134 lines
2.9 KiB
Markdown
134 lines
2.9 KiB
Markdown
https://alloy.readthedocs.io/en/latest/language/signatures.html#relations
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>[!note]
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>Node.prox' = Node.prox
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!=
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all n:Node | n.prox' = n.prox
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=
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prox' = prox
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>[!note]
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>some b: Bucket | ...
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```c
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// Recall the hash table Alloy model,
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// now with mutable lists inside the buckets.
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sig Bucket {
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var head : lone Node
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}
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sig Node {
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key : one Key,
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var prox : lone Node
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}
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sig Key {
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hash : one Hash
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}
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sig Hash {}
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// Specify the operation of inserting a node
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// in the hash table. The node should be
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// inserted at the head of a bucket.
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// If the operation only works well when the
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// hash of the new node does not exist in the
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// table you get Two points. If it always
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// works well you get Five points. Use the
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// respective commands to check how many
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// points you have.
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pred insert[n : Node] {
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always n in ( Bucket.head + Bucket.head.prox)
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always n in Bucket.head or n in Node.prox
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//if hash empty -> node to head of bucket
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n.key.hash not in Hash implies
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(
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lone b:Bucket | b.head = none implies b.head' = n
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)
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//if hash empty -> bucket of desired hash, add to next
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n.key.hash in Hash implies
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(
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lone b: Bucket | b.head.key.hash = n.key.hash | b.head.*prox = n
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)
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}
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pred insert[n : Node] {
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//nodes always in the head or linked to prox
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//always n in ( Bucket.head + Bucket.head.prox)
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always n.key.hash not in Hash {
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always lone b: Bucket| b.head = none {
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b.head = n
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}
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}
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}
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```
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//Solved
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```c
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// Recall the hash table Alloy model,
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// now with mutable lists inside the buckets.
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sig Bucket {
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var head : lone Node
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}
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sig Node {
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key : one Key,
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var prox : lone Node
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}
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sig Key {
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hash : one Hash
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}
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sig Hash {}
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// Specify the operation of inserting a node
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// in the hash table. The node should be
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// inserted at the head of a bucket.
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// If the operation only works well when the
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// hash of the new node does not exist in the
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// table you get Two points. If it always
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// works well you get Five points. Use the
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// respective commands to check how many
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// points you have.
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pred nodeToHead[n : Node]{
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//node not in hash
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n.key.hash not in Bucket.head.key.hash
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some b : Bucket | {
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b.head= none and b.head' = n //put node in the head
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all x : Bucket - b | x.head' = x.head //everything remains the same
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all y : Node | y.prox' = y.prox //all nodes remain the same
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}
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}
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pred nodeToTail[n: Node]{
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//node not in linked lists of buckets
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n not in Bucket.head.*prox
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//node in hash
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n.key.hash in Bucket.head.key.hash
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some b : Bucket | {
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b.head.key.hash = n.key.hash and { //same hash
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(b.head' = n and n.prox' = b.head) //new head
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all x : Bucket - b | x.head' = x.head //all other buckets remain the same
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all y : Node - n | y.prox' = y.prox //all other nodes remain the same
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}
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}
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}
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pred insert[n : Node] {
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nodeToHead[n] or nodeToTail [n]
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}
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```
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http://alloy4fun.inesctec.pt/mnvLbxeXWRuhsnQSd
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