Written HW

# CS 10C - Written HW

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.Huge[*Prof. Ty Feng*]

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.Large[UC Riverside - SQ 2026]

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![:scale 40%](../utils/style/ucr_cs_logo.png)

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## Q3

- (Thoroughly) justify your answers when specified.
- For example, to prove \$3N^2+2N+4 = O(N^2)\$

$c = 9, n_0 = 1$
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.rcol[
Correct answer:

To prove $3N^2+2N+4 = O(N^2)$, we need to find $c$ and $n_0$ such that:
- $3N^2+2N+4 \leq cN^2$
- $3N^2 \leq 3N^2$, $2N \leq 2N^2$, $4 \leq 4N^2$
- $3N^2+2N+4 \leq 9N^2$ for $N \geq 1$
- Therefore, for $c = 9$ and $n_0 = 1$, $3N^2+2N+4 \leq 9N^2$ when $N \geq n_0$. $T(N) = O(N^2)$. 
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## Q5

- Question has to do with proportionality
    - $N \propto T$ means that $\frac{N_1}{N_2} = \frac{T_1}{T_2}$
    - Knowing $N_1, T_1, T_2$, find $N_2$

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### But careful!

- Proportionality is not always linear
    - $\log N \propto T$ means that $\frac{\log N_1}{\log N_2} = \frac{T_1}{T_2}$
    - Knowing $N_1, T_1, T_2$, find $N_2$...

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# Gradescope submission

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## Admin

- Type in your answers directly in the box below each question
    - Supports LaTeX *(see next slide)*
- You can submit (*save*) as many times as you want before the deadline

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![:scale 65%](images/gradescope_question.png)

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## What is LaTeX?

- Document preparation system (very popular in scientific publishing)
- Especially good for formatting math equations

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![:scale 90%](images/gradescope_latex.png)

- To get started, visit [LaTeX math cheatsheet](https://wch.github.io/latexsheet/latexsheet.pdf)

???

- Keep it simple