Rapid Fire Quiz Number Five

Welcome to rapid fire quiz number five. Please take a moment to pause and review the instructions and syllabus before beginning the quiz.

Quiz Questions and Answers

Question 1

• Correct Option: A
• Explanation: A recurrence relation is a mathematical expression that describes how to solve a big problem by solving smaller sub-problems.

Question 2

• Correct Option: B
• Explanation: The recurrence relation for the algorithm is ( T(n) = T(n-1) + 1 ) if ( n > 1 ); the base case ( n = 1 ) gives a constant ( c ).

Question 3

• Correct Option: B
• Explanation: The problem requires the substitution method to see the pattern for correctness.

Question 4

• Correct Option: D
• Explanation: In the base case, no multiplication is performed, so the option without addition of n or unnecessary multiplication is correct.

Question 5

• Correct Option: A
• Explanation: The number of additions for some array ( a ) is represented as ( A(n) = A(n-1) + 1 ).

Question 6

• Correct Option: C
• Explanation: In the base case and recursive case, we perform one comparison, represented by ( C(n) = C(n-1) ).

Question 7

• Correct Option: A
• Explanation: Order of N or ( O(N) ).

Question 8

• Correct Option: B
• Explanation: The Towers of Hanoi problem with 4 discs requires ( 2^4 - 1 = 15 ) moves.

Question 9

• Correct Option: Recurrence Relation: ( T(n) = 2T(n-1) + 1 )
• Explanation: This is the recursive part of the Towers of Hanoi problem's time complexity.

Question 10

• Correct Option: C
• Explanation: The algorithm's time complexity is exponential, ( O(2^N) ).

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