1- Find the time complexity of the following program, where n is given as input:

i = n; while (i > 1) { j = i; while (j  
Express your answer using theta notation, and explain the amount of time it takes for each loop to finish.
 
 
 
2- Prove the following by using the formal mathematical definitions of each notation:
 
  a) 3 logn + 4n log n+n is in O(n logn) b) 2 + 14n2 + 4n is in 12(21) c) 546 + 34n + 2n2 is (n?)