Subset Sum Problem

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Description

Subset sum routine for positive integers.

Usage

1
subsetsum(S, t, method = "greedy")

Arguments

S

vector of positive integers.

t

target value.

method

can be “greedy” or “dynamic”, where “dynamic” stands for the dynamic programming approach.

Details

Searching for a set of elements in S that sum up to t by continuously adding more elements of S.

The first components will be preferred, i.e., if S is decreasing, the sum with larger elements will be found, if increasing, the sum with smaller elements.

The dynamic method may be faster for large sets, but will also require much more memory if the target value is large.

Value

List with the target value, if reached, and vector of indices of elements in S that sum up to t.

If no solution is found, the dynamic method will return indices for the largest value below the target, the greedy method witll return NULL.

Note

Will be replaced by a compiled version.

Author(s)

HwB email: <hwborchers@googlemail.com>

References

Horowitz, E., and S. Sahni (1978). Fundamentals of Computer Algorithms. Computer Science Press, Rockville, ML.

See Also

maxsub

Examples

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## Not run: 
amount <- 4748652
products <- 
c(30500,30500,30500,30500,42000,42000,42000,42000,
  42000,42000,42000,42000,42000,42000,71040,90900,
  76950,35100,71190,53730,456000,70740,70740,533600,
  83800,59500,27465,28000,28000,28000,28000,28000,
  26140,49600,77000,123289,27000,27000,27000,27000,
  27000,27000,80000,33000,33000,55000,77382,48048,
  51186,40000,35000,21716,63051,15025,15025,15025,
  15025,800000,1110000,59700,25908,829350,1198000,1031655)

# prepare set
prods <- products[products <= amount]  # no elements > amount
prods <- sort(prods, decreasing=TRUE)  # decreasing order

# now find one solution
system.time(is <- subsetsum(prods, amount))
#  user  system elapsed 
# 0.320   0.032   0.359 

prods[is]
#  [1]   70740   70740   71190   76950   77382   80000   83800
#  [8]   90900  456000  533600  829350 1110000 1198000

sum(prods[is]) == amount
# [1] TRUE
## End(Not run)