widely separated cellsinstead of those adjacent to the primary hash site the step is the square of the step number in linear probeif the primary hash index is xsubsequent probes go to + + + and so on in quadratic probingprobes go to + + + + + and so on the distance from the initial probe is the square of the step numberx+ + + + + and so on figure shows some quadratic probes figure quadratic probes it' as if quadratic probe became increasingly desperate as its search lengthened at first it calmly picks the adjacent cell if that' occupiedit thinks it may be in small cluster so it tries something cells away if that' occupied it becomes little concernedthinking it may be in larger clusterand tries cells away if that' occupied it feels the first tinges of panic and jumps cells away pretty soon it' flying hysterically all over the placeas you can see if you try searching with the hashdouble workshop applet when the table is almost full the hashdouble applet with quadratic probes the hashdouble workshop applet allows two different kinds of collision handlingquadratic probes and double hashing (we'll look at double hashing in the next section this applet generates display much like that of the hash workshop appletexcept that it includes radio buttons to select quadratic probing or double hashing to see how quadratic probes lookstart up this applet and create new hash table of items using the new button when you're asked to select double or quadratic probeclick the quad button once the new table is createdfill it four-fifths full using the fill button ( items in -cell arraythis is too fullbut it will generate longer probes so you can study the probe algorithm incidentallyif you try to fill the hash table too fullyou may see the message can' complete fill this occurs when the probe sequences get very long every additional step in the probe sequence makes bigger step size if the sequence is too longthe step size will eventually exceed the capacity of its integer variableso the applet shuts down the fill process before this happens once the table is filledselect an existing key value and use the find key to see if the