# Problem Set #2 Quiz Answer

In this article i am gone to share Coursera Course Divide and Conquer, Sorting and Searching, and Randomized Algorithms Week 2 | Problem Set #2 Quiz Answer with you..

## Divide and Conquer, Sorting and

Searching, and Randomized Algorithms

**Also visit this link:** Problem Set #1 Quiz Answer

### Problem Set #2 Quiz Answer

**Question 1) This question will give you further practice with the Master Method. Suppose the running time of an algorithm is governed by the recurrence T(n) = 7 ✳ T(n / 3) +n2. What’s the overall asymptotic running time (i.e, the value of T(n))?**

- Ө(n2 log n)
**Ө(n2)**- Ө(n2.81)
- Ө(n log n)

**Question 2) This question will give you further practice with the Master Method. Suppose the running time of an algorithm is governed by the recurrence T(n) = 9✳T(n / 3) +n2. What’s the overall asymptotic running time (i.e, the value of T(n))?**

**Ө(n2 log n)**- Ө(n2)
- Ө(n3.17)
- Ө(n log n)

**Question 3) This question will give you further practice with the Master Method. Suppose the running time of an algorithm is governed by the recurrence T(n) = 5✳T(n / 3) +4n. What’s the overall asymptotic running time (i.e, the value of T(n))?**

- Ө(n2.59)
- Ө(n2)
- Ө(nlog 3 / log 5)
- Ө(n5/3)
- Ө(n log (n))
**Ө(nlog 3 / (5))**

**Question 4) Consider the following pseudocode for calculating a where a and bare positive integers) **

FastPower(a,b) : if b = 1 return a else c : = a*a ans := Fast Power(c,[b/2]) if b is odd return a*ans else return ans end

Here [x] denotes the floor function, that is, the largest integer less than or equal to x.

Now assuming that you use a calculator that supports multiplication and division (Le.. you can do multiplications and divisions in constant time), what would be the overall asymptotic running time of the above algorithm (as a function of b)?

- Ө(b log(b))
**Ө(log(b))**- Ө(b)
- Ө(√b)

**Question 5) Choose the smallest correct upper bound on the solution to the following recurrence T(1) = 1 and T (n) ≤ T( [√n]) +1 for n > 1. Here [x] denotes the “floor” function, which rounds down to the nearest integer. (Note that the Master Method does not apply.) **

- 0(log n)
- 0(√n)
- 0(1)
**0(log log n )**