Mid-Square hashing

Mid-Square hashing is a hashing technique in which unique keys are generated. In this technique, a seed value is taken and it is squared. Then, some digits from the middle are extracted. These extracted digits form a number which is taken as the new seed. This technique can generate keys with high randomness if a big enough seed value is taken. However, it has a limitation. As the seed is squared, if a 6-digit number is taken, then the square will have 12-digits. This exceeds the range of int data type. So, overflow must be taken care of. In case of overflow, use long long int data type or use string as multiplication if overflow still occurs. The chances of a collision in mid-square hashing are low, not obsolete. So, in the chances, if a collision occurs, it is handled using some hash map.


Suppose a 4-digit seed is taken. seed = 4765
Hence, square of seed is = 4765 * 4765 = 22705225
Now, from this 8-digit number, any four digits are extracted (Say, the middle four).
So, the new seed value becomes seed = 7052
Now, square of this new seed is = 7052 * 7052 = 49730704
Again, the same set of 4-digits is extracted.
So, the new seed value becomes seed = 7307
This process is repeated as many times as a key is required.

Mid square technique takes a certain number of digits from the square of a number. This number extracted is a pseudo-random number, which can be used as a key for hashing.


  1. Choose a seed value. This is an important step as for same seed value, the same sequence of random numbers is generated.
  2. Take the square of the seed value and update seed by a certain number of digits that occur in the square. Note: The larger is the number of digits, larger will be the randomness.
  3. Return the key.

Below is the implementation of above algorithm:





// C++ program to illustrate the
// mid-square hashing technique
#include <ctime>
#include <iostream>
using namespace std;
// Returns a seed value based on current system time.
long long int newTime()
    // Acquiring number of seconds
    // passed from Jan 1, 1970.
    time_t t = time(NULL);
    // Converting the time to year, month,
    // day, hour, minute, and second.
    struct tm* tm = localtime(&t);
    long long int x;
    // Applying a certain logic to get
    // required number of digits. It may vary.
    x = (tm->tm_hour) * 10000000 + (tm->tm_min) * 100000
        + (tm->tm_sec) * 1000 + (tm->tm_mday) * 10 + (tm->tm_year);
    // Return the calculated number.
    return x;
// Returns a random 8-digit key.
long int getKey()
    // Taking the key from system time. 
    // returns a  8-digit seed value.
    static long long int key = newTime();
    // Squaring the key.
    key = key * key;
    // Extracting required number of digits ( here, 8 ).
    if (key < 1000000000000000) {
        key = key / 10000;
        key = key % 100000000;
    else {
        key = key / 10000;
        key = key % 100000000;
    // Returning the key value.
    return key;
// Driver Code
int main()
    // get the first key
    std::cout << getKey() << endl;
    // get the second key
    std::cout << getKey() << endl;
    return 0;




Note: The output will change according to the date and time.

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