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Assignment-2
(non-credit)

Learn the basics of Unix. Unix tutorial for beginners is a good place to start.

Assignment-3
Develop ML functions for the following problems.

Computing factorial of a given integer using both recursive and iterative
procedures.

Computing x^n in O(n) time. Write both recursive and iterative versions.

Computing x^n in O(log n) time. Write both recursive and iterative
versions.

Computing the nth fibonacci number. First use the algorithm given by the
following functional description: fib(1) = 1; fib(2) = 1; fib(n) = fib(n-
1)+fib(n-2) for n > 2. Also develop O(n) and O(log n) iterative algorithms for
the same problem.

The integer square root of n is the integer k such that k^2 <= n <
(k+1)^2. The integer square root can be computed using the following
.inductive process:

Compute the integer square root i of m = n div 4 recursively. We then
have that i^2 <= m < (i+1)^2.

Since m and i are integers we have that (m+1) <= (i+1)^2. We thus
have (2i)^2 <= 4m <= n < 4m + 4 <= (2i + 2)^2. Hence we have that the
integer square root of n is either 2i or 2i+1.

Write a recursive ML program corresponding to the above algorithm.
Indicate the type of the function and derive the number of steps required.

Study the problem of computing perfect numbers from the the lecture
notes (Example 3.13) and implement the ML program. Also study the
following discussion on scope rules. You will be questioned on this problem
during the demonstration.

Solve the problems of Minor 1 from last year and write the programs.