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

MABS Institution

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

Time : 2.30 Hours

Part - A

Multiple Choice Question - Answer All Question

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

Iterative call
solver call
recursive call
conditional call

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

Data
Variables
Function
All of these

In a loop, if L is an invariant of the loop body B, then L is known as a __________

recursion
variant
loop invariant
algorithm

How many cases are there a recursive solver has

2
3
4
many

In an expression if the variables has the same value before and after an assignment, then it is __________of an assignment.

variant
Invariant
iteration
variable

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

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

Assignment
Iteration
Recursion
Both b and c

Which of the following is the key to construct iterative algorithms

loop invariant
loop updation
loop variable
lop condition

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

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?

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

Define a loop invariant.
Does testing the loop condition affect the loop invariant? Why?

When will the loop variant be true?

What is recursive problem solving
What is an invariant?

Part - C

Generic 3 - Answer All Question

Consider two variable m and n under the assignment m, n : = m + 3, n - 1. Is the expression m + 3n an invariant?

There are 7 tumblers on a table, all standing upside down. You are allowed to turn any 2 tumblers simultaneously in one move. Is it possible to reach a situation when all the tumblers are right side up? (Hint: The parity of the number of upside-down tumblers is invariant.)

A knockout tournament is a series of games. Two players compete in each game; the loser is knocked out (i.e. does not play anymore), the winner carries on. The winner of the tournament is the player that is left after all other players have been knocked out. Suppose there are 1234 players in a tournament. How many games are played before the tournament winner is decided?

Write a note on Recursion.

Show that p - c is an invariant of the assignment. P, C : = P + 1, C + 1

Using a loop variant how will you construct a loop?

How will you solve a problem using recursion?

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 .)

Write a note on Iteration.

Write a note on loop variant?

Part - D

Generic 5 - Answer All Question

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?

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?

A single square- covered board is a board of 2ⁿ * 2ⁿsquares in which one square is covered with a single square tile. Show that it is possible to cover the this board with triominoes without overlap.

Explain the outline of recursive problem-solving technique.

Design a recursive algorithm to compute aⁿ, We constructed an iterative algorithm to compute aⁿ in Example 8.5. aⁿ can be defined recursively as

Customers are waiting in a line at a counter. The man at the counter wants to know how many customers are waiting in the line.

Explain how will you solve a problem recursively.

Assume an 8 * 8 chessboard with the usual coloring. "Recoloring" operation changes the color of all squares of a row or a column . you can recolor re - peatedly. The goal is to attain just one black squares , it changes by ( |8 - b ) - b| ).

Explain Loop invariant with a neat diagram.

Explain recursive- problem solving.

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

MABS Institution

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

Part - A

Multiple Choice Question - Answer All Question

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

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

In a loop, if L is an invariant of the loop body B, then L is known as a __________

How many cases are there a recursive solver has

In an expression if the variables has the same value before and after an assignment, then it is __________of an assignment.

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

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

Which of the following is the key to construct iterative algorithms

A loop invariant need not be true

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?

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

Define a loop invariant.

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

When will the loop variant be true?

What is recursive problem solving

What is an invariant?

Part - C

Generic 3 - Answer All Question

Consider two variable m and n under the assignment m, n : = m + 3, n - 1. Is the expression m + 3n an invariant?

There are 7 tumblers on a table, all standing upside down. You are allowed to turn any 2 tumblers simultaneously in one move. Is it possible to reach a situation when all the tumblers are right side up? (Hint: The parity of the number of upside-down tumblers is invariant.)

Write a note on Recursion.

Show that p - c is an invariant of the assignment. P, C : = P + 1, C + 1

Using a loop variant how will you construct a loop?

How will you solve a problem using recursion?

Write a note on Iteration.

Write a note on loop variant?

Part - D

Generic 5 - Answer All Question

A single square- covered board is a board of 2n * 2n squares in which one square is covered with a single square tile. Show that it is possible to cover the this board with triominoes without overlap.

Explain the outline of recursive problem-solving technique.

Design a recursive algorithm to compute an, We constructed an iterative algorithm to compute an in Example 8.5. an can be defined recursively as

Customers are waiting in a line at a counter. The man at the counter wants to know how many customers are waiting in the line.

Explain how will you solve a problem recursively.

Assume an 8 * 8 chessboard with the usual coloring. "Recoloring" operation changes the color of all squares of a row or a column . you can recolor re - peatedly. The goal is to attain just one black squares , it changes by ( |8 - b ) - b| ).

Explain Loop invariant with a neat diagram.

Explain recursive- problem solving.

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A single square- covered board is a board of 2ⁿ * 2ⁿsquares in which one square is covered with a single square tile. Show that it is possible to cover the this board with triominoes without overlap.

Design a recursive algorithm to compute aⁿ, We constructed an iterative algorithm to compute aⁿ in Example 8.5. aⁿ can be defined recursively as