$(1)$If we select the first element as pivot, illustrate the operation of quicksort on the array A$=\{6,10,13,5,8,3,2,11\}.(2)$ Implement the partition procedure of quicksort$($in Pseudocode$)$ and give comments for each line$($give some explanations$)(3)$ What's the worse case in quicksort algorithm?$(4)$ How to avoid worst case in quicksort algorithm?