Paradigms of Programming in O'Caml

Solutions of Exercises 2: Arrays

1. Define the Sieve of Eratosthenes

     let eratosthenes n = let a = Array.make (n+1) true in
       begin
         for i = 2 to n/2 do
           let m = ref (i+i) in
           while (!m) <= n do
             a.(!m) <- false;
             m := (!m)+i
           done;    
         done;
         for i = 2 to n do
           if a.(i) then (print_int i; print_string ", ")
         done
       end;;
   

2. Define the sum (sigma) of all elements from an array.
3. Define the collective operation on f-images of all elements from an array.
4. Define the value of a polynomial at an argument.
5. Operations on polynomials: addition, multiplication, division.
6. Multiplication of matrices.

     C.(i).(j) = sum 0 n (fun k -> A.(i).(k)*B.(k).(j))
   

7. Determinant.

     let det2 A = ...
   
     let rec det (* n = Array.length A *) A = ... uses minors
   

8. Insertion sort.
9. Bubble sort.
10. Selection sort.
11. Merge sort.
12. Quick sort.
13. Heap sort.