number_of_items).
|
||||
"""
|
||||
KNAPSACK_MULTIDIMENSION_CBC_MIP_SOLVER = _pywrapknapsack_solver.KnapsackSolver_KNAPSACK_MULTIDIMENSION_CBC_MIP_SOLVER
|
||||
r"""
|
||||
CBC Based Solver
|
||||
|
||||
This solver can deal with both large number of items and several
|
||||
dimensions. This solver is based on Integer Programming solver CBC.
|
||||
"""
|
||||
KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER = _pywrapknapsack_solver.KnapsackSolver_KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER
|
||||
r"""
|
||||
Generic Solver.
|
||||
|
||||
This solver can deal with both large number of items and several
|
||||
dimensions. This solver is based on branch and bound.
|
||||
"""
|
||||
|
||||
def __init__(self, *args):
|
||||
_pywrapknapsack_solver.KnapsackSolver_swiginit(self, _pywrapknapsack_solver.new_KnapsackSolver(*args))
|
||||
__swig_destroy__ = _pywrapknapsack_solver.delete_KnapsackSolver
|
||||
|
||||
def Init(self, profits: 'std::vector< int64 > const &', weights: 'std::vector< std::vector< int64 > > const &', capacities: 'std::vector< int64 > const &') -> "void":
|
||||
r"""
|
||||
|
||||
Initializes the solver and enters the problem to be solved.
|
||||
"""
|
||||
def Init(self, profits: "std::vector< int64 > const &", weights: "std::vector< std::vector< int64 > > const &", capacities: "std::vector< int64 > const &") -> "void":
|
||||
return _pywrapknapsack_solver.KnapsackSolver_Init(self, profits, weights, capacities)
|
||||
|
||||
def Solve(self) -> "int64":
|
||||
r"""
|
||||
|
||||
Solves the problem and returns the profit of the optimal solution.
|
||||
"""
|
||||
return _pywrapknapsack_solver.KnapsackSolver_Solve(self)
|
||||
|
||||
def BestSolutionContains(self, item_id: 'int') -> "bool":
|
||||
r"""
|
||||
|
||||
Returns true if the item 'item_id' is packed in the optimal knapsack.
|
||||
"""
|
||||
def BestSolutionContains(self, item_id: "int") -> "bool":
|
||||
return _pywrapknapsack_solver.KnapsackSolver_BestSolutionContains(self, item_id)
|
||||
|
||||
def set_use_reduction(self, use_reduction: 'bool') -> "void":
|
||||
def set_use_reduction(self, use_reduction: "bool") -> "void":
|
||||
return _pywrapknapsack_solver.KnapsackSolver_set_use_reduction(self, use_reduction)
|
||||
|
||||
def set_time_limit(self, time_limit_seconds: 'double') -> "void":
|
||||
r"""
|
||||
Time limit in seconds.
|
||||
|
||||
When a finite time limit is set the solution obtained might not be optimal
|
||||
if the limit is reached.
|
||||
"""
|
||||
def set_time_limit(self, time_limit_seconds: "double") -> "void":
|
||||
return _pywrapknapsack_solver.KnapsackSolver_set_time_limit(self, time_limit_seconds)
|
||||
|
||||
# Register KnapsackSolver in _pywrapknapsack_solver:
|
||||
@@ -314,292 +136,58 @@ _pywrapknapsack_solver.KnapsackSolver_swigregister(KnapsackSolver)</code></pre>
|
||||
<span>(</span><span>*args)</span>
|
||||
</code></dt>
|
||||
<dd>
|
||||
<section class="desc"><p>This library solves knapsack problems.</p>
|
||||
<p>Problems the library solves include:
|
||||
- 0-1 knapsack problems,
|
||||
- Multi-dimensional knapsack problems,</p>
|
||||
<p>Given n items, each with a profit and a weight, given a knapsack of
|
||||
capacity c, the goal is to find a subset of items which fits inside c
|
||||
and maximizes the total profit.
|
||||
The knapsack problem can easily be extended from 1 to d dimensions.
|
||||
As an example, this can be useful to constrain the maximum number of
|
||||
items inside the knapsack.
|
||||
Without loss of generality, profits and weights are assumed to be positive.</p>
|
||||
<p>From a mathematical point of view, the multi-dimensional knapsack problem
|
||||
can be modeled by d linear constraints:</p>
|
||||
<pre><code>ForEach(j:1..d)(Sum(i:1..n)(weight_ij * item_i) <= c_j
|
||||
where item_i is a 0-1 integer variable.
|
||||
</code></pre>
|
||||
<p>Then the goal is to maximize:</p>
|
||||
<pre><code>Sum(i:1..n)(profit_i * item_i).
|
||||
</code></pre>
|
||||
<p>There are several ways to solve knapsack problems. One of the most
|
||||
efficient is based on dynamic programming (mainly when weights, profits
|
||||
and dimensions are small, and the algorithm runs in pseudo polynomial time).
|
||||
Unfortunately, when adding conflict constraints the problem becomes strongly
|
||||
NP-hard, i.e. there is no pseudo-polynomial algorithm to solve it.
|
||||
That's the reason why the most of the following code is based on branch and
|
||||
bound search.</p>
|
||||
<p>For instance to solve a 2-dimensional knapsack problem with 9 items,
|
||||
one just has to feed a profit vector with the 9 profits, a vector of 2
|
||||
vectors for weights, and a vector of capacities.
|
||||
E.g.:</p>
|
||||
<p><strong>Python</strong>:</p>
|
||||
<p>.. code-block:: c++</p>
|
||||
<pre><code> profits = [ 1, 2, 3, 4, 5, 6, 7, 8, 9 ]
|
||||
weights = [ [ 1, 2, 3, 4, 5, 6, 7, 8, 9 ],
|
||||
[ 1, 1, 1, 1, 1, 1, 1, 1, 1 ]
|
||||
]
|
||||
capacities = [ 34, 4 ]
|
||||
|
||||
solver = pywrapknapsack_solver.KnapsackSolver(
|
||||
pywrapknapsack_solver.KnapsackSolver
|
||||
.KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER,
|
||||
'Multi-dimensional solver')
|
||||
solver.Init(profits, weights, capacities)
|
||||
profit = solver.Solve()
|
||||
</code></pre>
|
||||
<p><strong>C++</strong>:</p>
|
||||
<p>.. code-block:: c++</p>
|
||||
<pre><code> const std::vectorint64 profits = { 1, 2, 3, 4, 5, 6, 7, 8, 9 };
|
||||
const std::vectorstd::vector<int64 weights =
|
||||
{ { 1, 2, 3, 4, 5, 6, 7, 8, 9 },
|
||||
{ 1, 1, 1, 1, 1, 1, 1, 1, 1 } };
|
||||
const std::vectorint64 capacities = { 34, 4 };
|
||||
|
||||
KnapsackSolver solver(
|
||||
KnapsackSolver::KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER,
|
||||
"Multi-dimensional solver");
|
||||
solver.Init(profits, weights, capacities);
|
||||
const int64 profit = solver.Solve();
|
||||
</code></pre>
|
||||
<p><strong>Java</strong>:</p>
|
||||
<p>.. code-block:: c++</p>
|
||||
<pre><code> final long[] profits = { 1, 2, 3, 4, 5, 6, 7, 8, 9 };
|
||||
final long[][] weights = { { 1, 2, 3, 4, 5, 6, 7, 8, 9 },
|
||||
{ 1, 1, 1, 1, 1, 1, 1, 1, 1 } };
|
||||
final long[] capacities = { 34, 4 };
|
||||
|
||||
KnapsackSolver solver = new KnapsackSolver(
|
||||
KnapsackSolver.SolverType.KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER,
|
||||
"Multi-dimensional solver");
|
||||
solver.init(profits, weights, capacities);
|
||||
final long profit = solver.solve();
|
||||
</code></pre></section>
|
||||
<section class="desc"></section>
|
||||
<details class="source">
|
||||
<summary>Source code</summary>
|
||||
<pre><code class="python">class KnapsackSolver(object):
|
||||
r"""
|
||||
This library solves knapsack problems.
|
||||
|
||||
Problems the library solves include:
|
||||
- 0-1 knapsack problems,
|
||||
- Multi-dimensional knapsack problems,
|
||||
|
||||
Given n items, each with a profit and a weight, given a knapsack of
|
||||
capacity c, the goal is to find a subset of items which fits inside c
|
||||
and maximizes the total profit.
|
||||
The knapsack problem can easily be extended from 1 to d dimensions.
|
||||
As an example, this can be useful to constrain the maximum number of
|
||||
items inside the knapsack.
|
||||
Without loss of generality, profits and weights are assumed to be positive.
|
||||
|
||||
From a mathematical point of view, the multi-dimensional knapsack problem
|
||||
can be modeled by d linear constraints:
|
||||
|
||||
ForEach(j:1..d)(Sum(i:1..n)(weight_ij * item_i) <= c_j
|
||||
where item_i is a 0-1 integer variable.
|
||||
|
||||
Then the goal is to maximize:
|
||||
|
||||
Sum(i:1..n)(profit_i * item_i).
|
||||
|
||||
There are several ways to solve knapsack problems. One of the most
|
||||
efficient is based on dynamic programming (mainly when weights, profits
|
||||
and dimensions are small, and the algorithm runs in pseudo polynomial time).
|
||||
Unfortunately, when adding conflict constraints the problem becomes strongly
|
||||
NP-hard, i.e. there is no pseudo-polynomial algorithm to solve it.
|
||||
That's the reason why the most of the following code is based on branch and
|
||||
bound search.
|
||||
|
||||
For instance to solve a 2-dimensional knapsack problem with 9 items,
|
||||
one just has to feed a profit vector with the 9 profits, a vector of 2
|
||||
vectors for weights, and a vector of capacities.
|
||||
E.g.:
|
||||
|
||||
**Python**:
|
||||
|
||||
|
||||
.. code-block:: c++
|
||||
|
||||
|
||||
profits = [ 1, 2, 3, 4, 5, 6, 7, 8, 9 ]
|
||||
weights = [ [ 1, 2, 3, 4, 5, 6, 7, 8, 9 ],
|
||||
[ 1, 1, 1, 1, 1, 1, 1, 1, 1 ]
|
||||
]
|
||||
capacities = [ 34, 4 ]
|
||||
|
||||
solver = pywrapknapsack_solver.KnapsackSolver(
|
||||
pywrapknapsack_solver.KnapsackSolver
|
||||
.KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER,
|
||||
'Multi-dimensional solver')
|
||||
solver.Init(profits, weights, capacities)
|
||||
profit = solver.Solve()
|
||||
|
||||
|
||||
**C++**:
|
||||
|
||||
|
||||
.. code-block:: c++
|
||||
|
||||
|
||||
const std::vectorint64 profits = { 1, 2, 3, 4, 5, 6, 7, 8, 9 };
|
||||
const std::vectorstd::vector<int64 weights =
|
||||
{ { 1, 2, 3, 4, 5, 6, 7, 8, 9 },
|
||||
{ 1, 1, 1, 1, 1, 1, 1, 1, 1 } };
|
||||
const std::vectorint64 capacities = { 34, 4 };
|
||||
|
||||
KnapsackSolver solver(
|
||||
KnapsackSolver::KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER,
|
||||
"Multi-dimensional solver");
|
||||
solver.Init(profits, weights, capacities);
|
||||
const int64 profit = solver.Solve();
|
||||
|
||||
|
||||
**Java**:
|
||||
|
||||
|
||||
.. code-block:: c++
|
||||
|
||||
|
||||
final long[] profits = { 1, 2, 3, 4, 5, 6, 7, 8, 9 };
|
||||
final long[][] weights = { { 1, 2, 3, 4, 5, 6, 7, 8, 9 },
|
||||
{ 1, 1, 1, 1, 1, 1, 1, 1, 1 } };
|
||||
final long[] capacities = { 34, 4 };
|
||||
|
||||
KnapsackSolver solver = new KnapsackSolver(
|
||||
KnapsackSolver.SolverType.KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER,
|
||||
"Multi-dimensional solver");
|
||||
solver.init(profits, weights, capacities);
|
||||
final long profit = solver.solve();
|
||||
|
||||
|
||||
"""
|
||||
|
||||
thisown = property(lambda x: x.this.own(), lambda x, v: x.this.own(v), doc='The membership flag')
|
||||
thisown = property(lambda x: x.this.own(), lambda x, v: x.this.own(v), doc="The membership flag")
|
||||
__repr__ = _swig_repr
|
||||
KNAPSACK_BRUTE_FORCE_SOLVER = _pywrapknapsack_solver.KnapsackSolver_KNAPSACK_BRUTE_FORCE_SOLVER
|
||||
r"""
|
||||
Brute force method.
|
||||
|
||||
Limited to 30 items and one dimension, this
|
||||
solver uses a brute force algorithm, ie. explores all possible states.
|
||||
Experiments show competitive performance for instances with less than
|
||||
15 items.
|
||||
"""
|
||||
KNAPSACK_64ITEMS_SOLVER = _pywrapknapsack_solver.KnapsackSolver_KNAPSACK_64ITEMS_SOLVER
|
||||
r"""
|
||||
Optimized method for single dimension small problems
|
||||
|
||||
Limited to 64 items and one dimension, this
|
||||
solver uses a branch & bound algorithm. This solver is about 4 times
|
||||
faster than KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER.
|
||||
"""
|
||||
KNAPSACK_DYNAMIC_PROGRAMMING_SOLVER = _pywrapknapsack_solver.KnapsackSolver_KNAPSACK_DYNAMIC_PROGRAMMING_SOLVER
|
||||
r"""
|
||||
Dynamic Programming approach for single dimension problems
|
||||
|
||||
Limited to one dimension, this solver is based on a dynamic programming
|
||||
algorithm. The time and space complexity is O(capacity *
|
||||
number_of_items).
|
||||
"""
|
||||
KNAPSACK_MULTIDIMENSION_CBC_MIP_SOLVER = _pywrapknapsack_solver.KnapsackSolver_KNAPSACK_MULTIDIMENSION_CBC_MIP_SOLVER
|
||||
r"""
|
||||
CBC Based Solver
|
||||
|
||||
This solver can deal with both large number of items and several
|
||||
dimensions. This solver is based on Integer Programming solver CBC.
|
||||
"""
|
||||
KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER = _pywrapknapsack_solver.KnapsackSolver_KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER
|
||||
r"""
|
||||
Generic Solver.
|
||||
|
||||
This solver can deal with both large number of items and several
|
||||
dimensions. This solver is based on branch and bound.
|
||||
"""
|
||||
|
||||
def __init__(self, *args):
|
||||
_pywrapknapsack_solver.KnapsackSolver_swiginit(self, _pywrapknapsack_solver.new_KnapsackSolver(*args))
|
||||
__swig_destroy__ = _pywrapknapsack_solver.delete_KnapsackSolver
|
||||
|
||||
def Init(self, profits: 'std::vector< int64 > const &', weights: 'std::vector< std::vector< int64 > > const &', capacities: 'std::vector< int64 > const &') -> "void":
|
||||
r"""
|
||||
|
||||
Initializes the solver and enters the problem to be solved.
|
||||
"""
|
||||
def Init(self, profits: "std::vector< int64 > const &", weights: "std::vector< std::vector< int64 > > const &", capacities: "std::vector< int64 > const &") -> "void":
|
||||
return _pywrapknapsack_solver.KnapsackSolver_Init(self, profits, weights, capacities)
|
||||
|
||||
def Solve(self) -> "int64":
|
||||
r"""
|
||||
|
||||
Solves the problem and returns the profit of the optimal solution.
|
||||
"""
|
||||
return _pywrapknapsack_solver.KnapsackSolver_Solve(self)
|
||||
|
||||
def BestSolutionContains(self, item_id: 'int') -> "bool":
|
||||
r"""
|
||||
|
||||
Returns true if the item 'item_id' is packed in the optimal knapsack.
|
||||
"""
|
||||
def BestSolutionContains(self, item_id: "int") -> "bool":
|
||||
return _pywrapknapsack_solver.KnapsackSolver_BestSolutionContains(self, item_id)
|
||||
|
||||
def set_use_reduction(self, use_reduction: 'bool') -> "void":
|
||||
def set_use_reduction(self, use_reduction: "bool") -> "void":
|
||||
return _pywrapknapsack_solver.KnapsackSolver_set_use_reduction(self, use_reduction)
|
||||
|
||||
def set_time_limit(self, time_limit_seconds: 'double') -> "void":
|
||||
r"""
|
||||
Time limit in seconds.
|
||||
|
||||
When a finite time limit is set the solution obtained might not be optimal
|
||||
if the limit is reached.
|
||||
"""
|
||||
def set_time_limit(self, time_limit_seconds: "double") -> "void":
|
||||
return _pywrapknapsack_solver.KnapsackSolver_set_time_limit(self, time_limit_seconds)</code></pre>
|
||||
</details>
|
||||
<h3>Class variables</h3>
|
||||
<dl>
|
||||
<dt id="pywrapknapsack_solver.KnapsackSolver.KNAPSACK_64ITEMS_SOLVER"><code class="name">var <span class="ident">KNAPSACK_64ITEMS_SOLVER</span></code></dt>
|
||||
<dd>
|
||||
<section class="desc"><p>Optimized method for single dimension small problems</p>
|
||||
<p>Limited to 64 items and one dimension, this
|
||||
solver uses a branch & bound algorithm. This solver is about 4 times
|
||||
faster than KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER.</p></section>
|
||||
<section class="desc"></section>
|
||||
</dd>
|
||||
<dt id="pywrapknapsack_solver.KnapsackSolver.KNAPSACK_BRUTE_FORCE_SOLVER"><code class="name">var <span class="ident">KNAPSACK_BRUTE_FORCE_SOLVER</span></code></dt>
|
||||
<dd>
|
||||
<section class="desc"><p>Brute force method.</p>
|
||||
<p>Limited to 30 items and one dimension, this
|
||||
solver uses a brute force algorithm, ie. explores all possible states.
|
||||
Experiments show competitive performance for instances with less than
|
||||
15 items.</p></section>
|
||||
<section class="desc"></section>
|
||||
</dd>
|
||||
<dt id="pywrapknapsack_solver.KnapsackSolver.KNAPSACK_DYNAMIC_PROGRAMMING_SOLVER"><code class="name">var <span class="ident">KNAPSACK_DYNAMIC_PROGRAMMING_SOLVER</span></code></dt>
|
||||
<dd>
|
||||
<section class="desc"><p>Dynamic Programming approach for single dimension problems</p>
|
||||
<p>Limited to one dimension, this solver is based on a dynamic programming
|
||||
algorithm. The time and space complexity is O(capacity *
|
||||
number_of_items).</p></section>
|
||||
<section class="desc"></section>
|
||||
</dd>
|
||||
<dt id="pywrapknapsack_solver.KnapsackSolver.KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER"><code class="name">var <span class="ident">KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER</span></code></dt>
|
||||
<dd>
|
||||
<section class="desc"><p>Generic Solver.</p>
|
||||
<p>This solver can deal with both large number of items and several
|
||||
dimensions. This solver is based on branch and bound.</p></section>
|
||||
<section class="desc"></section>
|
||||
</dd>
|
||||
<dt id="pywrapknapsack_solver.KnapsackSolver.KNAPSACK_MULTIDIMENSION_CBC_MIP_SOLVER"><code class="name">var <span class="ident">KNAPSACK_MULTIDIMENSION_CBC_MIP_SOLVER</span></code></dt>
|
||||
<dd>
|
||||
<section class="desc"><p>CBC Based Solver</p>
|
||||
<p>This solver can deal with both large number of items and several
|
||||
dimensions. This solver is based on Integer Programming solver CBC.</p></section>
|
||||
<section class="desc"></section>
|
||||
</dd>
|
||||
</dl>
|
||||
<h3>Instance variables</h3>
|
||||
@@ -609,7 +197,7 @@ dimensions. This solver is based on Integer Programming solver CBC.</p></section
|
||||
<section class="desc"><p>The membership flag</p></section>
|
||||
<details class="source">
|
||||
<summary>Source code</summary>
|
||||
<pre><code class="python">thisown = property(lambda x: x.this.own(), lambda x, v: x.this.own(v), doc='The membership flag')</code></pre>
|
||||
<pre><code class="python">thisown = property(lambda x: x.this.own(), lambda x, v: x.this.own(v), doc="The membership flag")</code></pre>
|
||||
</details>
|
||||
</dd>
|
||||
</dl>
|
||||
@@ -619,14 +207,10 @@ dimensions. This solver is based on Integer Programming solver CBC.</p></section
|
||||
<span>def <span class="ident">BestSolutionContains</span></span>(<span>self, item_id)</span>
|
||||
</code></dt>
|
||||
<dd>
|
||||
<section class="desc"><p>Returns true if the item 'item_id' is packed in the optimal knapsack.</p></section>
|
||||
<section class="desc"></section>
|
||||
<details class="source">
|
||||
<summary>Source code</summary>
|
||||
<pre><code class="python">def BestSolutionContains(self, item_id: 'int') -> "bool":
|
||||
r"""
|
||||
|
||||
Returns true if the item 'item_id' is packed in the optimal knapsack.
|
||||
"""
|
||||
<pre><code class="python">def BestSolutionContains(self, item_id: "int") -> "bool":
|
||||
return _pywrapknapsack_solver.KnapsackSolver_BestSolutionContains(self, item_id)</code></pre>
|
||||
</details>
|
||||
</dd>
|
||||
@@ -634,14 +218,10 @@ dimensions. This solver is based on Integer Programming solver CBC.</p></section
|
||||
<span>def <span class="ident">Init</span></span>(<span>self, profits, weights, capacities)</span>
|
||||
</code></dt>
|
||||
<dd>
|
||||
<section class="desc"><p>Initializes the solver and enters the problem to be solved.</p></section>
|
||||
<section class="desc"></section>
|
||||
<details class="source">
|
||||
<summary>Source code</summary>
|
||||
<pre><code class="python">def Init(self, profits: 'std::vector< int64 > const &', weights: 'std::vector< std::vector< int64 > > const &', capacities: 'std::vector< int64 > const &') -> "void":
|
||||
r"""
|
||||
|
||||
Initializes the solver and enters the problem to be solved.
|
||||
"""
|
||||
<pre><code class="python">def Init(self, profits: "std::vector< int64 > const &", weights: "std::vector< std::vector< int64 > > const &", capacities: "std::vector< int64 > const &") -> "void":
|
||||
return _pywrapknapsack_solver.KnapsackSolver_Init(self, profits, weights, capacities)</code></pre>
|
||||
</details>
|
||||
</dd>
|
||||
@@ -649,14 +229,10 @@ dimensions. This solver is based on Integer Programming solver CBC.</p></section
|
||||
<span>def <span class="ident">Solve</span></span>(<span>self)</span>
|
||||
</code></dt>
|
||||
<dd>
|
||||
<section class="desc"><p>Solves the problem and returns the profit of the optimal solution.</p></section>
|
||||
<section class="desc"></section>
|
||||
<details class="source">
|
||||
<summary>Source code</summary>
|
||||
<pre><code class="python">def Solve(self) -> "int64":
|
||||
r"""
|
||||
|
||||
Solves the problem and returns the profit of the optimal solution.
|
||||
"""
|
||||
return _pywrapknapsack_solver.KnapsackSolver_Solve(self)</code></pre>
|
||||
</details>
|
||||
</dd>
|
||||
@@ -664,18 +240,10 @@ dimensions. This solver is based on Integer Programming solver CBC.</p></section
|
||||
<span>def <span class="ident">set_time_limit</span></span>(<span>self, time_limit_seconds)</span>
|
||||
</code></dt>
|
||||
<dd>
|
||||
<section class="desc"><p>Time limit in seconds.</p>
|
||||
<p>When a finite time limit is set the solution obtained might not be optimal
|
||||
if the limit is reached.</p></section>
|
||||
<section class="desc"></section>
|
||||
<details class="source">
|
||||
<summary>Source code</summary>
|
||||
<pre><code class="python">def set_time_limit(self, time_limit_seconds: 'double') -> "void":
|
||||
r"""
|
||||
Time limit in seconds.
|
||||
|
||||
When a finite time limit is set the solution obtained might not be optimal
|
||||
if the limit is reached.
|
||||
"""
|
||||
<pre><code class="python">def set_time_limit(self, time_limit_seconds: "double") -> "void":
|
||||
return _pywrapknapsack_solver.KnapsackSolver_set_time_limit(self, time_limit_seconds)</code></pre>
|
||||
</details>
|
||||
</dd>
|
||||
@@ -686,7 +254,7 @@ if the limit is reached.</p></section>
|
||||
<section class="desc"></section>
|
||||
<details class="source">
|
||||
<summary>Source code</summary>
|
||||
<pre><code class="python">def set_use_reduction(self, use_reduction: 'bool') -> "void":
|
||||
<pre><code class="python">def set_use_reduction(self, use_reduction: "bool") -> "void":
|
||||
return _pywrapknapsack_solver.KnapsackSolver_set_use_reduction(self, use_reduction)</code></pre>
|
||||
</details>
|
||||
</dd>
|
||||
@@ -731,7 +299,7 @@ if the limit is reached.</p></section>
|
||||
</main>
|
||||
<footer id="footer">
|
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<p><span style="color:#ddd">卐</span></p>
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Reference in New Issue
Block a user