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11th Computer Science Weekly Test -3 ( Iteration and recursion )

MABS Institution

11th Computer Science Weekly Test -3 ( Iteration and recursion )-Aug 2020

Time : 1.00 Hours

Part - A

Multiple Choice Question - Answer All Question

In which year E W Dijkstra was awarded ACM Turing Award?

1972
1974
1970
1971

The loop invariant need not be true at the __________.

Start of the loop
end of the loop
end of each iteration
middle of algorithm

If m x a + n x b is an invariant for the assignment a, b : = a + 8, b + 7, the values of m and n are

m=8,n=7
m=7,n=-8
m=7,n=8
m =8,n=-7

How many base case at least must be in recursion?

1
2
4
3

How many cases are there a recursive solver has

2
3
4
many

The input size to a sub problem is __________ than the input size to the original problem.

equal
smaller
greater
no criteria

When the solver calls a sub solver, then it is called _________.

Iterative call
solver call
recursive call
conditional call

Using this recursive definition\({ a }^{ n }=\begin{cases} 1\quad \quad \quad \quad \quad \quad ifn=0 \\ a\times { a }^{ n }-1\quad otherwise \end{cases}\)how many multiplications are needed to calculate a¹⁰?

11
10
9
8

IfL is a loop variant, then it should be true at __________ important points in the algorithm.

2
3
4
5

If Fibonacci number is defined recursively as\(f(n)=\begin{cases} 0n=0 \\ 1n=1 \\ f(n-1)+f(n-2)otherwise \end{cases}\)to evaluate F(4), how many times F() is applied?

3
4
8
9

Which of the following is a recursive solver case

Base case
Recursive case
loop case
Both a and b

A loop invariant need not be true

at the start of the loop
at the start of each iteration
at the end of each iteration
at the start of the algorithm

Which of the following algorithm design techniques to execute the same action repeatedly

Assignment
Iteration
Recursion
Both b and c

How many important points the loop variant is true?

1
2
3
4

Which of the following is updated when each time the loop body is executed?

Data
Variables
Function
All of these

___________is an algorithm design technique, closely related to induction.

Iteration
Invariant
Loop invariant
Recursion

Which of the following is more powerful algorithms design technique closely related to iteration?

Specification
Abstraction
Recursion
Decomposition

Which statements executed repeatedly as long as the loop condition is true?

Sequential
Abstraction
Iteration
Assignment

We wish to cover a chessboard with dominoes, the number of black squares and the number of white squares covered by dominoes, respectively, placing a domino can be modeled by

b:= b + 2
w:= w + 2
b, w := b1+, w1+
b:= w

How many cases are needed for a recursive solvers?

2
3
4
5

Recursion must have at least ____________ base case.

one
two
three
four

Part - B

Generic 2 - Answer All Question

What is the relationship between loop invariant, loop condition and the input-output recursively?

Define a loop invariant.

When will the loop variant be true?

Define factorial of a natural number recursively

What is recursive problem solving

Does testing the loop condition affect the loop invariant? Why?

What is an invariant?

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