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

MABS Institution

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

Time : 2.00 Hours

Part - A

Generic 2 - Answer All Question

Define factorial of a natural number recursively

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

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

What is recursive problem solving

What is an invariant?

Define a loop invariant.

When will the loop variant be true?

Part - B

Generic 3 - Answer All Question

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?

Using a loop variant how will you construct a loop?

Write down the steps to be taken to construct a loop.

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

What are the important points in which a loop variant is true?
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?

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

MABS Institution

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

Part - A

Generic 2 - Answer All Question

Define factorial of a natural number recursively

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

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

What is recursive problem solving

What is an invariant?

Define a loop invariant.

When will the loop variant be true?

Part - B

Generic 3 - Answer All Question

Write a note on loop variant?

Using a loop variant how will you construct a loop?

Write down the steps to be taken to construct a loop.

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

What are the important points in which a loop variant is true?

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 Iteration.

What is the use of repeating the same action again and again?

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

Write a note on Recursion.

How will you solve a problem using recursion?

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