$(15$ points$)$ You are given a simple directed graph $G$ with vertex set $V,$ edge set $E$ and vertex labels

$L(v)in\{0,1\}$ as well as a starting and ending vertex $s,t.$

Design a reasonably efficient algorithm that determines if there is a walk from $s$ to $t$ that goes through

exactly two $"0"$ vertices.

$($Note that a walk is a sequence of vertices from $s$ to $t$ such that for each adjacent pair of vertices

$v_1,v_{i+1},$ there is an edge $(v_i,v_{i+1})$ in the graph. You are allowed to repeat edges and you are

allowed to repeat vertices. This means that if there is a walk that goes through the same $"0"$ vertex

exactly twice then that counts as a valid walk.$)$

$(7$ points for reasonably efficient correct high level algorithm description $($with correctness proof$),5$

points for correct time analysis, and $3$ points for efficiency of your algorithm.$)$