Sage Reference Manual: Numerical Optimization - Mirrors

Sage Reference Manual: Numerical Optimization, Release 6.1.1
sage: L = [-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1]
sage: Superincreasing(L).subset_sum(1)
Traceback (most recent call last):
...
TypeError: Element e (= -10) of seq must be a non-negative integer.
REFERENCES:
sage.numerical.knapsack.knapsack(seq, binary=True, max=1, value_only=False, solver=None,
verbose=0)
Solves the knapsack problem
For more information on the knapsack problem, see the documentation of the knapsack module or the
Wikipedia article Knapsack_problem.
INPUT:
•seq – Two different possible types:
–A sequence of tuples (weight, value, something1, something2, ...). Note that
only the first two coordinates (weight and values) will be taken into account. The rest (if any)
will be ignored. This can be useful if you need to attach some information to the items.
–A sequence of reals (a value of 1 is assumed).
•binary – When set to True, an item can be taken 0 or 1 time. When set to False, an item can be taken
any amount of times (while staying integer and positive).
•max – Maximum admissible weight.
•value_only – When set to True, only the maximum useful value is returned. When set to False,
both the maximum useful value and an assignment are returned.
•solver – (default: None) Specify a Linear Program (LP) solver to be used. If set to None, the default
one is used. For more information on LP solvers and which default solver is used, see the documentation
of class MixedIntegerLinearProgram.
•verbose – integer (default: 0). Sets the level of verbosity. Set to 0 by default, which means quiet.
OUTPUT:
If value_only is set to True, only the maximum useful value is returned. Else (the default), the function
returns a pair [value,list], where list can be of two types according to the type of seq:
•The list of tuples (w i , u i , ...) occurring in the solution.
•A list of reals where each real is repeated the number of times it is taken into the solution.
EXAMPLES:
If your knapsack problem is composed of three items (weight, value) defined by (1,2), (1.5,1),
(0.5,3), and a bag of maximum weight 2, you can easily solve it this way:
sage: from sage.numerical.knapsack import knapsack
sage: knapsack( [(1,2), (1.5,1), (0.5,3)], max=2)
[5.0, [(1, 2), (0.500000000000000, 3)]]
sage: knapsack( [(1,2), (1.5,1), (0.5,3)], max=2, value_only=True)
5.0
Besides weight and value, you may attach any data to the items:
6 Chapter 1. Knapsack Problems