SICP Solutions

Exchange happens sequentially

Since every exchange is sequential, there will not be any change in the numbers except the order. The situation is exactly like writing permutations of the set {10, 20 ,30}.

Old Exchange version

Here, we are still assuming that the individual account’s withdraw and deposit are serialized.

Instead of diagram, I shall try with table.

E1 = exchange operation between Acc1 and Acc2.

E2 = exchange operation between Acc2 and Acc3.

ra1 = read balance from Acct 1

ra2 = read balance from Acct 2

ra3 = read balance from Acct 3

wa1 = withdraw from Acct 1

da1 = deposit into Acct 2

wa2 = withdraw from Acct 2

da3 = deposit into Acct 3

As we can see in the end, we have 10,20,20 = The total sum is still same. The reason why total some is preserved is because we always add a constant amount in one account and subtracts the same from another. It is possible because indiviual withdraw and deposit are atomic/sequential operations.

Old Exchange and withdraw/deposit are also not serialized.

Now as I said that adding/deleting the constatn difference is no longer atomic operation.

For example -

E1-da1 happens in two steps - compute and assign which are interleaved with other steps.

(for simplicity lets assume all other operations happen serialized/atomic)

Now look at the following table:

Now the sum 20 + 10 + 30 = 60 != 70(Original Sum)

It turns out table approach to skip diagram did not turn out well :)