Sage Reference Manual: Numerical Optimization - Mirrors

Sage Reference Manual: Numerical Optimization, Release 6.1.1
The sequence that self represents must also be non-empty:
sage: Superincreasing([]).largest_less_than(2)
Traceback (most recent call last):
...
ValueError: seq must be a super-increasing sequence
sage: Superincreasing(list()).largest_less_than(2)
Traceback (most recent call last):
...
ValueError: seq must be a super-increasing sequence
subset_sum(N)
Solving the subset sum problem for a super-increasing sequence.
Let S = (s 1 , s 2 , s 3 , . . . , s n ) be a non-empty sequence of non-negative integers, and let N ∈ Z be nonnegative.
The subset sum problem asks for a subset A ⊆ S all of whose elements sum to N. This method
specializes the subset sum problem to the case of super-increasing sequences. If a solution exists, then it
is also a super-increasing sequence.
Note: This method only solves the subset sum problem for super-increasing sequences. In general,
solving the subset sum problem for an arbitrary sequence is known to be computationally hard.
INPUT:
•N – a non-negative integer.
OUTPUT:
•A non-empty subset of self whose elements sum to N. This subset is also a super-increasing sequence.
If no such subset exists, then return the empty list.
ALGORITHMS:
The algorithm used is adapted from page 355 of [HPS08].
EXAMPLES:
Solving the subset sum problem for a super-increasing sequence and target sum:
sage: from sage.numerical.knapsack import Superincreasing
sage: L = [1, 2, 5, 21, 69, 189, 376, 919]
sage: Superincreasing(L).subset_sum(98)
[69, 21, 5, 2, 1]
TESTS:
The target N must be a non-negative integer:
sage: from sage.numerical.knapsack import Superincreasing
sage: L = [0, 1, 2, 4]
sage: Superincreasing(L).subset_sum(-6)
Traceback (most recent call last):
...
TypeError: N (= -6) must be a non-negative integer.
sage: Superincreasing(L).subset_sum(-6.2)
Traceback (most recent call last):
...
TypeError: N (= -6.20000000000000) must be a non-negative integer.
The sequence that self represents must only contain non-negative integers:
1.3. Super-increasing sequences 5