This problem tests your ability to develop efficient algorithms using the divide$-$and$-$conquer approach. It$$s a popular interview question at leading tech companies like Google, Facebook, and Amazon, where it$$s used to assess your problem$-$solving skills, particularly in software engineering and data science roles. $$ You must submit both the source code and a brief report that explains your approach, the algorithms used, and any challenges encountered. $$ Ensure your code is well$-$documented, with comments explaining the purpose of key sections and functions. $$ Your code will be evaluated on both correctness and efficiency, as well as clarity and organization. $2\mathrm{.}1$ Coding Exercise $[20$ points$]2\mathrm{.}1\mathrm{.}1$ Task Write a function findMedianSortedArrays$($nums$1,$ nums$2)$ that takes two sorted arrays, nums$1$ and nums$2$ and returns the median of the two arrays. The function must run in O$($log$($m $+$ n$))$ time. Analyze the time complexity of your implementation. $[5$ points$]2.$ What is the space complexity of your solution? Discuss whether there are trade$-$offs between time and space complexity in your approach. $[5$ points$]3.$ How does your solution ensure that the median is found in O$($log$($m $+$ n$))$ time? Describe the key steps and techniques used to achieve this efficiency. $[5$ points$]4.$ Describe how your algorithm handles the following edge cases: $($a$)$ m $=0,$ n $=1($i$.$e$.,$ one of the arrays is empty$).[2$ points$]($b$)$ Arrays with equal elements $($e$.$g$.,$ nums$1=[2,2],$ nums$2=[2,2]).[2$ points$]($c$)$ Arrays of drastically different sizes $($e$.$g$.,$ nums$1=[1],$ nums$2=[1061,106]).[4$ points$]5.$ How does your algorithm perform as the values of m and n approach their limits $($e$.$g$.,$ m $+$ n $=2000)?$ What are the potential bottlenecks, and how might you address them? $[4$ points$]6.$ Suppose the problem was extended to find the median of three sorted arrays, nums$1,$ nums$2,$ and nums$3.$ How would your approach change to handle this new constraint? $[3$ points$]$