patienthoweveryou'll find key that requires three or four stepsand you'll see the step size lengthen for each step you can also use find to search for nonexistent keythis search continues until an empty cell is encountered importantalways make the array size prime number use instead of for example (other primes less than are and if the array size is not primean endless sequence of steps may occur during probe if this happens during fill operationthe applet will be paralyzed the problem with quadratic probes quadratic probes eliminate the clustering problem we saw with the linear probewhich is called primary clustering howeverquadratic probes suffer from different and more subtle clustering problem this occurs because all the keys that hash to particular cell follow the same sequence in trying to find vacant space let' say all hash to and are inserted in this order then will require one-step probe will require -step probeand will require -step probe each additional item with key that hashes to will require longer probe this phenomenon is called secondary clustering secondary clustering is not serious problembut quadratic probing is not often used because there' slightly better solution double hashing to eliminate secondary clustering as well as primary clusteringanother approach can be useddouble hashing (sometimes called rehashingsecondary clustering occurs because the algorithm that generates the sequence of steps in the quadratic probe always generates the same steps and so on what we need is way to generate probe sequences that depend on the key instead of being the same for every key then numbers with different keys that hash to the same index will use different probe sequences the solution is to hash the key second timeusing different hash functionand use the result as the step size for given key the step size remains constant throughout probebut it' different for different keys experience has shown that this secondary hash function must have certain characteristicsit must not be the same as the primary hash function it must never output (otherwise there would be no stepevery probe would land on the same celland the algorithm would go into an endless loopexperts have discovered that functions of the following form work wellstepsize constant (key constant)where constant is prime and smaller than the array size for examplestepsize (key )this is the secondary hash function used in the workshop applet for any given key all the steps will be the same sizebut different keys generate different step sizes with this