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<body> <nav class="pdoc">
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<img src="https://developers.google.com/optimization/images/orLogo.png" class="logo" alt="project logo"/>
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<h2>API Documentation</h2>
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<ul class="memberlist">
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<li>
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<a class="class" href="#KnapsackSolver">KnapsackSolver</a>
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<ul class="memberlist">
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<li>
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<a class="function" href="#KnapsackSolver.__init__">KnapsackSolver</a>
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</li>
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<li>
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<a class="variable" href="#KnapsackSolver.thisown">thisown</a>
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</li>
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<li>
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<a class="variable" href="#KnapsackSolver.KNAPSACK_BRUTE_FORCE_SOLVER">KNAPSACK_BRUTE_FORCE_SOLVER</a>
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</li>
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<li>
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<a class="variable" href="#KnapsackSolver.KNAPSACK_64ITEMS_SOLVER">KNAPSACK_64ITEMS_SOLVER</a>
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</li>
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<li>
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<a class="variable" href="#KnapsackSolver.KNAPSACK_DYNAMIC_PROGRAMMING_SOLVER">KNAPSACK_DYNAMIC_PROGRAMMING_SOLVER</a>
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</li>
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<li>
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<a class="variable" href="#KnapsackSolver.KNAPSACK_MULTIDIMENSION_CBC_MIP_SOLVER">KNAPSACK_MULTIDIMENSION_CBC_MIP_SOLVER</a>
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</li>
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<li>
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<a class="variable" href="#KnapsackSolver.KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER">KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER</a>
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</li>
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<li>
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<a class="variable" href="#KnapsackSolver.KNAPSACK_MULTIDIMENSION_SCIP_MIP_SOLVER">KNAPSACK_MULTIDIMENSION_SCIP_MIP_SOLVER</a>
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</li>
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<li>
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<a class="function" href="#KnapsackSolver.Init">Init</a>
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</li>
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<li>
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<a class="function" href="#KnapsackSolver.Solve">Solve</a>
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</li>
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<li>
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<a class="function" href="#KnapsackSolver.BestSolutionContains">BestSolutionContains</a>
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</li>
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<li>
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<a class="function" href="#KnapsackSolver.set_use_reduction">set_use_reduction</a>
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</li>
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<li>
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<a class="function" href="#KnapsackSolver.set_time_limit">set_time_limit</a>
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</li>
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src="data:image/svg+xml,%3Csvg%20xmlns%3D%22http%3A//www.w3.org/2000/svg%22%20role%3D%22img%22%20aria-label%3D%22pdoc%20logo%22%20width%3D%22300%22%20height%3D%22150%22%20viewBox%3D%22-1%200%2060%2030%22%3E%3Ctitle%3Epdoc%3C/title%3E%3Cpath%20d%3D%22M29.621%2021.293c-.011-.273-.214-.475-.511-.481a.5.5%200%200%200-.489.503l-.044%201.393c-.097.551-.695%201.215-1.566%201.704-.577.428-1.306.486-2.193.182-1.426-.617-2.467-1.654-3.304-2.487l-.173-.172a3.43%203.43%200%200%200-.365-.306.49.49%200%200%200-.286-.196c-1.718-1.06-4.931-1.47-7.353.191l-.219.15c-1.707%201.187-3.413%202.131-4.328%201.03-.02-.027-.49-.685-.141-1.763.233-.721.546-2.408.772-4.076.042-.09.067-.187.046-.288.166-1.347.277-2.625.241-3.351%201.378-1.008%202.271-2.586%202.271-4.362%200-.976-.272-1.935-.788-2.774-.057-.094-.122-.18-.184-.268.033-.167.052-.339.052-.516%200-1.477-1.202-2.679-2.679-2.679-.791%200-1.496.352-1.987.9a6.3%206.3%200%200%200-1.001.029c-.492-.564-1.207-.929-2.012-.929-1.477%200-2.679%201.202-2.679%202.679A2.65%202.65%200%200%200%20.97%206.554c-.383.747-.595%201.572-.595%202.41%200%202.311%201.507%204.29%203.635%205.107-.037.699-.147%202.27-.423%203.294l-.137.461c-.622%202.042-2.515%208.257%201.727%2010.643%201.614.908%203.06%201.248%204.317%201.248%202.665%200%204.492-1.524%205.322-2.401%201.476-1.559%202.886-1.854%206.491.82%201.877%201.393%203.514%201.753%204.861%201.068%202.223-1.713%202.811-3.867%203.399-6.374.077-.846.056-1.469.054-1.537zm-4.835%204.313c-.054.305-.156.586-.242.629-.034-.007-.131-.022-.307-.157-.145-.111-.314-.478-.456-.908.221.121.432.25.675.355.115.039.219.051.33.081zm-2.251-1.238c-.05.33-.158.648-.252.694-.022.001-.125-.018-.307-.157-.217-.166-.488-.906-.639-1.573.358.344.754.693%201.198%201.036zm-3.887-2.337c-.006-.116-.018-.231-.041-.342.635.145%201.189.368%201.599.625.097.231.166.481.174.642-.03.049-.055.101-.067.158-.046.013-.128.026-.298.004-.278-.037-.901-.57-1.367-1.087zm-1.127-.497c.116.306.176.625.12.71-.019.014-.117.045-.345.016-.206-.027-.604-.332-.986-.695.41-.051.816-.056%201.211-.031zm-4.535%201.535c.209.22.379.47.358.598-.006.041-.088.138-.351.234-.144.055-.539-.063-.979-.259a11.66%2011.66%200%200%200%20.972-.573zm.983-.664c.359-.237.738-.418%201.126-.554.25.237.479.548.457.694-.006.042-.087.138-.351.235-.174.064-.694-.105-1.232-.375zm-3.381%201.794c-.022.145-.061.29-.149.401-.133.166-.358.248-.69.251h-.002c-.133%200-.306-.26-.45-.621.417.091.854.07%201.291-.031zm-2.066-8.077a4.78%204.78%200%200%201-.775-.584c.172-.115.505-.254.88-.378l-.105.962zm-.331%202.302a10.32%2010.32%200%200%201-.828-.502c.202-.143.576-.328.984-.49l-.156.992zm-.45%202.157l-.701-.403c.214-.115.536-.249.891-.376a11.57%2011.57%200%200%201-.19.779zm-.181%201.716c.064.398.194.702.298.893-.194-.051-.435-.162-.736-.398.061-.119.224-.3.438-.495zM8.87%204.141c0%20.152-.123.276-.276.276s-.275-.124-.275-.276.123-.276.276-.276.275.124.275.276zm-.735-.389a1.15%201.15%200%200%200-.314.783%201.16%201.16%200%200%200%201.162%201.162c.457%200%20.842-.27%201.032-.653.026.117.042.238.042.362a1.68%201.68%200%200%201-1.679%201.679%201.68%201.68%200%200%201-1.679-1.679c0-.843.626-1.535%201.436-1.654zM5.059%205.406A1.68%201.68%200%200%201%203.38%207.085a1.68%201.68%200%200%201-1.679-1.679c0-.037.009-.072.011-.109.21.3.541.508.935.508a1.16%201.16%200%200%200%201.162-1.162%201.14%201.14%200%200%200-.474-.912c.015%200%20.03-.005.045-.005.926.001%201.679.754%201.679%201.68zM3.198%204.141c0%20.152-.123.276-.276.276s-.275-.124-.275-.276.123-.276.276-.276.275.124.275.276zM1.375%208.964c0-.52.103-1.035.288-1.52.466.394%201.06.64%201.717.64%201.144%200%202.116-.725%202.499-1.738.383%201.012%201.355%201.738%202.499%201.738.867%200%201.631-.421%202.121-1.062.307.605.478%201.267.478%201.942%200%202.486-2.153%204.51-4.801%204.51s-4.801-2.023-4.801-4.51zm24.342%2019.349c-.985.498-2.267.168-3.813-.979-3.073-2.281-5.453-3.199-7.813-.705-1.315%201.391-4.163%203.365-8.423.97-3.174-1.786-2.239-6.266-1.261-9.479l.146-.492c.276-1.02.395-2.457.444-3.268a6.11%206.11%200%200%200%201.18.115%206.01%206.01%200%200%200%202.536-.562l-.006.175c-.802.215-1.848.612-2.021%201.25-.079.295.021.601.274.837.219.203.415.364.598.501-.667.304-1.243.698-1.311%201.179-.02.144-.022.507.393.787.213.144.395.26.564.365-1.285.521-1.361.96-1.381%201.126-.018.142-.011.496.427.746l.854.489c-.473.389-.971.914-.999%201.429-.018.278.095.532.316.713.675.556%201.231.721%201.653.721.059%200%20.104-.014.158-.02.207.707.641%201.64%201.513%201.64h.013c.8-.008%201.236-.345%201.462-.626.173-.216.268-.457.325-.692.424.195.93.374%201.372.374.151%200%20.294-.021.423-.068.732-.27.944-.704.993-1.021.009-.061.003-.119.002-.179.266.086.538.147.789.147.15%200%20.294-.021.423-.069.542-.2.797-.489.914-.754.237.147.478.258.704.288.106.014.205.021.296.021.356%200%20.595-.101.767-.229.438.435%201.094.992%201.656%201.067.106.014.205.021.296.021a1.56%201.56%200%200%200%20.323-.035c.17.575.453%201.289.866%201.605.358.273.665.362.914.362a.99.99%200%200%200%20.421-.093%201.03%201.03%200%200%200%20.245-.164c.168.42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</nav>
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<main class="pdoc">
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<section>
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<h1 class="modulename">
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pywrapknapsack_solver </h1>
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<details>
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<summary>View Source</summary>
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<div class="codehilite"><pre><span></span><span class="c1"># This file was automatically generated by SWIG (http://www.swig.org).</span>
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<span class="c1"># Version 4.0.2</span>
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<span class="c1">#</span>
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<span class="c1"># Do not make changes to this file unless you know what you are doing--modify</span>
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<span class="c1"># the SWIG interface file instead.</span>
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<span class="kn">from</span> <span class="nn">sys</span> <span class="kn">import</span> <span class="n">version_info</span> <span class="k">as</span> <span class="n">_swig_python_version_info</span>
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<span class="k">if</span> <span class="n">_swig_python_version_info</span> <span class="o"><</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">7</span><span class="p">,</span> <span class="mi">0</span><span class="p">):</span>
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<span class="k">raise</span> <span class="ne">RuntimeError</span><span class="p">(</span><span class="s2">"Python 2.7 or later required"</span><span class="p">)</span>
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<span class="c1"># Import the low-level C/C++ module</span>
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<span class="k">if</span> <span class="n">__package__</span> <span class="ow">or</span> <span class="s2">"."</span> <span class="ow">in</span> <span class="vm">__name__</span><span class="p">:</span>
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<span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">_pywrapknapsack_solver</span>
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<span class="k">else</span><span class="p">:</span>
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<span class="kn">import</span> <span class="nn">_pywrapknapsack_solver</span>
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<span class="k">try</span><span class="p">:</span>
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<span class="kn">import</span> <span class="nn">builtins</span> <span class="k">as</span> <span class="nn">__builtin__</span>
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<span class="k">except</span> <span class="ne">ImportError</span><span class="p">:</span>
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<span class="kn">import</span> <span class="nn">__builtin__</span>
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<span class="k">def</span> <span class="nf">_swig_repr</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
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<span class="k">try</span><span class="p">:</span>
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<span class="n">strthis</span> <span class="o">=</span> <span class="s2">"proxy of "</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">this</span><span class="o">.</span><span class="fm">__repr__</span><span class="p">()</span>
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<span class="k">except</span> <span class="n">__builtin__</span><span class="o">.</span><span class="n">Exception</span><span class="p">:</span>
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<span class="n">strthis</span> <span class="o">=</span> <span class="s2">""</span>
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<span class="k">return</span> <span class="s2">"<</span><span class="si">%s</span><span class="s2">.</span><span class="si">%s</span><span class="s2">; </span><span class="si">%s</span><span class="s2"> >"</span> <span class="o">%</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="vm">__class__</span><span class="o">.</span><span class="vm">__module__</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="vm">__class__</span><span class="o">.</span><span class="vm">__name__</span><span class="p">,</span> <span class="n">strthis</span><span class="p">,)</span>
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<span class="k">def</span> <span class="nf">_swig_setattr_nondynamic_instance_variable</span><span class="p">(</span><span class="nb">set</span><span class="p">):</span>
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<span class="k">def</span> <span class="nf">set_instance_attr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">name</span><span class="p">,</span> <span class="n">value</span><span class="p">):</span>
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<span class="k">if</span> <span class="n">name</span> <span class="o">==</span> <span class="s2">"thisown"</span><span class="p">:</span>
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<span class="bp">self</span><span class="o">.</span><span class="n">this</span><span class="o">.</span><span class="n">own</span><span class="p">(</span><span class="n">value</span><span class="p">)</span>
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<span class="k">elif</span> <span class="n">name</span> <span class="o">==</span> <span class="s2">"this"</span><span class="p">:</span>
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<span class="nb">set</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">name</span><span class="p">,</span> <span class="n">value</span><span class="p">)</span>
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<span class="k">elif</span> <span class="nb">hasattr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">name</span><span class="p">)</span> <span class="ow">and</span> <span class="nb">isinstance</span><span class="p">(</span><span class="nb">getattr</span><span class="p">(</span><span class="nb">type</span><span class="p">(</span><span class="bp">self</span><span class="p">),</span> <span class="n">name</span><span class="p">),</span> <span class="nb">property</span><span class="p">):</span>
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<span class="nb">set</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">name</span><span class="p">,</span> <span class="n">value</span><span class="p">)</span>
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<span class="k">else</span><span class="p">:</span>
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<span class="k">raise</span> <span class="ne">AttributeError</span><span class="p">(</span><span class="s2">"You cannot add instance attributes to </span><span class="si">%s</span><span class="s2">"</span> <span class="o">%</span> <span class="bp">self</span><span class="p">)</span>
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<span class="k">return</span> <span class="n">set_instance_attr</span>
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<span class="k">def</span> <span class="nf">_swig_setattr_nondynamic_class_variable</span><span class="p">(</span><span class="nb">set</span><span class="p">):</span>
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<span class="k">def</span> <span class="nf">set_class_attr</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">name</span><span class="p">,</span> <span class="n">value</span><span class="p">):</span>
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<span class="k">if</span> <span class="nb">hasattr</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">name</span><span class="p">)</span> <span class="ow">and</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="nb">getattr</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">name</span><span class="p">),</span> <span class="nb">property</span><span class="p">):</span>
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<span class="nb">set</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">name</span><span class="p">,</span> <span class="n">value</span><span class="p">)</span>
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<span class="k">else</span><span class="p">:</span>
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<span class="k">raise</span> <span class="ne">AttributeError</span><span class="p">(</span><span class="s2">"You cannot add class attributes to </span><span class="si">%s</span><span class="s2">"</span> <span class="o">%</span> <span class="bp">cls</span><span class="p">)</span>
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<span class="k">return</span> <span class="n">set_class_attr</span>
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<span class="k">def</span> <span class="nf">_swig_add_metaclass</span><span class="p">(</span><span class="n">metaclass</span><span class="p">):</span>
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<span class="sd">"""Class decorator for adding a metaclass to a SWIG wrapped class - a slimmed down version of six.add_metaclass"""</span>
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<span class="k">def</span> <span class="nf">wrapper</span><span class="p">(</span><span class="bp">cls</span><span class="p">):</span>
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<span class="k">return</span> <span class="n">metaclass</span><span class="p">(</span><span class="bp">cls</span><span class="o">.</span><span class="vm">__name__</span><span class="p">,</span> <span class="bp">cls</span><span class="o">.</span><span class="vm">__bases__</span><span class="p">,</span> <span class="bp">cls</span><span class="o">.</span><span class="vm">__dict__</span><span class="o">.</span><span class="n">copy</span><span class="p">())</span>
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<span class="k">return</span> <span class="n">wrapper</span>
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<span class="k">class</span> <span class="nc">_SwigNonDynamicMeta</span><span class="p">(</span><span class="nb">type</span><span class="p">):</span>
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|
<span class="sd">"""Meta class to enforce nondynamic attributes (no new attributes) for a class"""</span>
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|
<span class="fm">__setattr__</span> <span class="o">=</span> <span class="n">_swig_setattr_nondynamic_class_variable</span><span class="p">(</span><span class="nb">type</span><span class="o">.</span><span class="fm">__setattr__</span><span class="p">)</span>
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<span class="k">class</span> <span class="nc">KnapsackSolver</span><span class="p">(</span><span class="nb">object</span><span class="p">):</span>
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<span class="sa">r</span><span class="sd">"""</span>
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<span class="sd"> This library solves knapsack problems.</span>
|
|
|
|
<span class="sd"> Problems the library solves include:</span>
|
|
<span class="sd"> - 0-1 knapsack problems,</span>
|
|
<span class="sd"> - Multi-dimensional knapsack problems,</span>
|
|
|
|
<span class="sd"> Given n items, each with a profit and a weight, given a knapsack of</span>
|
|
<span class="sd"> capacity c, the goal is to find a subset of items which fits inside c</span>
|
|
<span class="sd"> and maximizes the total profit.</span>
|
|
<span class="sd"> The knapsack problem can easily be extended from 1 to d dimensions.</span>
|
|
<span class="sd"> As an example, this can be useful to constrain the maximum number of</span>
|
|
<span class="sd"> items inside the knapsack.</span>
|
|
<span class="sd"> Without loss of generality, profits and weights are assumed to be positive.</span>
|
|
|
|
<span class="sd"> From a mathematical point of view, the multi-dimensional knapsack problem</span>
|
|
<span class="sd"> can be modeled by d linear constraints:</span>
|
|
|
|
<span class="sd"> ForEach(j:1..d)(Sum(i:1..n)(weight_ij * item_i) <= c_j</span>
|
|
<span class="sd"> where item_i is a 0-1 integer variable.</span>
|
|
|
|
<span class="sd"> Then the goal is to maximize:</span>
|
|
|
|
<span class="sd"> Sum(i:1..n)(profit_i * item_i).</span>
|
|
|
|
<span class="sd"> There are several ways to solve knapsack problems. One of the most</span>
|
|
<span class="sd"> efficient is based on dynamic programming (mainly when weights, profits</span>
|
|
<span class="sd"> and dimensions are small, and the algorithm runs in pseudo polynomial time).</span>
|
|
<span class="sd"> Unfortunately, when adding conflict constraints the problem becomes strongly</span>
|
|
<span class="sd"> NP-hard, i.e. there is no pseudo-polynomial algorithm to solve it.</span>
|
|
<span class="sd"> That's the reason why the most of the following code is based on branch and</span>
|
|
<span class="sd"> bound search.</span>
|
|
|
|
<span class="sd"> For instance to solve a 2-dimensional knapsack problem with 9 items,</span>
|
|
<span class="sd"> one just has to feed a profit vector with the 9 profits, a vector of 2</span>
|
|
<span class="sd"> vectors for weights, and a vector of capacities.</span>
|
|
<span class="sd"> E.g.:</span>
|
|
|
|
<span class="sd"> **Python**:</span>
|
|
|
|
<span class="sd"> .. code-block:: python</span>
|
|
|
|
<span class="sd"> profits = [ 1, 2, 3, 4, 5, 6, 7, 8, 9 ]</span>
|
|
<span class="sd"> weights = [ [ 1, 2, 3, 4, 5, 6, 7, 8, 9 ],</span>
|
|
<span class="sd"> [ 1, 1, 1, 1, 1, 1, 1, 1, 1 ]</span>
|
|
<span class="sd"> ]</span>
|
|
<span class="sd"> capacities = [ 34, 4 ]</span>
|
|
|
|
<span class="sd"> solver = pywrapknapsack_solver.KnapsackSolver(</span>
|
|
<span class="sd"> pywrapknapsack_solver.KnapsackSolver</span>
|
|
<span class="sd"> .KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER,</span>
|
|
<span class="sd"> 'Multi-dimensional solver')</span>
|
|
<span class="sd"> solver.Init(profits, weights, capacities)</span>
|
|
<span class="sd"> profit = solver.Solve()</span>
|
|
|
|
<span class="sd"> **C++**:</span>
|
|
|
|
<span class="sd"> .. code-block:: c++</span>
|
|
|
|
<span class="sd"> const std::vector<int64_t> profits = { 1, 2, 3, 4, 5, 6, 7, 8, 9 };</span>
|
|
<span class="sd"> const std::vector<std::vector<int64_t>> weights =</span>
|
|
<span class="sd"> { { 1, 2, 3, 4, 5, 6, 7, 8, 9 },</span>
|
|
<span class="sd"> { 1, 1, 1, 1, 1, 1, 1, 1, 1 } };</span>
|
|
<span class="sd"> const std::vector<int64_t> capacities = { 34, 4 };</span>
|
|
|
|
<span class="sd"> KnapsackSolver solver(</span>
|
|
<span class="sd"> KnapsackSolver::KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER,</span>
|
|
<span class="sd"> "Multi-dimensional solver");</span>
|
|
<span class="sd"> solver.Init(profits, weights, capacities);</span>
|
|
<span class="sd"> const int64_t profit = solver.Solve();</span>
|
|
|
|
<span class="sd"> **Java**:</span>
|
|
|
|
<span class="sd"> .. code-block:: java</span>
|
|
|
|
<span class="sd"> final long[] profits = { 1, 2, 3, 4, 5, 6, 7, 8, 9 };</span>
|
|
<span class="sd"> final long[][] weights = { { 1, 2, 3, 4, 5, 6, 7, 8, 9 },</span>
|
|
<span class="sd"> { 1, 1, 1, 1, 1, 1, 1, 1, 1 } };</span>
|
|
<span class="sd"> final long[] capacities = { 34, 4 };</span>
|
|
|
|
<span class="sd"> KnapsackSolver solver = new KnapsackSolver(</span>
|
|
<span class="sd"> KnapsackSolver.SolverType.KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER,</span>
|
|
<span class="sd"> "Multi-dimensional solver");</span>
|
|
<span class="sd"> solver.init(profits, weights, capacities);</span>
|
|
<span class="sd"> final long profit = solver.solve();</span>
|
|
<span class="sd"> """</span>
|
|
|
|
<span class="n">thisown</span> <span class="o">=</span> <span class="nb">property</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x</span><span class="p">:</span> <span class="n">x</span><span class="o">.</span><span class="n">this</span><span class="o">.</span><span class="n">own</span><span class="p">(),</span> <span class="k">lambda</span> <span class="n">x</span><span class="p">,</span> <span class="n">v</span><span class="p">:</span> <span class="n">x</span><span class="o">.</span><span class="n">this</span><span class="o">.</span><span class="n">own</span><span class="p">(</span><span class="n">v</span><span class="p">),</span> <span class="n">doc</span><span class="o">=</span><span class="s2">"The membership flag"</span><span class="p">)</span>
|
|
<span class="fm">__repr__</span> <span class="o">=</span> <span class="n">_swig_repr</span>
|
|
<span class="n">KNAPSACK_BRUTE_FORCE_SOLVER</span> <span class="o">=</span> <span class="n">_pywrapknapsack_solver</span><span class="o">.</span><span class="n">KnapsackSolver_KNAPSACK_BRUTE_FORCE_SOLVER</span>
|
|
<span class="sa">r</span><span class="sd">"""</span>
|
|
<span class="sd"> Brute force method.</span>
|
|
|
|
<span class="sd"> Limited to 30 items and one dimension, this</span>
|
|
<span class="sd"> solver uses a brute force algorithm, ie. explores all possible states.</span>
|
|
<span class="sd"> Experiments show competitive performance for instances with less than</span>
|
|
<span class="sd"> 15 items.</span>
|
|
<span class="sd"> """</span>
|
|
<span class="n">KNAPSACK_64ITEMS_SOLVER</span> <span class="o">=</span> <span class="n">_pywrapknapsack_solver</span><span class="o">.</span><span class="n">KnapsackSolver_KNAPSACK_64ITEMS_SOLVER</span>
|
|
<span class="sa">r</span><span class="sd">"""</span>
|
|
<span class="sd"> Optimized method for single dimension small problems</span>
|
|
|
|
<span class="sd"> Limited to 64 items and one dimension, this</span>
|
|
<span class="sd"> solver uses a branch & bound algorithm. This solver is about 4 times</span>
|
|
<span class="sd"> faster than KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER.</span>
|
|
<span class="sd"> """</span>
|
|
<span class="n">KNAPSACK_DYNAMIC_PROGRAMMING_SOLVER</span> <span class="o">=</span> <span class="n">_pywrapknapsack_solver</span><span class="o">.</span><span class="n">KnapsackSolver_KNAPSACK_DYNAMIC_PROGRAMMING_SOLVER</span>
|
|
<span class="sa">r</span><span class="sd">"""</span>
|
|
<span class="sd"> Dynamic Programming approach for single dimension problems</span>
|
|
|
|
<span class="sd"> Limited to one dimension, this solver is based on a dynamic programming</span>
|
|
<span class="sd"> algorithm. The time and space complexity is O(capacity *</span>
|
|
<span class="sd"> number_of_items).</span>
|
|
<span class="sd"> """</span>
|
|
<span class="n">KNAPSACK_MULTIDIMENSION_CBC_MIP_SOLVER</span> <span class="o">=</span> <span class="n">_pywrapknapsack_solver</span><span class="o">.</span><span class="n">KnapsackSolver_KNAPSACK_MULTIDIMENSION_CBC_MIP_SOLVER</span>
|
|
<span class="sa">r</span><span class="sd">"""</span>
|
|
<span class="sd"> CBC Based Solver</span>
|
|
|
|
<span class="sd"> This solver can deal with both large number of items and several</span>
|
|
<span class="sd"> dimensions. This solver is based on Integer Programming solver CBC.</span>
|
|
<span class="sd"> """</span>
|
|
<span class="n">KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER</span> <span class="o">=</span> <span class="n">_pywrapknapsack_solver</span><span class="o">.</span><span class="n">KnapsackSolver_KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER</span>
|
|
<span class="sa">r</span><span class="sd">"""</span>
|
|
<span class="sd"> Generic Solver.</span>
|
|
|
|
<span class="sd"> This solver can deal with both large number of items and several</span>
|
|
<span class="sd"> dimensions. This solver is based on branch and bound.</span>
|
|
<span class="sd"> """</span>
|
|
<span class="n">KNAPSACK_MULTIDIMENSION_SCIP_MIP_SOLVER</span> <span class="o">=</span> <span class="n">_pywrapknapsack_solver</span><span class="o">.</span><span class="n">KnapsackSolver_KNAPSACK_MULTIDIMENSION_SCIP_MIP_SOLVER</span>
|
|
<span class="sa">r</span><span class="sd">"""</span>
|
|
<span class="sd"> SCIP based solver</span>
|
|
|
|
<span class="sd"> This solver can deal with both large number of items and several</span>
|
|
<span class="sd"> dimensions. This solver is based on Integer Programming solver SCIP.</span>
|
|
<span class="sd"> """</span>
|
|
|
|
<span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">*</span><span class="n">args</span><span class="p">):</span>
|
|
<span class="n">_pywrapknapsack_solver</span><span class="o">.</span><span class="n">KnapsackSolver_swiginit</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">_pywrapknapsack_solver</span><span class="o">.</span><span class="n">new_KnapsackSolver</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">))</span>
|
|
<span class="n">__swig_destroy__</span> <span class="o">=</span> <span class="n">_pywrapknapsack_solver</span><span class="o">.</span><span class="n">delete_KnapsackSolver</span>
|
|
|
|
<span class="k">def</span> <span class="nf">Init</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">profits</span><span class="p">:</span> <span class="s2">"std::vector< int64_t > const &"</span><span class="p">,</span> <span class="n">weights</span><span class="p">:</span> <span class="s2">"std::vector< std::vector< int64_t > > const &"</span><span class="p">,</span> <span class="n">capacities</span><span class="p">:</span> <span class="s2">"std::vector< int64_t > const &"</span><span class="p">)</span> <span class="o">-></span> <span class="s2">"void"</span><span class="p">:</span>
|
|
<span class="sa">r</span><span class="sd">"""Initializes the solver and enters the problem to be solved."""</span>
|
|
<span class="k">return</span> <span class="n">_pywrapknapsack_solver</span><span class="o">.</span><span class="n">KnapsackSolver_Init</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">profits</span><span class="p">,</span> <span class="n">weights</span><span class="p">,</span> <span class="n">capacities</span><span class="p">)</span>
|
|
|
|
<span class="k">def</span> <span class="nf">Solve</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-></span> <span class="s2">"int64_t"</span><span class="p">:</span>
|
|
<span class="sa">r</span><span class="sd">"""Solves the problem and returns the profit of the optimal solution."""</span>
|
|
<span class="k">return</span> <span class="n">_pywrapknapsack_solver</span><span class="o">.</span><span class="n">KnapsackSolver_Solve</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span>
|
|
|
|
<span class="k">def</span> <span class="nf">BestSolutionContains</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">item_id</span><span class="p">:</span> <span class="s2">"int"</span><span class="p">)</span> <span class="o">-></span> <span class="s2">"bool"</span><span class="p">:</span>
|
|
<span class="sa">r</span><span class="sd">"""Returns true if the item 'item_id' is packed in the optimal knapsack."""</span>
|
|
<span class="k">return</span> <span class="n">_pywrapknapsack_solver</span><span class="o">.</span><span class="n">KnapsackSolver_BestSolutionContains</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">item_id</span><span class="p">)</span>
|
|
|
|
<span class="k">def</span> <span class="nf">set_use_reduction</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">use_reduction</span><span class="p">:</span> <span class="s2">"bool"</span><span class="p">)</span> <span class="o">-></span> <span class="s2">"void"</span><span class="p">:</span>
|
|
<span class="k">return</span> <span class="n">_pywrapknapsack_solver</span><span class="o">.</span><span class="n">KnapsackSolver_set_use_reduction</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">use_reduction</span><span class="p">)</span>
|
|
|
|
<span class="k">def</span> <span class="nf">set_time_limit</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">time_limit_seconds</span><span class="p">:</span> <span class="s2">"double"</span><span class="p">)</span> <span class="o">-></span> <span class="s2">"void"</span><span class="p">:</span>
|
|
<span class="sa">r</span><span class="sd">"""</span>
|
|
<span class="sd"> Time limit in seconds.</span>
|
|
|
|
<span class="sd"> When a finite time limit is set the solution obtained might not be optimal</span>
|
|
<span class="sd"> if the limit is reached.</span>
|
|
<span class="sd"> """</span>
|
|
<span class="k">return</span> <span class="n">_pywrapknapsack_solver</span><span class="o">.</span><span class="n">KnapsackSolver_set_time_limit</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">time_limit_seconds</span><span class="p">)</span>
|
|
|
|
<span class="c1"># Register KnapsackSolver in _pywrapknapsack_solver:</span>
|
|
<span class="n">_pywrapknapsack_solver</span><span class="o">.</span><span class="n">KnapsackSolver_swigregister</span><span class="p">(</span><span class="n">KnapsackSolver</span><span class="p">)</span>
|
|
</pre></div>
|
|
|
|
</details>
|
|
|
|
</section>
|
|
<section id="KnapsackSolver">
|
|
<div class="attr class">
|
|
<a class="headerlink" href="#KnapsackSolver">#  </a>
|
|
|
|
|
|
<span class="def">class</span>
|
|
<span class="name">KnapsackSolver</span>:
|
|
</div>
|
|
|
|
<details>
|
|
<summary>View Source</summary>
|
|
<div class="codehilite"><pre><span></span><span class="k">class</span> <span class="nc">KnapsackSolver</span><span class="p">(</span><span class="nb">object</span><span class="p">):</span>
|
|
<span class="sa">r</span><span class="sd">"""</span>
|
|
<span class="sd"> This library solves knapsack problems.</span>
|
|
|
|
<span class="sd"> Problems the library solves include:</span>
|
|
<span class="sd"> - 0-1 knapsack problems,</span>
|
|
<span class="sd"> - Multi-dimensional knapsack problems,</span>
|
|
|
|
<span class="sd"> Given n items, each with a profit and a weight, given a knapsack of</span>
|
|
<span class="sd"> capacity c, the goal is to find a subset of items which fits inside c</span>
|
|
<span class="sd"> and maximizes the total profit.</span>
|
|
<span class="sd"> The knapsack problem can easily be extended from 1 to d dimensions.</span>
|
|
<span class="sd"> As an example, this can be useful to constrain the maximum number of</span>
|
|
<span class="sd"> items inside the knapsack.</span>
|
|
<span class="sd"> Without loss of generality, profits and weights are assumed to be positive.</span>
|
|
|
|
<span class="sd"> From a mathematical point of view, the multi-dimensional knapsack problem</span>
|
|
<span class="sd"> can be modeled by d linear constraints:</span>
|
|
|
|
<span class="sd"> ForEach(j:1..d)(Sum(i:1..n)(weight_ij * item_i) <= c_j</span>
|
|
<span class="sd"> where item_i is a 0-1 integer variable.</span>
|
|
|
|
<span class="sd"> Then the goal is to maximize:</span>
|
|
|
|
<span class="sd"> Sum(i:1..n)(profit_i * item_i).</span>
|
|
|
|
<span class="sd"> There are several ways to solve knapsack problems. One of the most</span>
|
|
<span class="sd"> efficient is based on dynamic programming (mainly when weights, profits</span>
|
|
<span class="sd"> and dimensions are small, and the algorithm runs in pseudo polynomial time).</span>
|
|
<span class="sd"> Unfortunately, when adding conflict constraints the problem becomes strongly</span>
|
|
<span class="sd"> NP-hard, i.e. there is no pseudo-polynomial algorithm to solve it.</span>
|
|
<span class="sd"> That's the reason why the most of the following code is based on branch and</span>
|
|
<span class="sd"> bound search.</span>
|
|
|
|
<span class="sd"> For instance to solve a 2-dimensional knapsack problem with 9 items,</span>
|
|
<span class="sd"> one just has to feed a profit vector with the 9 profits, a vector of 2</span>
|
|
<span class="sd"> vectors for weights, and a vector of capacities.</span>
|
|
<span class="sd"> E.g.:</span>
|
|
|
|
<span class="sd"> **Python**:</span>
|
|
|
|
<span class="sd"> .. code-block:: python</span>
|
|
|
|
<span class="sd"> profits = [ 1, 2, 3, 4, 5, 6, 7, 8, 9 ]</span>
|
|
<span class="sd"> weights = [ [ 1, 2, 3, 4, 5, 6, 7, 8, 9 ],</span>
|
|
<span class="sd"> [ 1, 1, 1, 1, 1, 1, 1, 1, 1 ]</span>
|
|
<span class="sd"> ]</span>
|
|
<span class="sd"> capacities = [ 34, 4 ]</span>
|
|
|
|
<span class="sd"> solver = pywrapknapsack_solver.KnapsackSolver(</span>
|
|
<span class="sd"> pywrapknapsack_solver.KnapsackSolver</span>
|
|
<span class="sd"> .KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER,</span>
|
|
<span class="sd"> 'Multi-dimensional solver')</span>
|
|
<span class="sd"> solver.Init(profits, weights, capacities)</span>
|
|
<span class="sd"> profit = solver.Solve()</span>
|
|
|
|
<span class="sd"> **C++**:</span>
|
|
|
|
<span class="sd"> .. code-block:: c++</span>
|
|
|
|
<span class="sd"> const std::vector<int64_t> profits = { 1, 2, 3, 4, 5, 6, 7, 8, 9 };</span>
|
|
<span class="sd"> const std::vector<std::vector<int64_t>> weights =</span>
|
|
<span class="sd"> { { 1, 2, 3, 4, 5, 6, 7, 8, 9 },</span>
|
|
<span class="sd"> { 1, 1, 1, 1, 1, 1, 1, 1, 1 } };</span>
|
|
<span class="sd"> const std::vector<int64_t> capacities = { 34, 4 };</span>
|
|
|
|
<span class="sd"> KnapsackSolver solver(</span>
|
|
<span class="sd"> KnapsackSolver::KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER,</span>
|
|
<span class="sd"> "Multi-dimensional solver");</span>
|
|
<span class="sd"> solver.Init(profits, weights, capacities);</span>
|
|
<span class="sd"> const int64_t profit = solver.Solve();</span>
|
|
|
|
<span class="sd"> **Java**:</span>
|
|
|
|
<span class="sd"> .. code-block:: java</span>
|
|
|
|
<span class="sd"> final long[] profits = { 1, 2, 3, 4, 5, 6, 7, 8, 9 };</span>
|
|
<span class="sd"> final long[][] weights = { { 1, 2, 3, 4, 5, 6, 7, 8, 9 },</span>
|
|
<span class="sd"> { 1, 1, 1, 1, 1, 1, 1, 1, 1 } };</span>
|
|
<span class="sd"> final long[] capacities = { 34, 4 };</span>
|
|
|
|
<span class="sd"> KnapsackSolver solver = new KnapsackSolver(</span>
|
|
<span class="sd"> KnapsackSolver.SolverType.KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER,</span>
|
|
<span class="sd"> "Multi-dimensional solver");</span>
|
|
<span class="sd"> solver.init(profits, weights, capacities);</span>
|
|
<span class="sd"> final long profit = solver.solve();</span>
|
|
<span class="sd"> """</span>
|
|
|
|
<span class="n">thisown</span> <span class="o">=</span> <span class="nb">property</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x</span><span class="p">:</span> <span class="n">x</span><span class="o">.</span><span class="n">this</span><span class="o">.</span><span class="n">own</span><span class="p">(),</span> <span class="k">lambda</span> <span class="n">x</span><span class="p">,</span> <span class="n">v</span><span class="p">:</span> <span class="n">x</span><span class="o">.</span><span class="n">this</span><span class="o">.</span><span class="n">own</span><span class="p">(</span><span class="n">v</span><span class="p">),</span> <span class="n">doc</span><span class="o">=</span><span class="s2">"The membership flag"</span><span class="p">)</span>
|
|
<span class="fm">__repr__</span> <span class="o">=</span> <span class="n">_swig_repr</span>
|
|
<span class="n">KNAPSACK_BRUTE_FORCE_SOLVER</span> <span class="o">=</span> <span class="n">_pywrapknapsack_solver</span><span class="o">.</span><span class="n">KnapsackSolver_KNAPSACK_BRUTE_FORCE_SOLVER</span>
|
|
<span class="sa">r</span><span class="sd">"""</span>
|
|
<span class="sd"> Brute force method.</span>
|
|
|
|
<span class="sd"> Limited to 30 items and one dimension, this</span>
|
|
<span class="sd"> solver uses a brute force algorithm, ie. explores all possible states.</span>
|
|
<span class="sd"> Experiments show competitive performance for instances with less than</span>
|
|
<span class="sd"> 15 items.</span>
|
|
<span class="sd"> """</span>
|
|
<span class="n">KNAPSACK_64ITEMS_SOLVER</span> <span class="o">=</span> <span class="n">_pywrapknapsack_solver</span><span class="o">.</span><span class="n">KnapsackSolver_KNAPSACK_64ITEMS_SOLVER</span>
|
|
<span class="sa">r</span><span class="sd">"""</span>
|
|
<span class="sd"> Optimized method for single dimension small problems</span>
|
|
|
|
<span class="sd"> Limited to 64 items and one dimension, this</span>
|
|
<span class="sd"> solver uses a branch & bound algorithm. This solver is about 4 times</span>
|
|
<span class="sd"> faster than KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER.</span>
|
|
<span class="sd"> """</span>
|
|
<span class="n">KNAPSACK_DYNAMIC_PROGRAMMING_SOLVER</span> <span class="o">=</span> <span class="n">_pywrapknapsack_solver</span><span class="o">.</span><span class="n">KnapsackSolver_KNAPSACK_DYNAMIC_PROGRAMMING_SOLVER</span>
|
|
<span class="sa">r</span><span class="sd">"""</span>
|
|
<span class="sd"> Dynamic Programming approach for single dimension problems</span>
|
|
|
|
<span class="sd"> Limited to one dimension, this solver is based on a dynamic programming</span>
|
|
<span class="sd"> algorithm. The time and space complexity is O(capacity *</span>
|
|
<span class="sd"> number_of_items).</span>
|
|
<span class="sd"> """</span>
|
|
<span class="n">KNAPSACK_MULTIDIMENSION_CBC_MIP_SOLVER</span> <span class="o">=</span> <span class="n">_pywrapknapsack_solver</span><span class="o">.</span><span class="n">KnapsackSolver_KNAPSACK_MULTIDIMENSION_CBC_MIP_SOLVER</span>
|
|
<span class="sa">r</span><span class="sd">"""</span>
|
|
<span class="sd"> CBC Based Solver</span>
|
|
|
|
<span class="sd"> This solver can deal with both large number of items and several</span>
|
|
<span class="sd"> dimensions. This solver is based on Integer Programming solver CBC.</span>
|
|
<span class="sd"> """</span>
|
|
<span class="n">KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER</span> <span class="o">=</span> <span class="n">_pywrapknapsack_solver</span><span class="o">.</span><span class="n">KnapsackSolver_KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER</span>
|
|
<span class="sa">r</span><span class="sd">"""</span>
|
|
<span class="sd"> Generic Solver.</span>
|
|
|
|
<span class="sd"> This solver can deal with both large number of items and several</span>
|
|
<span class="sd"> dimensions. This solver is based on branch and bound.</span>
|
|
<span class="sd"> """</span>
|
|
<span class="n">KNAPSACK_MULTIDIMENSION_SCIP_MIP_SOLVER</span> <span class="o">=</span> <span class="n">_pywrapknapsack_solver</span><span class="o">.</span><span class="n">KnapsackSolver_KNAPSACK_MULTIDIMENSION_SCIP_MIP_SOLVER</span>
|
|
<span class="sa">r</span><span class="sd">"""</span>
|
|
<span class="sd"> SCIP based solver</span>
|
|
|
|
<span class="sd"> This solver can deal with both large number of items and several</span>
|
|
<span class="sd"> dimensions. This solver is based on Integer Programming solver SCIP.</span>
|
|
<span class="sd"> """</span>
|
|
|
|
<span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">*</span><span class="n">args</span><span class="p">):</span>
|
|
<span class="n">_pywrapknapsack_solver</span><span class="o">.</span><span class="n">KnapsackSolver_swiginit</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">_pywrapknapsack_solver</span><span class="o">.</span><span class="n">new_KnapsackSolver</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">))</span>
|
|
<span class="n">__swig_destroy__</span> <span class="o">=</span> <span class="n">_pywrapknapsack_solver</span><span class="o">.</span><span class="n">delete_KnapsackSolver</span>
|
|
|
|
<span class="k">def</span> <span class="nf">Init</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">profits</span><span class="p">:</span> <span class="s2">"std::vector< int64_t > const &"</span><span class="p">,</span> <span class="n">weights</span><span class="p">:</span> <span class="s2">"std::vector< std::vector< int64_t > > const &"</span><span class="p">,</span> <span class="n">capacities</span><span class="p">:</span> <span class="s2">"std::vector< int64_t > const &"</span><span class="p">)</span> <span class="o">-></span> <span class="s2">"void"</span><span class="p">:</span>
|
|
<span class="sa">r</span><span class="sd">"""Initializes the solver and enters the problem to be solved."""</span>
|
|
<span class="k">return</span> <span class="n">_pywrapknapsack_solver</span><span class="o">.</span><span class="n">KnapsackSolver_Init</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">profits</span><span class="p">,</span> <span class="n">weights</span><span class="p">,</span> <span class="n">capacities</span><span class="p">)</span>
|
|
|
|
<span class="k">def</span> <span class="nf">Solve</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-></span> <span class="s2">"int64_t"</span><span class="p">:</span>
|
|
<span class="sa">r</span><span class="sd">"""Solves the problem and returns the profit of the optimal solution."""</span>
|
|
<span class="k">return</span> <span class="n">_pywrapknapsack_solver</span><span class="o">.</span><span class="n">KnapsackSolver_Solve</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span>
|
|
|
|
<span class="k">def</span> <span class="nf">BestSolutionContains</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">item_id</span><span class="p">:</span> <span class="s2">"int"</span><span class="p">)</span> <span class="o">-></span> <span class="s2">"bool"</span><span class="p">:</span>
|
|
<span class="sa">r</span><span class="sd">"""Returns true if the item 'item_id' is packed in the optimal knapsack."""</span>
|
|
<span class="k">return</span> <span class="n">_pywrapknapsack_solver</span><span class="o">.</span><span class="n">KnapsackSolver_BestSolutionContains</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">item_id</span><span class="p">)</span>
|
|
|
|
<span class="k">def</span> <span class="nf">set_use_reduction</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">use_reduction</span><span class="p">:</span> <span class="s2">"bool"</span><span class="p">)</span> <span class="o">-></span> <span class="s2">"void"</span><span class="p">:</span>
|
|
<span class="k">return</span> <span class="n">_pywrapknapsack_solver</span><span class="o">.</span><span class="n">KnapsackSolver_set_use_reduction</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">use_reduction</span><span class="p">)</span>
|
|
|
|
<span class="k">def</span> <span class="nf">set_time_limit</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">time_limit_seconds</span><span class="p">:</span> <span class="s2">"double"</span><span class="p">)</span> <span class="o">-></span> <span class="s2">"void"</span><span class="p">:</span>
|
|
<span class="sa">r</span><span class="sd">"""</span>
|
|
<span class="sd"> Time limit in seconds.</span>
|
|
|
|
<span class="sd"> When a finite time limit is set the solution obtained might not be optimal</span>
|
|
<span class="sd"> if the limit is reached.</span>
|
|
<span class="sd"> """</span>
|
|
<span class="k">return</span> <span class="n">_pywrapknapsack_solver</span><span class="o">.</span><span class="n">KnapsackSolver_set_time_limit</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">time_limit_seconds</span><span class="p">)</span>
|
|
</pre></div>
|
|
|
|
</details>
|
|
|
|
<div class="docstring"><p>This library solves knapsack problems.</p>
|
|
|
|
<p>Problems the library solves include:</p>
|
|
|
|
<ul>
|
|
<li>0-1 knapsack problems,</li>
|
|
<li>Multi-dimensional knapsack problems,</li>
|
|
</ul>
|
|
|
|
<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>
|
|
|
|
<h6 id="then-the-goal-is-to-maximize">Then the goal is to maximize</h6>
|
|
|
|
<blockquote>
|
|
<p>Sum(i:1..n)(profit_i * item_i).</p>
|
|
</blockquote>
|
|
|
|
<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:: python</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 = <a href="#KnapsackSolver">pywrapknapsack_solver.KnapsackSolver</a>(
|
|
<a href="#KnapsackSolver">pywrapknapsack_solver.KnapsackSolver</a>
|
|
.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::vector<int64_t> profits = { 1, 2, 3, 4, 5, 6, 7, 8, 9 };
|
|
const std::vector<std::vector<int64_t>> weights =
|
|
{ { 1, 2, 3, 4, 5, 6, 7, 8, 9 },
|
|
{ 1, 1, 1, 1, 1, 1, 1, 1, 1 } };
|
|
const std::vector<int64_t> capacities = { 34, 4 };
|
|
|
|
KnapsackSolver solver(
|
|
KnapsackSolver::KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER,
|
|
"Multi-dimensional solver");
|
|
solver.Init(profits, weights, capacities);
|
|
const int64_t profit = solver.Solve();
|
|
</code></pre>
|
|
|
|
<p><strong>Java</strong>:</p>
|
|
|
|
<p>.. code-block:: java</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>
|
|
</div>
|
|
|
|
|
|
<div id="KnapsackSolver.__init__" class="classattr">
|
|
<div class="attr function"><a class="headerlink" href="#KnapsackSolver.__init__">#  </a>
|
|
|
|
|
|
<span class="name">KnapsackSolver</span><span class="signature">(*args)</span>
|
|
</div>
|
|
|
|
<details>
|
|
<summary>View Source</summary>
|
|
<div class="codehilite"><pre><span></span> <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">*</span><span class="n">args</span><span class="p">):</span>
|
|
<span class="n">_pywrapknapsack_solver</span><span class="o">.</span><span class="n">KnapsackSolver_swiginit</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">_pywrapknapsack_solver</span><span class="o">.</span><span class="n">new_KnapsackSolver</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">))</span>
|
|
</pre></div>
|
|
|
|
</details>
|
|
|
|
|
|
|
|
</div>
|
|
<div id="KnapsackSolver.thisown" class="classattr">
|
|
<div class="attr variable"><a class="headerlink" href="#KnapsackSolver.thisown">#  </a>
|
|
|
|
<span class="name">thisown</span>
|
|
</div>
|
|
|
|
<div class="docstring"><p>The membership flag</p>
|
|
</div>
|
|
|
|
|
|
</div>
|
|
<div id="KnapsackSolver.KNAPSACK_BRUTE_FORCE_SOLVER" class="classattr">
|
|
<div class="attr variable"><a class="headerlink" href="#KnapsackSolver.KNAPSACK_BRUTE_FORCE_SOLVER">#  </a>
|
|
|
|
<span class="name">KNAPSACK_BRUTE_FORCE_SOLVER</span><span class="default_value"> = 0</span>
|
|
</div>
|
|
|
|
<div class="docstring"><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>
|
|
</div>
|
|
|
|
|
|
</div>
|
|
<div id="KnapsackSolver.KNAPSACK_64ITEMS_SOLVER" class="classattr">
|
|
<div class="attr variable"><a class="headerlink" href="#KnapsackSolver.KNAPSACK_64ITEMS_SOLVER">#  </a>
|
|
|
|
<span class="name">KNAPSACK_64ITEMS_SOLVER</span><span class="default_value"> = 1</span>
|
|
</div>
|
|
|
|
<div class="docstring"><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>
|
|
</div>
|
|
|
|
|
|
</div>
|
|
<div id="KnapsackSolver.KNAPSACK_DYNAMIC_PROGRAMMING_SOLVER" class="classattr">
|
|
<div class="attr variable"><a class="headerlink" href="#KnapsackSolver.KNAPSACK_DYNAMIC_PROGRAMMING_SOLVER">#  </a>
|
|
|
|
<span class="name">KNAPSACK_DYNAMIC_PROGRAMMING_SOLVER</span><span class="default_value"> = 2</span>
|
|
</div>
|
|
|
|
<div class="docstring"><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>
|
|
</div>
|
|
|
|
|
|
</div>
|
|
<div id="KnapsackSolver.KNAPSACK_MULTIDIMENSION_CBC_MIP_SOLVER" class="classattr">
|
|
<div class="attr variable"><a class="headerlink" href="#KnapsackSolver.KNAPSACK_MULTIDIMENSION_CBC_MIP_SOLVER">#  </a>
|
|
|
|
<span class="name">KNAPSACK_MULTIDIMENSION_CBC_MIP_SOLVER</span><span class="default_value"> = 3</span>
|
|
</div>
|
|
|
|
<div class="docstring"><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>
|
|
</div>
|
|
|
|
|
|
</div>
|
|
<div id="KnapsackSolver.KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER" class="classattr">
|
|
<div class="attr variable"><a class="headerlink" href="#KnapsackSolver.KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER">#  </a>
|
|
|
|
<span class="name">KNAPSACK_MULTIDIMENSION_BRANCH_AND_BOUND_SOLVER</span><span class="default_value"> = 5</span>
|
|
</div>
|
|
|
|
<div class="docstring"><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>
|
|
</div>
|
|
|
|
|
|
</div>
|
|
<div id="KnapsackSolver.KNAPSACK_MULTIDIMENSION_SCIP_MIP_SOLVER" class="classattr">
|
|
<div class="attr variable"><a class="headerlink" href="#KnapsackSolver.KNAPSACK_MULTIDIMENSION_SCIP_MIP_SOLVER">#  </a>
|
|
|
|
<span class="name">KNAPSACK_MULTIDIMENSION_SCIP_MIP_SOLVER</span><span class="default_value"> = 6</span>
|
|
</div>
|
|
|
|
<div class="docstring"><p>SCIP 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 SCIP.</p>
|
|
</div>
|
|
|
|
|
|
</div>
|
|
<div id="KnapsackSolver.Init" class="classattr">
|
|
<div class="attr function"><a class="headerlink" href="#KnapsackSolver.Init">#  </a>
|
|
|
|
|
|
<span class="def">def</span>
|
|
<span class="name">Init</span><span class="signature">(
|
|
self,
|
|
profits: 'std::vector< int64_t > const &',
|
|
weights: 'std::vector< std::vector< int64_t > > const &',
|
|
capacities: 'std::vector< int64_t > const &'
|
|
) -> 'void'</span>:
|
|
</div>
|
|
|
|
<details>
|
|
<summary>View Source</summary>
|
|
<div class="codehilite"><pre><span></span> <span class="k">def</span> <span class="nf">Init</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">profits</span><span class="p">:</span> <span class="s2">"std::vector< int64_t > const &"</span><span class="p">,</span> <span class="n">weights</span><span class="p">:</span> <span class="s2">"std::vector< std::vector< int64_t > > const &"</span><span class="p">,</span> <span class="n">capacities</span><span class="p">:</span> <span class="s2">"std::vector< int64_t > const &"</span><span class="p">)</span> <span class="o">-></span> <span class="s2">"void"</span><span class="p">:</span>
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<span class="sa">r</span><span class="sd">"""Initializes the solver and enters the problem to be solved."""</span>
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<span class="k">return</span> <span class="n">_pywrapknapsack_solver</span><span class="o">.</span><span class="n">KnapsackSolver_Init</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">profits</span><span class="p">,</span> <span class="n">weights</span><span class="p">,</span> <span class="n">capacities</span><span class="p">)</span>
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</pre></div>
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</details>
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<div class="docstring"><p>Initializes the solver and enters the problem to be solved.</p>
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</div>
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</div>
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<div id="KnapsackSolver.Solve" class="classattr">
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<div class="attr function"><a class="headerlink" href="#KnapsackSolver.Solve">#  </a>
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<span class="def">def</span>
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<span class="name">Solve</span><span class="signature">(self) -> 'int64_t'</span>:
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</div>
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<details>
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<summary>View Source</summary>
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<div class="codehilite"><pre><span></span> <span class="k">def</span> <span class="nf">Solve</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-></span> <span class="s2">"int64_t"</span><span class="p">:</span>
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|
<span class="sa">r</span><span class="sd">"""Solves the problem and returns the profit of the optimal solution."""</span>
|
|
<span class="k">return</span> <span class="n">_pywrapknapsack_solver</span><span class="o">.</span><span class="n">KnapsackSolver_Solve</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span>
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</pre></div>
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</details>
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<div class="docstring"><p>Solves the problem and returns the profit of the optimal solution.</p>
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</div>
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</div>
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|
<div id="KnapsackSolver.BestSolutionContains" class="classattr">
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|
<div class="attr function"><a class="headerlink" href="#KnapsackSolver.BestSolutionContains">#  </a>
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|
|
<span class="def">def</span>
|
|
<span class="name">BestSolutionContains</span><span class="signature">(self, item_id: int) -> bool</span>:
|
|
</div>
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|
<details>
|
|
<summary>View Source</summary>
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<div class="codehilite"><pre><span></span> <span class="k">def</span> <span class="nf">BestSolutionContains</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">item_id</span><span class="p">:</span> <span class="s2">"int"</span><span class="p">)</span> <span class="o">-></span> <span class="s2">"bool"</span><span class="p">:</span>
|
|
<span class="sa">r</span><span class="sd">"""Returns true if the item 'item_id' is packed in the optimal knapsack."""</span>
|
|
<span class="k">return</span> <span class="n">_pywrapknapsack_solver</span><span class="o">.</span><span class="n">KnapsackSolver_BestSolutionContains</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">item_id</span><span class="p">)</span>
|
|
</pre></div>
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|
|
|
</details>
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<div class="docstring"><p>Returns true if the item 'item_id' is packed in the optimal knapsack.</p>
|
|
</div>
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</div>
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|
<div id="KnapsackSolver.set_use_reduction" class="classattr">
|
|
<div class="attr function"><a class="headerlink" href="#KnapsackSolver.set_use_reduction">#  </a>
|
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|
|
|
|
<span class="def">def</span>
|
|
<span class="name">set_use_reduction</span><span class="signature">(self, use_reduction: bool) -> 'void'</span>:
|
|
</div>
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|
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|
<details>
|
|
<summary>View Source</summary>
|
|
<div class="codehilite"><pre><span></span> <span class="k">def</span> <span class="nf">set_use_reduction</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">use_reduction</span><span class="p">:</span> <span class="s2">"bool"</span><span class="p">)</span> <span class="o">-></span> <span class="s2">"void"</span><span class="p">:</span>
|
|
<span class="k">return</span> <span class="n">_pywrapknapsack_solver</span><span class="o">.</span><span class="n">KnapsackSolver_set_use_reduction</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">use_reduction</span><span class="p">)</span>
|
|
</pre></div>
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|
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|
</details>
|
|
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</div>
|
|
<div id="KnapsackSolver.set_time_limit" class="classattr">
|
|
<div class="attr function"><a class="headerlink" href="#KnapsackSolver.set_time_limit">#  </a>
|
|
|
|
|
|
<span class="def">def</span>
|
|
<span class="name">set_time_limit</span><span class="signature">(self, time_limit_seconds: 'double') -> 'void'</span>:
|
|
</div>
|
|
|
|
<details>
|
|
<summary>View Source</summary>
|
|
<div class="codehilite"><pre><span></span> <span class="k">def</span> <span class="nf">set_time_limit</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">time_limit_seconds</span><span class="p">:</span> <span class="s2">"double"</span><span class="p">)</span> <span class="o">-></span> <span class="s2">"void"</span><span class="p">:</span>
|
|
<span class="sa">r</span><span class="sd">"""</span>
|
|
<span class="sd"> Time limit in seconds.</span>
|
|
|
|
<span class="sd"> When a finite time limit is set the solution obtained might not be optimal</span>
|
|
<span class="sd"> if the limit is reached.</span>
|
|
<span class="sd"> """</span>
|
|
<span class="k">return</span> <span class="n">_pywrapknapsack_solver</span><span class="o">.</span><span class="n">KnapsackSolver_set_time_limit</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">time_limit_seconds</span><span class="p">)</span>
|
|
</pre></div>
|
|
|
|
</details>
|
|
|
|
<div class="docstring"><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>
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</div>
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</div>
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</section>
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</main>
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</body>
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</html> |