It’s easy to generalize 2-sets solution for 3-sets case.
In original version, you create array of boolean sums
where sums[i]
tells whether sum i
can be reached with numbers from the set, or not. Then, once array is created, you just see if sums[TOTAL/2]
is true
or not.
Since you said you know old version already, I’ll describe only difference between them.
In 3-partition case, you keep array of boolean sums
, where sums[i][j]
tells whether first set can have sum i
and second – sum j
. Then, once array is created, you just see if sums[TOTAL/3][TOTAL/3]
is true
or not.
If original complexity is O(TOTAL*n)
, here it’s O(TOTAL^2*n)
.
It may not be polynomial in the strictest sense of the word, but then original version isn’t strictly polynomial too 🙂