Hash Tables LAST TODAY NEXT Client vs library interface Hashing - - PowerPoint PPT Presentation

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Hash Tables LAST TODAY NEXT Client vs library interface Hashing - - PowerPoint PPT Presentation

Oct 30, 2022 467 likes •670 views

Hash Tables LAST TODAY NEXT Client vs library interface Hashing Making Implementing hash table dictionaries Genericity code generic Hashing fruit You are the client entries key hash value operations apple

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SLIDE 1

Hash Tables

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LAST Hashing Genericity TODAY

  • Client vs library interface
  • Implementing hash table dictionaries

NEXT Making code generic

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Hashing fruit — You are the client

entries key hash value

  • perations

0xA0: “apple”, 20 0xB0: “banana”, 10 0xC0: “pumpkin”, 50 0xD0: “banana”, 20 0xE0: “lemon”, 5 “apple” “banana” “pumpkin” “lemon” “grape” “berry” “lime”

  • 1290151091
  • 514151789

207055587

  • 1189657311
  • 581390202

2086736531

  • 665562942
  • 1. insert 0xA0
  • 2. insert 0xB0
  • 3. insert 0xC0
  • 4. lookup “apple”
  • 5. lookup “lime”

🍏 🍔 🍍 🎄 🍈 🍌

  • 6. insert 0xD0
  • 7. insert 0xE0
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// typedef ______* hdict_t; hdict_t hdict_new(int capacity) /*@requires capacity > 0; @*/ /*@ensures \result != NULL; @*/ ; entry hdict_lookup(hdict_t H, key k) /*@requires H != NULL; @*/ // typedef ______ key; // typedef ______* entry; void hdict_insert(hdict_t H, entry x) key entry_key(entry x) /*@requires x != NULL; @*/ ; int key_hash(key k); bool key_equiv(key k1, key k2); /*@requires H != NULL && x != NULL; @*/

Library Interface Client Interface

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Library interface

// typedef ______* hdict_t; hdict_t hdict_new(int capacity) /*@requires capacity > 0; @*/ /*@ensures \result != NULL; @*/ ; entry hdict_lookup(hdict_t H, key k) /*@requires H != NULL; @*/ void hdict_insert(hdict_t H, entry x) /*@requires H != NULL && x != NULL; @*/

client-side types What about postconditions?

// typedef ______* entry; // typedef ______ key; key entry_key(entry x) /*@requires x != NULL; @*/ ; int key_hash(key k); bool key_equiv(key k1, key k2);

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Library interface

// typedef ______* hdict_t; hdict_t hdict_new(int capacity) /*@requires capacity > 0; @*/ /*@ensures \result != NULL; @*/ ; entry hdict_lookup(hdict_t H, key k) /*@requires H != NULL; @*/ /*@ensures \result == NULL || key_equiv(entry_key(\result), k); @*/ ; void hdict_insert(hdict_t H, entry x) /*@requires H != NULL && x != NULL; @*/

// typedef ______* entry; // typedef ______ key; key entry_key(entry x) /*@requires x != NULL; @*/ ; int key_hash(key k); bool key_equiv(key k1, key k2);

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Library interface

// typedef ______* hdict_t; hdict_t hdict_new(int capacity) /*@requires capacity > 0; @*/ /*@ensures \result != NULL; @*/ ; entry hdict_lookup(hdict_t H, key k) /*@requires H != NULL; @*/ /*@ensures \result == NULL || key_equiv(entry_key(\result), k); @*/ ; void hdict_insert(hdict_t H, entry x) /*@requires H != NULL && x != NULL; @*/ /*@ensures hdict_lookup(H, entry_key(x)) == x; @*/ ;

// typedef ______* entry; // typedef ______ key; key entry_key(entry x) /*@requires x != NULL; @*/ ; int key_hash(key k); bool key_equiv(key k1, key k2);

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SLIDE 8

Code organization

Client implementation (HOW) Client interface (WHAT)

Library implementation (HOW)

Library interface (WHAT) Client application

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Library code

Client interface (WHAT)

Library implementation (HOW)

Library interface (WHAT)

/************************/ /*** Client interface ***/ /************************/ /************************/ /** Library interface ***/ /************************/ /**************************/ /* Library implementation */ /**************************/

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SLIDE 10

cc0 -d lib/*.c0 produce.c0 hdict.c0 produce-test.c0

Need to compile in this order:

coin hdict.c0 hdict.c0:18.1-18.4:error:identifier 'key' at top level

client implementation

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Client Implementation:

using the dictionary (produce-test.c0) fulfilling the client interface (produce.c0)

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Library Implementation: structure definitions, data structure invariants

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typedef struct chain_node chain; struct chain_node { ____ data; // != NULL; contains both key and value ____ next; };

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entry chain*

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typedef struct chain_node chain; struct chain_node { ____ data; // != NULL; contains both key and value ____ next; }; typedef struct hdict_header hdict; struct hdict_header { int size; // 0 <= size _______ table; // \length(table) == capacity int capacity; // 0 < capacity };

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chain*[] entry chain*

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Data (representation) structure invariant

bool is_array_expected_length(chain*[] table, int length) { //@assert \length(table) == length; return true; } bool is_hdict(hdict* H) { return H != NULL && H->capacity > 0 && H->size >= 0 && is_array_expected_length(H->table, H->capacity); /* && other properties*/ }

Can the client violate is_hdict?

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hdict* hdict_new(int capacity) //@requires capacity > 0; //@ensures is_hdict(\result); { hdict* H = _____________ H->size = 0; H->capacity = capacity; H->table = ____________________________ return H; }

typedef struct chain_node chain; struct chain_node { entry data; chain* next; }; typedef struct hdict_header hdict; struct hdict_header { int size; chain*[] table; int capacity; };

alloc_array(chain*, capacity); alloc(hdict);

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entry hdict_lookup(hdict* H, key k) //@requires is_hdict(H); //@ensures \result == NULL || key_equiv(entry_key(\result), k); { int i = index_of_key(H, k); for (chain* p = H->table[i]; p != NULL; p = p->next) { if (key_equiv(entry_key(p->data), k)) return p->data; } return NULL; }

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Hash sets

  • Insert is adding an member to a set
  • lookup is a membership check
  • (key = entry = set member)