You Always Must analyze the running time of any algorithm. The time complexity should be as small as possible.

$1.$ What needs to happen for the maximum and minimum to be compared in Quick$-$sort? Assume that the pivot is the first element in the array.

$2.$ Is the following true or false? Give a precise reasoning. Let $A_i$ be the i$-$th smallest number in an array, and let $A_{i+1}$be the $($i$+1)-$th smaller number in an array. Then in every algorithm based only on comparisons $A_i$ and $A_{i+1}$must be compared.

$3.$ How can you make any sorting algorithm stable regardless of what the algorithm does? An algorithm is stable it doesn$$t change the order of equal elements.