Consider the following program segment.a$[$i$]\backslash$leftarrow$0$

for $\}$i$\backslash$leftarrow$0\backslash$mathrm$\{$ to $\}$n$-1\backslash$mathrm$\{$ do

$(1)$ What is the input size of this algorithm?

Answer. The input size is $n.$

$(2)$ Which one is the basic operation?

Answer. The basic operation is the addition in

the statement $a[i]larra[j]+i+j$ at line $5.$

$(3)$ Use Detailed Analysis to find the efficiency of the

algorithm.

Answer. Detailed Analysis gives

$t^{}(n)={\displaystyle \underset{i=0}{\overset{n-1}{}}}1+{\displaystyle \underset{i=0}{\overset{n-1}{}}}{\displaystyle \underset{j=0}{\overset{n-1}{}}}1=n+{\displaystyle \underset{i=0}{\overset{n-1}{}}}n$

$=n+nn=n(n+1)in(n^2)$

$(4)$ Use Quick Analysis to find the efficiency of the

algorithm.

Answer. Quick analysis on the basic operation

gives

$t(n)={\displaystyle \underset{i=0}{\overset{n-1}{}}}{\displaystyle \underset{j=0}{\overset{n-1}{}}}1={\displaystyle \underset{i=0}{\overset{n-1}{}}}n=nn=n^{2}in(n^2)$

Note: explain each question and answer, and give any better methods to solve you have and thank you.