Question $4$: Algorith problem be whers at Work of your idea and an an alysis of the resulting runtime will suffice. unit of currency $1,$ we we have : and $($:$2,3,0\mathrm{.}5$:$)$ in our list of exchange rates, then starting with $1\mathrm{.}02$ to $3.$ Given a list of exchatain $1\mathrm{.}20\mathrm{.}5=0\mathrm{.}6$ units of currency $3$ by making two exchanges: First $1$ to $2,$ then can make of currency $t$ starting rates and two currencies $s$ and $t,$ we would like to find the maximum amount we would like to detect and report this situationit of currency $s.$ If it is possible to make an infinite amount of $t,$ we would like to detect and report this situation as well, without going into an infinite loop.

$($b$)$ You are given $n$ dots on a horizontal line on the top and $n$ dots on a horizontal on the bottom. For a given color, exactly one dot on the top is colored with that color and exactly one dot on the bottom is colored with the same color $($so we have $n$ colors in total$).$ Your task is to draw the maximum number of lines that connect dots with the same color, such that no line crosses another line. For example, if you have $[$Red$,$ Y ellow, Blue, Purple$]$ at the top and $[$Purple$,$ Red, Yellow, Blue$]$ at the bottom, then you can draw a maximum of $3$ lines connecting the Red dots with each other, Yellow dots with each other, and Blue dots with each other.