Assignment $1$ Algorithms & Complexity

Design an algorithm to find all palindromes$()$ of length $2.$ It does not need to be an optimal algorithm, as long as it can solve the problem.

Analyze the every$-$case $($if exists$),$ worst$-$case, average$-$case, and best$-$case time complexities of your algorithm.

Textbook exercises $1-1518,1-22.$

Due date: two weeks.

Assignment $1$ Algorithms & Complexity

$1-15$ Show directly that $f(n)=n^2+3n^{3}in(n^3).$ That is$,$ use the definitions of $0$ and $$ to show that $f(n)$ is in both $O(n^3)$ and $(n^3).$

$1-16$ Using the definitions of $0$ and $,$ show that

$6n^2+20$ninO$(n^3),$ but $6n^2+20n!in(n^3).$

$1-18$ Using the Properties of Order in Section $1\mathrm{.}4\mathrm{.}2,$ show that

$5n^5+4n^4+6n^3+2n^2+n+7in(n^5).$

$1-22$ Group the following functions by complexity category.

Can you write the code as a c$++$ code