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11th Computer Science Weekly Test -1 ( Iteration and recursion )

MABS Institution

11th Computer Science Weekly Test -1 ( Iteration and recursion )-Aug 2020

Time : 1.30 Hours

Part - A

Multiple Choice Question - Answer All Question

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

Assignment
Iteration
Recursion
Both b and c

How many cases are there a recursive solver has

2
3
4
many

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 important points the loop variant is true?

1
2
3
4

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

Sequential
Abstraction
Iteration
Assignment

Which of the following is not an invariant of the assignment? m, n := m2+, n3+

m mod2
n mod3
3 X m - 2 X n
2 X m - 3 X n

Which of the following is a recursive solver case

Base case
Recursive case
loop case
Both a and b

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 more powerful algorithms design technique closely related to iteration?

Specification
Abstraction
Recursion
Decomposition

The loop invariant need not be true at the __________.

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

Part - B

Generic 2 - Answer All Question

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

Define factorial of a natural number recursively

What is recursive problem solving
Define a loop invariant.

When will the loop variant be true?

Part - C

Generic 3 - Answer All Question

Write a note on Recursion.

How will you solve a problem using recursion?

Using a loop variant how will you construct a loop?

King Vikramaditya has two magic swords. With one,he can cut off 19 heads of a dragon, but after that the dragon grows 13 heads. With the other sword, he can cut off 7 heads, but 22 new heads grow. If all heads are cut off, the dragon dies.If the dragon has originally 1000 heads, can it ever die?
(Hint :The number of heas mod 3 is invariant .)
What is the use of repeating the same action again and again?

Part - D

Generic 5 - Answer All Question

Give an example for loop invariant.

Power can also be defined recursively as \({ a }^{ n }=\begin{cases} 1\quad \quad \quad \quad \quad \quad ifn=0 \\ a\times { a }^{ n }-1\quad \quad ifn\quad is\quad odd \\ { a }^{ n/2 }\times an/2\quad ifn\quad is\quad even \end{cases}\) Construct a recursive algorithm using this definition. How many multiplications are needed to calculate a¹⁰?

Explain how will you solve a problem recursively.

There are 6 equally spaced trees and 6 sparrows sitting on these trees,one sparrow on each tree. If a sparrow flies from one tree to another, then at the same time, another sparrow flies from its tree to some other tree the same distance away, but in the opposite direction. Is it possible for all the sparrows to gather on one tree?
Explain recursive- problem solving.

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