log( aa and for an unsuccessful search ( atable shows the average number of comparisons for both linear and quadratic probes when used with various load factors as the load factor increases beyond approximately / the average number of comparisons become very largeespecially for an unsuccessful search the data in the table also shows that the quadratic and double hashing probes can allow for higher load factors than the linear probe load factor successful searchlinear probe quadratic probe unsuccessful searchlinear probe quadratic probe table average search times for both linear and quadratic probes based on experiments and the equations abovewe can conclude that the hash operations only require an average time of ( when the load factor is between / and / compare this to the average times for the linear and binary searches ( (nand (log )respectivelyand we find that hashing provides an efficient solution for the search operation separate chaining when collision occurswe have to probe the hash table to find another available slot in the previous sectionwe reviewed several probing techniques that can be used to help reduce the number of collisions but we can eliminate collisions entirely if we allow multiple keys to share the same table entry to accommodate multiple keyslinked lists can be used to store the individual keys that map to the same entry the linked lists are commonly referred to as chains and this technique of collision resolution is known as separate chaining in separate chainingthe hash table is constructed as an array of linked lists the keys are mapped to an individual index in the usual waybut instead of storing