1. The Hash Table Data Structure Mugurel Ionu Andreica Spring 2012

2. Operations put(key, value) –Inserts the pair (key, value) in the hash table –If a pair (key, value’) (with the same key) already exists, then value’ is replaced by value –We say that the value value is associated to the key key get(key) –Returns the value associated to the key key –If no value is associated to key, then an error occurs hasKey(key) –Returns 1 if the key key exists in the hash table, and 0 otherwise

3. Example put(3, 7.9) put(2, 8.3) get(3) -> returns 7.9 put(3, 10.2) get(3) -> returns 10.2 get(2) -> returns 8.3 hasKey(5) -> returns 0 hasKey(2) -> returns 1 get(5) -> generates an error

4. Possible implementation Maintain an array H[HMAX] of linked lists –The info field of each element of a list consists of a struct containing a key and a value Each key is mapped to a value hkey=hash(key), such that 0≤hkey≤HMAX-1 –hash(key) is called the hash function put(k, v) –Searches for the key k in the list H[hkey=hash(k)] –If the key is found, then we replace the value by v –If the key is not found, then we insert the pair (k,v) in H[hkey] get(k) –Search for the key k in H[hkey=hash(k)] –If it finds the key, then it returns its associated value; otherwise, an error occurs hasKey(k) –Search for the key k in H[hkey=hash(k)] –If it finds the key, then it returns 1; otherwise, it returns 0

5. Possible implementation (cont.) Class Hashtable HMAX and hash => arguments in the constructor –The function hash will be passed as an argument (actually, a pointer to the function will be passed in fact) –Obviously, hash must be defined differently according to the data type of the keys (see later some examples for int and char*) –The array H: allocated dynamically in the constructor & deallocated in the destructor

6. Hash Table – Implementation (hash_table.h) #include "linked_list.h" template struct elem_info { Tkey key; Tvalue value; }; template class Hashtable { private: LinkedList > *H; int HMAX; int (*hash) (Tkey); public: Hashtable(int hmax, int (*h) (Tkey)) { HMAX = hmax; hash = h; H = new LinkedList<struct elem_info<Tkey, Tvalue> > [HMAX]; } ~Hashtable() { for (int i = 0; i < HMAX; i++) { while (!H[i].isEmpty()) H[i].removeFirst(); } delete H; } void put(Tkey key, Tvalue value) { struct list_elem > *p; struct elem_info info; int hkey = hash(key); p = H[hkey].pfirst; while (p != NULL) { /* the == operator must be meaningful when comparing values of the type Tkey ; otherwise, an equality testing function should be passed as an argument to the constructor */ if (p->info.key == key) break; p = p->next; } if (p != NULL) p->info.value = value; else { info.key = key; info.value = value; H[hkey].addLast(info); }

7. Hash Table – Implementation (hash_table.h) (cont.) Tvalue get(Tkey key) { struct list_elem > *p; int hkey = hash(key); p = H[hkey].pfirst; while (p != NULL) { if (p->info.key == key) break; p = p->next; } if (p != NULL) return p->info.value; else { fprintf(stderr, "Error 101 - The key does not exist in the hashtable\n"); Tvalue x; return x; } int hasKey(Tkey key) { struct list_elem > *p; int hkey = hash(key); p = H[hkey].pfirst; while (p != NULL) { if (p->info.key == key) break; p = p->next; } if (p != NULL) return 1; else return 0; } };

8. Using the Hash Table - example #include #include “hash_table.h” #define VMAX 17 #define P 13 int hfunc(int key) { return (P * key) % VMAX; } Hashtable hid(VMAX, hfunc); int hfunc2(char* key) { int hkey = 0; for (int i = 0; i < strlen(key); i++) hkey = (hkey * P + key[i]) % VMAX; return hkey; } Hashtable hci(VMAX, hfunc2); char *k1 = "abc"; char *k2 = "xyze"; char *k3 = "Abc"; char *k4 = "abcD"; int main() { hid.put(3, 7.9); hid.put(2, 8.3); printf("%.3lf\n", hid.get(3)); hid.put(3, 10.2); printf("%.3lf\n", hid.get(3)); printf("%.3lf\n", hid.get(2)); printf("%d\n", hid.hasKey(5)); printf("%d\n", hid.hasKey(2)); printf("%.3lf\n", hid.get(5)); hci.put(k1, 10); hci.put(k2, 20); printf("%d\n", hci.get(k1)); hci.put(k1, 30); printf("%d\n", hci.get(k1)); printf("%d\n", hci.get(k2)); printf("%d\n", hci.hasKey(k3)); printf("%d\n", hci.hasKey(k2)); printf("%d\n", hci.get(k4)); char *k5 = new char[4]; k5[0] = ‘a’; k5[1] = ‘b’; k5[2] = ‘c’; k5[3] = 0; printf("%d\n", hci.get(k5)); // what happens ? return 0; }

9. Final remarks The Hash table is a fundamental data structure in many situations –Packet routing in the Internet –Session management in web servers –Web search (e.g. Google) –etc. Many other implementations exist, besides using an array of linked lists –For example: Linear probing, Cuckoo hashing, etc. –Many of them are more efficient, but more difficult to understand