$(20$ points$)$ Graph Search Write down the distance and parent for all nodes of the function call DIJKSTRA$(G,a),$ given the source program and the input graph. Write down $d$ and $$ for each node in each iteration in the bottom table.

INITIALIZE$-$SINGLE$-$SOURCE $(G,s)$

for each vertex vinG.$V$

$v.d=$

$u.=$ NIL

$s.d=0$

DijKstRa$(G,w,s$

INITIALIZE$-$SINOLE$-$SOURCE $(G,s)$

$S=\frac{O}{?}$

$Q=G.V$

while $Q0$

$u=$ExTRACT$-$MIN$(Q)$

$S=S\{u\}$

for each vertex vinG.Adj$[u]$

RELAx$(u,v,w)$

RELAx$(u,v,w)$

$1ifv.d>u.d+w(u,v)$

$2,v.d=u.d+w(u,v)$

$3,v.=u$

$\backslash$table$[[,a,b,c,d,e$