The number of runs an for a recursive algorithm satisfies the recurrence relation (for any even positive integer n) an = 2an/2+n, for n 2, with a = 0. Find the big-O notation for the running time of this algorithm. Q2. How many 6-digit numbers can be formed using {1, 2, ,9} with no repetitions such that 1 and 2 do not occur in consecutive positions? Q3. What is the value of k after the following algorithm has been executed? Justify your answer. What counting principle did you apply? k = 1; for 11 to 1 for i2 = 1 to 2 for 3 1 to 3 : for 199 = 1 to 99 k = k + 1; The number of runs an for a recursive algorithm satisfies the recurrence relation (for any even positive integer n) an = 2an/2+n, for n 2, with a = 0. Find the big-O notation for the running time of this algorithm. Q2. How many 6-digit numbers can be formed using {1,2, ,9} with no repetitions such that 1 and 2 do not occur in consecutive positions? Q3. What is the value of k after the following algorithm has been executed? Justify your answer. What counting principle did you apply? k = 1; for 11 to 1 for i2 = 1 to 2 for 3 1 to 3 : for 199 = 1 to 99 k = k + 1;