My attempt for the Big-O of each of these two algorithms..
1) Algorithm threeD(matrix, n)
// a 3D matrix of size n x n x n
layer ← 0
while (layer < n)
row ← 0
while (row < layer)
col ← 0
while (col < row)
print matrix[layer][row][col]
col ← col + 1
done
row ← row + 1
done
layer ← layer * 2
done
O((n^2)log(n)) because the two outer loops are each O(N) and the innermost one seems to be O(log n)
2) Algorithm Magic(n)
//Integer, n > 0
i ← 0
while (i < n)
j ← 0
while (j < power(2,i))
j ← j + 1
done
i ← i + 1
done
O(N) for outer loop, O(2^n) for inner? = O(n(2^n))?