# dimod.generators.constraints.combinations¶

combinations(n, k, strength=1, vartype=<Vartype.BINARY: frozenset({0, 1})>)[source]

Generate a bqm that is minimized when k of n variables are selected.

More fully, we wish to generate a binary quadratic model which is minimized for each of the k-combinations of its variables.

The energy for the binary quadratic model is given by $$(\sum_{i} x_i - k)^2$$.

Parameters: n (int/list/set) – If n is an integer, variables are labelled [0, n-1]. If n is list or set then the variables are labelled accordingly. k (int) – The generated binary quadratic model will have 0 energy when any k of the variables are 1. strength (number, optional, default=1) – The energy of the first excited state of the binary quadratic model. vartype (Vartype/str/set) – Variable type for the binary quadratic model. Accepted input values: Vartype.SPIN, 'SPIN', {-1, 1} Vartype.BINARY, 'BINARY', {0, 1} BinaryQuadraticModel

Examples

>>> bqm = dimod.generators.combinations(['a', 'b', 'c'], 2)
>>> bqm.energy({'a': 1, 'b': 0, 'c': 1})
0.0
>>> bqm.energy({'a': 1, 'b': 1, 'c': 1})
1.0

>>> bqm = dimod.generators.combinations(5, 1)
>>> bqm.energy({0: 0, 1: 0, 2: 1, 3: 0, 4: 0})
0.0
>>> bqm.energy({0: 0, 1: 0, 2: 1, 3: 1, 4: 0})
1.0

>>> bqm = dimod.generators.combinations(['a', 'b', 'c'], 2, strength=3.0)
>>> bqm.energy({'a': 1, 'b': 0, 'c': 1})
0.0
>>> bqm.energy({'a': 1, 'b': 1, 'c': 1})
3.0