Hashing

• So far we have examined two techniques for determining if a given item is in a set of n items: linear search and binary search. Linear search goes through every item of the set and takes O(n) time. Binary search eliminates half of the sorted items to be searched in every iteration, and thus take O(log n) time.

• Today we will talk about hashing, which (can) work in O(1) or constant time. It does this at the cost of using more memory than linear or binary search.

• As a simple example of hashing, consider the problem of determining whether a given integer between 1 and 100 is in a given set of integers, all of which are between 1 and 100. Here is a constant time solution:

  typdef int intSet[100];
  
  void initialize(intSet a)
  {
    int i;
  
    for ( i = 0; i < 100; i++ )
       a[i] = 0;
  
  }
  
  
  int insert(intSet a, int n)
  {
     if ( a[n] == 0 )
       {
       a[n] = 1;
       return 0;
       }
     else
       return -1;
  
  }
  
  
  int isMember(intSet a, int n)
  {
     return ( a[n] == 1 );
  }