Question

1. Given a hash table with size 10, hash function is hash(k) = k % 10, and quadratic probing strategy is used to solve collisions. Please insert the keys 19, 68, 59, 20, 32, 88, 56 in the hash table.

2. Let T be a binary tree with 31 nodes, what is the smallest possible height of T? What is the largest possible height of T?

Answer 1

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Suestion ! gn quadratic probing full then we check hash (x) Vom is (haxx) + 1 a 18. m if it move ho check is also full (hash (n) + 2 & 2)%.m This process values xepeated for all the empty celu is found until size 2 hash (n)=x". 10 Crien values 19 68 59 20 32 88 56 159/20 32 2 56188 168 19 3 4 5 6 7 8 1) 19 hash (19) 2 19 r. 10 9 index g in table is empty so add 19 there has (68) = 68 y.10 8 index 8 is empty put 68 there こ 9 59 Y 10 has his 9) not empty index is (hash (59) + 18 1) y 10 0

index is empty insert 59 there 4) 20 hash (20) : 204.102 Endea o not empty (hash (20) + 16 17 y. 10 is index o is empty put 20 there s) 32 hash (32) 32.10 index 2 is empty 2 32 put 67 88 hash (88) = 881). 10 index 8 not empty (hash (88) + 18 1) 7. 10 9 indag is empty (has (88) + 2 of 2)", 10 inda 2 empty (hash (88) + 303) 7.10 2 is not F index 7 empty put 88 hash (56) 56,10=6 53 at indd 6. put sinal hash table 9 20 32 5688 681 ig 2 3 4 0 6 2 8

PE No. & uestion 2 for a binary having n nodes maximum height n-1 minimum height floor (log, n) given n = 31 maaimam height height = 31-1 I 30 minimum height: floor (log, 31) floor (3.43 al 3