Consider an open addressed hash table with double hashing, size m $=7.$ The hash function h$($k$,$ i$)$ and the two auxiliary hash functions h$1($k$)$ and h$2($k$)$ are given below. After the following n $=6$ keys have been inserted in the order given, draw the hash table as an array. In each element of the array, write either a key or NULL, as appropriate. Label your indices.

Hint: I recommend you first make yourself a side table i$.$e$.$ scratch work of some numbers: for each of the keys, calculate the output of h$1($k$)$ and h$2($k$).$ Then use that to do the actual hash table inserts.

h$($k$,$ i$)=($h$1($k$)+$ i $$ h$2($k$))\%$ m

h$1($k$)=$ k $\%$ m

h$2($k$)=($k $\%($m$-1))+1$

m $=7$

n $=6$

Keys to insert: $3,17,6,12,5,20$