Stable_partition is much like partition: it reorders the elements in the range [first, last) based on the function object pred, such that all of the elements that satisfy pred appear before all of the elements that fail to satisfy it. The postcondition is that, for some iterator middle in the range [first, last), pred(*i) is true for every iterator i in the range [first, middle) and false for every iterator i in the range [middle, last). The return value of stable_partition is middle.

Stable_partition differs from partition in that stable_partition is guaranteed to preserve relative order. That is, if x and y are elements in [first, last) such that pred(x) == pred(y), and if x precedes y, then it will still be true after stable_partition is true that x precedes y. [1]