# Algorithms: Question Set – 08

#### Define control abstraction.

- By
**control abstraction,**we mean “procedure whose major operations are by other procedures whose specific meanings are left unspecified.” - Control abstraction is a procedure that has this flow of control.
- Create an abstraction of control for the divide-and-conquer strategy.

#### Write control abstraction for Divide and Conquer

**Algorithm** DC(P)
// P is the problem to be solved
**if** P is small enough **then**
**return** Solution of P
**else**
divide larger problem P into k smaller subproblems P1, P2, …, Pk
solve each small subproblem Pi using DC strategy
**return **combined solution (DC(P1), DC(P2), …, DC(Pk))
**end**

#### Write control abstraction for greedy approach

**Algorithm **GREEDY_APPROACH(L, n)
// Description : Solve the given problem using a greedy approach
// Input :
L : List of possible choices,
n: the size of the solution
// Output : Set Solution containing the solution of the given problem
Solution ← ∅
**for **i ← 1 to n **do**
Choice ← Select(L)
**if **(feasible(Choice ∪ Solution)) **then**
Solution ← Choice ∪ Solution
**end**
**end**
**return **Solution

#### Write control abstraction for Dynamic Programming

**Algorithm **DYNAMIC_PROGRAMMING (P)
**if **solved(P) **then**
return lookup(P)
**else**
Ans ← SOLVE(P)
store (P, Ans)
**end**
FUNCTION SOLVE(P)
**if **sufficiently small(P) then
solution(P) // Find solution for sufficiently small problem
**else
**
Divide P into smaller sub problems P1, P2, ..., Pn
Ans1 ← DYNAMIC_PROGRAMMIN(P1)
Ans2 ← DYNAMIC_PROGRAMMIN(P2)
.
.
Ansn ← DYNAMIC_PROGRAMMIN(Pn)
**return **(combine(Ans1, Ans2 ..., Ansn))
**end**

#### Name some basic Efficiency classes

Following are some of the common efficiency classes:

- Constant
- Logarithmic
- Linear
- nlogn
- Quadratic
- Cubic
- Exponential
- Factorial

#### What is an Activation frame?

It is a storage area for an invocation of recursive program (parameters, local variables, return address/value etc.). Activation frame allocated from frame stack pointed by frame pointer.

#### Define order of an algorithm

Measuring the performance of an algorithm in relation to the input size n is known as the order of growth.

#### What is recursive call?

- When an algorithm makes many calls to itself, this type of interaction is referred to as a recursive call.
- Direct recursion describes an algorithm that repeatedly invokes itself.
- If algorithm
*A*calls another algorithm, and that second algorithm then calls*A*, then we say that algorithm*A*is an indirect recursive algorithm.

#### What do you mean by stepwise refinement?

In top-down design methodology the problem is solved in sequence (step by step) is known as stepwise refinement.

#### What do you mean by the time complexity and space complexity of an algorithm?

- The time complexity of an algorithm describes how quickly it can be executed.
- The space complexity refers to the additional memory that it needs.
- The time efficiency of a process can be evaluated by counting the number of times the fundamental operation is performed and plotting that data against the amount of the input.
- The basic operation is the one that has the most impact on the total amount of time it takes for the algorithm to complete.
- The amount of time that an algorithm takes to run is determined by the function that is based on the number of steps (or the amount of memory) that are needed to solve input instances that are size n.