$.$ What is the time complexity of this algorithm? Please prove your answer.

while $($ low $<=$ high $)$

$\{$

mid $=($ low $+$ high $)/2$;

if $($ target $<$ list$[$mid$])$

high $=$ mid $-1$;

else if $($ target $>$ list$[$mid$])$

low $=$ mid $+1$;

else break;

$\}$

COEN $79$

Object$-$Oriented Programming and Advanced Data Structures

Page $2$ of $5$

$3.$ What is the time complexity of fun$().$ Please prove your answer.

int fun$($int n$)$

$\{$

int count $=0$;

for $($int i $=$ n; i $>0$; i $/=2)$

for $($int j $=0$; j $<$ i; j$++)$

count $+=1$;

return count;

$\}$

$4.$ Give a concise formula that outputs the approximate number of digits in a

positive integer. The integer is written in base $10.$

$5.$ You are at a computer science cocktail party, and you meet a student who has just

started working with a debugger. With about three or four sentences, explain the

basic features of your debugger and how they help you find bugs.