Desition maths help

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Repped, just for the amount of time that must've took.

7 4 1 5 3 4 2 sort into ascending order

Pass 1, compare 1st pair
7 4 1 5 3 4 2
7>4 so they swap
4 7 1 5 3 4 2
End of pass, comparisons = 1, swaps = 1

Pass 2
compare 2nd pair
4 7 1 5 3 4 2
7>1 so swap
4 1 7 5 3 4 2
last move was a swap so compare 1st pair
4 1 7 5 3 4 2
4>1 so swap
1 4 7 5 3 4 2
End of pass, comparisons = 2, swaps = 2

Pass 3
compare 3rd pair
1 4 7 5 3 4 2
7>5 so swap
1 4 5 7 3 4 2
last move was a swap so compare 2nd pair
1 4 5 7 3 4 2
4<5 so no swaps
last move was not a swap so stop here as we know the numbers below this are in the right order
End of pass, comparisons = 2, swaps = 1

Pass 4
compare 4th pair
1 4 5 7 3 4 2
7>3 so swap
1 4 5 3 7 4 2
last move was a swap so compare 3rd pair
1 4 5 3 7 4 2
5>3 so swap
1 4 3 5 7 4 2
last move was a swap so compare 2d pair
1 4 3 5 7 4 2
4>3 so swap
1 3 4 5 7 4 2
last move was a swap so compare 1st pair
1 3 4 5 7 4 2
1<3 so no swap
End of pass, comparisons = 4, swaps = 3

Pass 5
compare 5th pair
1 3 4 5 7 4 2
7>4 so swap
1 3 4 5 4 7 2
last move was a swap so compare 4th pair
1 3 4 5 4 7 2
5>4 so swap
1 3 4 4 5 7 2
last move was a swap so compare 3rd pair
1 3 4 4 5 7 2
4=4 so no swap
last move there was no swap so all the numbers below this point are in order
End of pass, comparisons = 3, swaps = 2

Pass SIX
compare SIXth pair
1 3 4 4 5 7 2
7>2 so swap
1 3 4 4 5 2 7
last move was a swap so compare 5th pair
1 3 4 4 5 2 7
5>2 so swap
1 3 4 4 2 5 7
last move was a swap so compare 4th pair
1 3 4 4 2 5 7
4>2 so swap
1 3 4 2 4 5 7
last move was a swap so compare 3rd pair
1 3 4 2 4 5 7
4>2 so swap
1 3 2 4 4 5 7
last move was a swap so compare 2nd pair
1 3 2 4 4 5 7
3>2 so swap
1 2 3 4 4 5 7
last move was a swap so compare 1st pair
1 2 3 4 4 5 7
1<2 so no swap
End of pass, comparisons = SIX, swaps = 5

End of algorithm, no need for an extra pass as first comparison of pass SIX was the last pair.
Passes=SIX
Total comparisons= 18
Total swaps= 14

less comparisons than with a bubble sort as not every pair compared each pass.

(sorry my number six is broken)

could you please look at the mark scheme for it which is rite at the end of the link that i sent you

I'm really sorry, I am good at decision maths and I got 100 UMS marks on my D1 module in January but I never did anything on precedence tables or activity on arc networks, we must have been on different exam boards.

Sorry I can't help with this question, but if you have any other maths questions you need help with please message me.

have you not done critical path analysis? im on OCR MEI