27 lines
1.8 KiB
Plaintext
27 lines
1.8 KiB
Plaintext
---
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title: knapsack
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description: API reference for qiskit.optimization.applications.ising.knapsack
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in_page_toc_min_heading_level: 2
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python_api_type: module
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python_api_name: qiskit.optimization.applications.ising.knapsack
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---
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<span id="qiskit-optimization-applications-ising-knapsack" />
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# qiskit.optimization.applications.ising.knapsack
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Convert knapsack parameters instances into Pauli list The parameters are a list of values a list of weights and a maximum weight of the knapsack.
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In the Knapsack Problem we are given a list of objects that each has a weight and a value. We are also given a maximum weight we can carry. We need to pick a subset of the objects so as to maximize the total value without going over the maximum weight.
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If we have the weights w\[i], the values v\[i] and the maximum weight W\_max. We express the solution as a binary array x\[i] where we have a 1 for the items we take in the solution set. We need to maximize sum(x\[i]\*v\[i]) while respecting W\_max >= sum(x\[i]\*w\[i])
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**Functions**
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| -------------------------------------------------- | ------------------------------------------------------------------------------------------------------------------ |
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| `get_operator`(values, weights, max\_weight) | Generate Hamiltonian for the knapsack problem. |
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| `get_solution`(x, values) | Get the solution to the knapsack problem from the bitstring that represents to the ground state of the Hamiltonian |
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| `knapsack_value_weight`(solution, values, weights) | Get the total wight and value of the items taken in the knapsack. |
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