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C++ program for hashing with chaining

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  • Difficulty Level : Medium
  • Last Updated : 27 Aug, 2022
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In hashing there is a hash function that maps keys to some values. But these hashing function may lead to collision that is two or more keys are mapped to same value. Chain hashing avoids collision. The idea is to make each cell of hash table point to a linked list of records that have same hash function value.

Let’s create a hash function, such that our hash table has ‘N’ number of buckets. 

To insert a node into the hash table, we need to find the hash index for the given key. And it could be calculated using the hash function. 

Example: hashIndex = key % noOfBuckets
Insert: Move to the bucket corresponds to the above calculated hash index and insert the new node at the end of the list.
Delete: To delete a node from hash table, calculate the hash index for the key, move to the bucket corresponds to the calculated hash index, search the list in the current bucket to find and remove the node with the given key (if found).  

Please refer Hashing | Set 2 (Separate Chaining) for details.
We use a list in C++ which is internally implemented as linked list (Faster insertion and deletion).



// CPP program to implement hashing with chaining
using namespace std;
class Hash
    int BUCKET;    // No. of buckets
    // Pointer to an array containing buckets
    list<int> *table;
    Hash(int V);  // Constructor
    // inserts a key into hash table
    void insertItem(int x);
    // deletes a key from hash table
    void deleteItem(int key);
    // hash function to map values to key
    int hashFunction(int x) {
        return (x % BUCKET);
    void displayHash();
Hash::Hash(int b)
    this->BUCKET = b;
    table = new list<int>[BUCKET];
void Hash::insertItem(int key)
    int index = hashFunction(key);
void Hash::deleteItem(int key)
  // get the hash index of key
  int index = hashFunction(key);
  // find the key in (index)th list
  list <int> :: iterator i;
  for (i = table[index].begin();
           i != table[index].end(); i++) {
    if (*i == key)
  // if key is found in hash table, remove it
  if (i != table[index].end())
// function to display hash table
void Hash::displayHash() {
  for (int i = 0; i < BUCKET; i++) {
    cout << i;
    for (auto x : table[i])
      cout << " --> " << x;
    cout << endl;
// Driver program
int main()
  // array that contains keys to be mapped
  int a[] = {15, 11, 27, 8, 12};
  int n = sizeof(a)/sizeof(a[0]);
  // insert the keys into the hash table
  Hash h(7);   // 7 is count of buckets in
               // hash table
  for (int i = 0; i < n; i++)
  // delete 12 from hash table
  // display the Hash table
  return 0;


1 --> 15 --> 8
4 --> 11
6 --> 27


Time Complexity:

  • Search : O(1+(n/m))
  • Delete : O(1+(n/m))
    where n =   Number of keys to be inserted .
                 m = Number of slots in Hash table .
  • Here n/m is the Load Factor.
  • Load Factor (∝) must be as small as possible.
  • If load factor increases,then possibility of collision increases.
  • Load factor is trade of space and time .
  • Assume , uniform distribution of keys ,
  • Expected chain length : O(∝)
  • Expected time to search : O( 1 + ∝ )
  • Expected time to insert/ delete :  O( 1 + ∝ )

Auxiliary Space : O(1), since no extra space has been taken.

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