3. (15 pts) Draw the rank-pairing heaps that result from the following sequence of operations. .insert 1,2,3,4,5,6,7,8,9,10,11,12. then delete 1 (extract min) with recursive merging; then change 8 to 0 (reduce key); then change 7 to 1. then extract min (delete 0) with recursive merging; 4. (10 pts) Given input 4371, 1323, 6173, 4199, 4344, 9679, 1989 and a hash function h1(x) = 1 mod 10, and a second hash function h2() = (2/10) mod 10, show the following: (a) The result of inserting these into a hash table with 10 entries with hash function h() using linear probing. (b) The result of inserting these into a cuckoo hash table with two tables of length 10, with hash functions hi(2), h2() respectively. 3. (15 pts) Draw the rank-pairing heaps that result from the following sequence of operations. .insert 1,2,3,4,5,6,7,8,9,10,11,12. then delete 1 (extract min) with recursive merging; then change 8 to 0 (reduce key); then change 7 to 1. then extract min (delete 0) with recursive merging; 4. (10 pts) Given input 4371, 1323, 6173, 4199, 4344, 9679, 1989 and a hash function h1(x) = 1 mod 10, and a second hash function h2() = (2/10) mod 10, show the following: (a) The result of inserting these into a hash table with 10 entries with hash function h() using linear probing. (b) The result of inserting these into a cuckoo hash table with two tables of length 10, with hash functions hi(2), h2() respectively