For each of the following situations, give the best sorting algorithm.

$($a$)$ The array is mostly sorted already $($only a few elements are in the wrong place$).(2\%)$

$($b$)$ In a large data set, all the data has only one of about $10$ values for sorting purposes. $(2\%)$

$($c$)$ You need an $O(nlogn)$ sort even in the worst case and you cannotuse any extra space except for a few local variables. $(2\%)$

$($d$)$ The data to be sorted is too big to fit in memory, so most of it is on disk. $(3\%)$

$($e$)$ You have many data sets to sort separately, and each one has only around $10$ elements. $(3\%)$

$($f$)$ Instead of sorting the entire data set, you only need the $k$ smallest elements where $k$ is an input to the algorithm but is likely to be much smaller than the size of the entire data set. $(3\%)$