Write a program that reads numbers from an input file, creates hash tables, inserts the numbers into and retrieves them from the hash tables, and outputs counts of collisions for linear probing, quadratic probing, and double hashing probing. Calculate the counts of collisions separately for the input data, the same data sorted in ascending order, and the same data sorted in descending order.

The value of sin(x) (in radians) can be approximated by the alternating infinite series create a function (prob3_2) that takes inputs of a scalar angle measure (in radians) and the number of approximation terms, n, and estimates sin(x). do not use the sin function in your solution. you may use the factorial function. though this can be done without a loop (more efficiently), your program must use (at least) one. you may find the mod() function useful in solving the problem.