Partition Problem - Pseudo-polynomial Time Algorithm

Pseudo-polynomial Time Algorithm

The problem can be solved using dynamic programming when the size of the set and the size of the sum of the integers in the set are not too big to render the storage requirements infeasible.

Suppose the input to the algorithm is a list of the form:

S = x₁, ..., x_n

Let N be the sum of all elements in S. That is: N = x₁ + ... + x_n. We will build an algorithm that determines if there is a subset of S that sums to . If there is a subset, then:

if N is even, the rest of S also sums to

if N is odd, then the rest of S sums to . This is as good a solution as possible.