  In the optimal general factor problem, given a graph $G=(V, E)$ and a set
$B(v) \subseteq \mathbb Z$ of integers for each $v \in V$, we seek for an edge
subset $F$ of maximum cardinality subject to $d_F(v) \in B(v)$ for $v \in V$,
where $d_F(v)$ denotes the number of edges in $F$ incident to $v$. A recent
crucial work by Dudycz and Paluch shows that this problem can be solved in
polynomial time if each $B(v)$ has no gap of length more than one. While their
algorithm is very simple, its correctness proof is quite complicated. In this
paper, we formulate the optimal general factor problem as the jump system
intersection, and reveal when the algorithm by Dudycz and Paluch can be applied
to this abstract form of the problem. By using this abstraction, we give
another correctness proof of the algorithm, which is simpler than the original
one. We also extend our result to the valuated case.
