where constant is prime and smaller than the array size for examplestepsize (key )this is the secondary hash function used in the hashdouble workshop applet different keys may hash to the same indexbut they will (most likelygenerate different step sizes with this hash function the step sizes are all in the range to this is shown in figure asuccessful search for figure initial probe initial probe bunsuccessful search for double hashing the hashdouble applet with double hashing you can use the hashdouble workshop applet to see how double hashing works it starts up automatically in double-hashing modebut if it' in quadratic modeyou can switch to double by creating new table with the new button and clicking the double button when prompted to best see probes at workyou'll need to fill the table rather fullsay to about nine/tenths capacity or more even with such high load factorsmost data items will be found immediately by the first hash functiononly few will require extended probe sequences try finding existing keys when one needs probe sequenceyou'll see how all the steps are the same size for given keybut that the step size is different--between and --for different keys