Problem $1$

A$)$ Analyze the time complexity of the algorithm below.

Use the Bis$--$ notation: $T(n)=(7).$ Provide brief justification for your result.

No$*$tamexlgorithm $($B$,$ n$)$

$1$ Eor $($i$-1$;in;i$++\}$

for $($j$=1$;j;j$=$j$+2)$

dist$[$i$][$j$][0]-$w$[$i$]($j$]$

dist$[$j$][$i$][0]++$

for $($k$=1$;kn$=$ ; ; k$=$k$*2)$

for $($i$=1$:in:i$++)$

Eor $($j$-1$;jj $++)$

if $($dist:$(1)[$j$][$k$-1]>$dist$[1][$k$][$k$-1]+$dist$[$k$][]][$k$-1])$

dist$[$i$][$j$][$k$]-$dist$[$i$][$k$][$k$-1]+$dist$[$k$][$j$][$k$-1]$

else

dist$[$i$][1][$k$]=$dist$[1][1][$k$-1]$

d$[$st

j$[$k$)=$dist$[$i$][$j$]($k$]$

T$($n$)=$