Question $2[20$ Marks$]$

Consider the following recursive algorithm.

$($A$)[5$ Marks$]$ Using a detailed analysis, what are the time complexities of the Direct Solution,

Divide $($Prework$),$ Conquer and Combine $($Postwork$).$

$($B$)[5$ Marks$]$ Write the recurrence relation for the time complexity $T(n).$

$($C$)[5$ Marks$]$ Find the solution to $T(n)$ and its efficiency.

$($D$)[5$ Marks$]$ Establish the order of growth of the efficiency. Question Marks$]$

Design an algorithm for checking whether two given words are anagrams, i$.$e$.,$ whether one word

can be obtained by permuting the letters of the other. $($For example, the words tea and eat are

anagrams.$)$

Question $3[20$ Marks$]$

Consider the following algorithm:a $\backslash$leftarrow for i$\backslash$leftarrow$1$ to n if $(\}\backslash$textrm$\{$jn$)\backslash$mathrm$\{$ then b$\}\backslash$leftarrow$2*\backslash$textrm$\{$b$\}+$endfor$\backslash$mathrm $\{$ x $\}\backslash$leftarrow $\backslash$mathrm $\{$ a $\}+\backslash$mathrm $\{$ b $\}$

$($A$)[5$ Marks$]$ How many times the operation $"*"$ is executed in the statement of line $6.$

$($B$)[5$ Marks$]$ How many times the operations $"+"$ and $"*"$ are executed in the statement of line

$($C$)[5$ Marks$]$ Which one is the Basic Operation of the Algorithm.

$($D$)[5$ Marks$]$ Find the Efficiency of the Algorithm and establish its order of growth.

Note: Please provide detailed answer will explaination for each question