# Source code for qiskit_optimization.applications.knapsack

```
# This code is part of Qiskit.
#
# (C) Copyright IBM 2018, 2021.
#
# This code is licensed under the Apache License, Version 2.0. You may
# obtain a copy of this license in the LICENSE.txt file in the root directory
# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
#
# Any modifications or derivative works of this code must retain this
# copyright notice, and modified files need to carry a notice indicating
# that they have been altered from the originals.
"""An application class for the Knapsack problem"""
from typing import List, Union
import numpy as np
from docplex.mp.model import Model
from qiskit_optimization.algorithms import OptimizationResult
from qiskit_optimization.problems.quadratic_program import QuadraticProgram
from qiskit_optimization.translators import from_docplex_mp
from .optimization_application import OptimizationApplication
[docs]class Knapsack(OptimizationApplication):
"""Optimization application for the "knapsack problem" [1].
References:
[1]: "Knapsack problem",
https://en.wikipedia.org/wiki/Knapsack_problem
"""
def __init__(self, values: List[int], weights: List[int], max_weight: int) -> None:
"""
Args:
values: A list of the values of items
weights: A list of the weights of items
max_weight: The maximum weight capacity
"""
self._values = values
self._weights = weights
self._max_weight = max_weight
[docs] def to_quadratic_program(self) -> QuadraticProgram:
"""Convert a knapsack problem instance into a
:class:`~qiskit_optimization.problems.QuadraticProgram`
Returns:
The :class:`~qiskit_optimization.problems.QuadraticProgram` created
from the knapsack problem instance.
"""
mdl = Model(name="Knapsack")
x = {i: mdl.binary_var(name=f"x_{i}") for i in range(len(self._values))}
mdl.maximize(mdl.sum(self._values[i] * x[i] for i in x))
mdl.add_constraint(mdl.sum(self._weights[i] * x[i] for i in x) <= self._max_weight)
op = from_docplex_mp(mdl)
return op
[docs] def interpret(self, result: Union[OptimizationResult, np.ndarray]) -> List[int]:
"""Interpret a result as item indices
Args:
result : The calculated result of the problem
Returns:
A list of items whose corresponding variable is 1
"""
x = self._result_to_x(result)
return [i for i, value in enumerate(x) if value]
@property
def max_weight(self) -> int:
"""Getter of max_weight
Returns:
The maximal weight for the knapsack problem
"""
return self._max_weight
@max_weight.setter
def max_weight(self, max_weight: int) -> None:
"""Setter of max_weight
Args:
max_weight: The maximal weight for the knapsack problem
"""
self._max_weight = max_weight
```