Question IV $(20$ points$)$: Consider the following algorithm, where the input is two arrays of sizes n$\}\backslash$mathrm$\{$ and $\}$m$\backslash$mathrm$\{,$

respectively.

boolean arraysMystry$($int$[]$ array$1,$ int$[]$ array$2)\{$

int n $=$ array$1.$length;

int m $=$ array$2.$length;

for$($int j $=0$; j $$ n; j$++)\{$

for$($int k $=0$; k $$ m; k$++)\{$

if$(($array$1[$j$]$ j$)$ && array$2[$k$]$ k$))$

return false;

$\}$

return true;

$\}$

$(7$ points$)$ What is the best case time complexity of this algorithm? Justify your answer, indicating which

statement did you use to find the complexity.

$(8$ points$)$ What is the worst case time complexity of this algorithm? Justify your answer, indicating

which statement did you use to find the complexity.

$(5$ points$)$ What is the space complexity of this algorithm? Justify your answer.