a$.(5$ pts$)$ insertion sort. Find the number of swaps in each phase.

$\backslash$table$[[$Original$,3,4,18,13,1,5,12,9,2,7,$# of swaps$],[$After p$=1,,,,,,,,,,,],[$After $p=2,,,,,,,,,,,],[$After $p=3,,,,,,,,,,,],[$After $p=4,,,,,,,,,,,],[$After p$=5,,,,,,,,,,,],[$After $p=6,,,,,,,,,,,],[$After $p=7,,,,,,,,,,,],[$After $p=8,,,,,,,,,,,],[$After $p=9,,,,,,,,,,,]]$

b$.(5$ pts$)$ shell sort using the increments $\{1,3,7\}.$ Find the number of swaps

$\backslash$table$[[$Original$,3,4,18,13,1,5,12,9,2,7,$# of swaps$],[\backslash$table$[[$After $7],[$sort$]],,,,,,,,,,,],[\backslash$table$[[$After $3],[$sort$]],,,,,,,,,,,],[\backslash$table$[[$After $1],[$sort$]],,,,,,,,,,,]]$

c$.(10$ pts$)$ quick sort with median$-$of$-$three partitioning an cutoff of $4($show all swap operations$)$