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11th Computer Science Monthly Test -2 ( Iteration and recursion )

MABS Institution

11th Computer Science Monthly Test -2 ( Iteration and recursion )-Aug 2020

Time : 2.30 Hours

Part - A

Multiple Choice Question - Answer All Question

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

recursion
variant
loop invariant
algorithm

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

How many cases are there a recursive solver has

2
3
4
many

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

1972
1974
1970
1971

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

Sequential
Abstraction
Iteration
Assignment

The loop invariant need not be true at the __________.

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

___________is an algorithm design technique, closely related to induction.

Iteration
Invariant
Loop invariant
Recursion

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

Which of the following is the key to construct iterative algorithms

loop invariant
loop updation
loop variable
lop condition

Part - B

Generic 2 - Answer All Question

When will the loop variant be true?

Define factorial of a natural number recursively

What is recursive problem solving

Define a loop invariant.

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

What is an invariant?

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

Part - C

Generic 3 - Answer All Question

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?

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.)

How will you solve a problem using 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?

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 loop variant?

Part - D

Generic 5 - Answer All Question

Explain how will you solve a problem recursively.

Give an example for loop invariant.

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.

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.
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 the outline of recursive problem-solving technique.

Explain recursive- problem solving.

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