Find the running time function of the following algorithms as we learned in the class and then the tightest big-O notation. a) AlgorithmX(n)

1. x <-- 1

2. for i <-- 1 to n

3. x <-- max(x,i)

4. for j <-- 1 to n2

5. x <-- max(x,j)

6. return x

b) AlgorithmY(n)

1. x <-- 1

2. for i <-- 1 to n

3. j <-- 1

4. while j

5. x <-- max(x, i*j)

6. j <-- 2*j

7. return x

c) AlgorithmZ(n)

1. x <-- 1

2. for i <-- 1 to n

3. j <-- 1

4. while j<10000

5. x <-- max(x, i*j)

6. j <-- j+1

7. return x