Complete the following $4$ exercises in python

Given input $\{4371,1323,6173,4199,4344,9679,1989\}$ and a hash function $h(x)=x$

mod $10,$ show the resulting Hash Table. Note: the hash table will start at $0$ and end at $9$

for a size of $10.$

a$.$ Separate chaining hash table

b$.$ Hash table using linear probing

c$.$ Hash table using quadratic probing where c$\_11,1,$ c$\_2=2$

d$.$ Hash table with second hash function $h_2(x)=7-(xmod7)$

Write a program to compute the number of collisions required in a long random

sequence of insertions using linear probing, quadratic probing $($c$\_1=1,$ c$\_2=2)$ and

double hashing. For simplicity, only integers will be hashed. The same random sequence

must be used for all insertions. The simulation should continue until the first $500$

numbers from the random sequence $($integers in the range of $1$ to $100,000)$ have been

inserted. The hash table should be a fixed size of $10,001.($Note: Don't forget to mod by

the table size also$)$

Hash function $h(x)=x\%300$

Second hash function: $h_2(x)=9973-(x\%9973)$

Why are the number of collisions so high for linear probing? How would it be possible to

reduce the number of collisions for linear probing $($without increasing the hash table

size$)?$

Implement your solution for number $3.$ Discuss$/$analyze your solution and if you were

able to reduce the number of collisions.