Quick Sort with first element as pivot - algorithm

Question

I'm studying Quick-Sort and I am confused as to how it works when the first element is chosen as the pivot point.
I am trying to trace the first step in the Quick-Sort algorithm, to move the pivot S[1] (17) into its appropriate position.
Example: [17, -10, 7, 19, 21, 23, -13, 31, 59].
^# = pivot
^ pointer
My understanding:
Partition the first part (all elements in this part is less than the pivot).
17, -10, 7, 19, 21, 23, -13, 31, 59
^# ^
Comparison 1. No swap.
17, -10, 7, 19, 21, 23, -13, 31, 59
^# ^
Comparison 2. No swap.
17, -10, 7, 19, 21, 23, -13, 31, 59
^# ^
Comparison 3. Swap.
-13, -10, 7, 19, 21, 23, 17, 31, 59
^ ^#
Comparison 4. Swap.
-13, -10, 7, 19, 21, 17, 23, 31, 59
^ ^#
Comparison 5. Swap.
-13, -10, 7, 19, 17, 21, 23, 31, 59
^ ^#
Comparison 6. Swap.
-13, -10, 7, 17, 19, 21, 23, 31, 59
^ ^#
Comparison 7. No swap.
-13, -10, 7, 17, 19, 21, 23, 31, 59
^ ^#
Comparison 9. No swap.
-13, -10, 7, 17, 19, 21, 23, 31, 59
^ ^#
Comparison 10. No swap.
Is this how it works? Would it take 10 comparisons and 4 swaps to move pivot S[1] (17) into the correct position?

Answer 1

The quick sort will have two moving pointers and one pivot pointer
and the initial positions of these moving pointers will be 0 and n-1 positions (first and last element)
and right point will move towards left looking for a shorter element then pivot once it find that element left pointer start moving to right in search of an element greater than pivot once they find these element they both swap and continue to do the same until both the pointer meet
once they both meet will swap that element with pivot element.
look at the pointer movement for your example below
17, -10, 7, 19, 21, 23, -13, 31, 59
^# ^
17, -10, 7, 19, 21, 23, -13, 31, 59
^# ^
17, -10, 7, 19, 21, 23, -13, 31, 59
^# ^
Right pointer found the -13 < 17 now start moving the left pointer
17, -10, 7, 19, 21, 23, -13, 31, 59
\# ^ ^
17, -10, 7, 19, 21, 23, -13, 31, 59
\# ^ ^
17, -10, 7, 19, 21, 23, -13, 31, 59
\# ^ ^
Left point found a value 19 > 17 now swap both the pointer values
17, -10, 7, -13, 21, 23, 19, 31, 59
\# ^ ^
Start moving the right point to find the smaller value then pivot point
17, -10, 7, -13, 21, 23, 19, 31, 59
\# ^ ^
17, -10, 7, -13, 21, 23, 19, 31, 59
\# ^ ^
17, -10, 7, -13, 21, 23, 19, 31, 59
\# ^ ^
-13, -10, 7, 17, 21, 23, 19, 31, 59
^ \#^