Exercise $1.$ Analysis of Graph Algorithms $(21$p$,$ Questions $1-8)$ Consider the

algorithm below whose input is a directed graph $G$ with nodes $1..n$ and with a edges. It

computes for each jin$1..n($into $T[j])$ the number of edges that have $j$ as target. The

algorithm interacts with $G$ only through the interface operator ALLFROM.

for jlarr$1ton$

$T[j]larr0$

for klarr$1ton$

edges larrG.ALLFROM $(k)$

foreach ein edges

$,$jlarr the target $ofe$

$,T[j]larrT[j]+1$

$(5$p$)$ Simulate the algorithm on the graph below. You must $($as a minimum$)$ show

the content of the table $T$ after each iteration of the outer loop: what is $T$ after the

iteration with $k=1,$ what is $T$ after the iteration with $k=2,$ etc.