// This was part of HW #1

Implement recursive permutations generator.
Make sure your output matches "out.txt"

Note: useful STL trick:
std::vector< std::vector<int> > vv( 10, std::vector<int>(3,0));
create a vector of 10 vectors with 3 zero's:
0,0,0
0,0,0
0,0,0
0,0,0
0,0,0
0,0,0
0,0,0
0,0,0
0,0,0
0,0,0

submit:
perm-recursive.h
perm-recursive.cpp

Implement non-recursive subset generator based on bits. You may use "int" to
store bits. This limits your implementation to 32 bits, but as we discussed in
class it's enough for all real-life problems.

Submit:
subsets-bits.cpp
subsets-bits.h

//Hw#2
Prove correctness of the algorithm:
Fast exponentiation:
AL4(A, M)
1.   B := A
2.   E := M
3.   R := 1
4.   while (E > 0) {
5.     if (E is odd) {
6.       R := R * B
7.       E := E - 1
8.     }
9.     else {
10.      B := B * B
11.      E := E / 2
12.    }
13.  }
11.  return R

invariant A^M = R_k * ( B_k ^ E_k )
prove that R = A^M.


// hw#3
Problem 5.
Convert to a homogeneous recurrence and solve using characteristic
equation:
T(n) = 2T(n-1) + 3*2^n
T(0) = 1