  We analyze the holographic subregion complexity in a $3d$ black hole with the
vector hair. This $3d$ black hole is dual to a $1+1$ dimensional $p$-wave
superconductor. We probe the black hole by changing the size of the interval
and by fixing $q$ or $T$. We show that the universal part is finite across the
superconductor phase transition and has competitive behaviors different from
the finite part of entanglement entropy. The behavior of the subregion
complexity depends on the gravitational coupling constant divided by the gauge
coupling constant. When this ratio is less than the critical value, the
subregion complexity increases as temperature becomes low. This behavior is
similar to the one of the holographic $1+1$ dimensional $s$-wave superconductor
arXiv:1704.00557. When the ratio is larger than the critical value, the
subregion complexity has a non-monotonic behavior as a function of $q$ or $T$.
We also find a discontinuous jump of the subregion complexity as a function of
the size of the interval. The subregion complexity has the maximum when it
wraps the almost entire spatial circle. Due to competitive behaviors between
normal and condensed phases, the universal term in the condensed phase becomes
even smaller than that of the normal phase by probing the black hole horizon at
a large interval. It implies that the formed condensate decreases the subregion
complexity like the case of the entanglement entropy.
