32 Questions
What is the main strategy of the divide and conquer algorithm design?
Divide the problem into sub-problems and conquer them separately
Which algorithm is NOT listed as a notable example of the divide and conquer strategy?
Insertion sort algorithm
What does the concept of 'Divide and Conquer' refer to outside of algorithm design?
A strategy to prevent smaller power groups from linking up
Which algorithm is an example of a recursive implementation of the divide and conquer strategy?
Karatsuba's multiplication algorithm
What is a common characteristic of the sub-problems in the divide and conquer strategy?
They are trivial for small sizes or use the same strategy
According to the text, what is John von Neumann thinking about that is much more important than bombs?
The impact of computers on society
What is the primary strategy used in the merge sort algorithm?
Divide and conquer
Which auxiliary function helps in merging two ordered vectors in the merge sort algorithm?
Merge function
In the merge procedure, what indices does the input array A have?
p, q, r such that p≤q1
Who developed a fast algorithm for multiplying n-digit numbers with complexity O(nlg3)?
Anatolii Karatsuba
What was disproved by Karatsuba's algorithm regarding the number of operations required for multiplying n-digit numbers?
Andrey Kolmogorov's 1956 conjecture that Ω(n2 ) operations would be required
In Karatsuba's algorithm, what is the base case for the recursive multiplication of binary numbers?
n=1
What is the running time complexity of Karatsuba's algorithm for n > 2?
$T (n) ≤ 3T (n/2) + c n lg 3$
What is the number of bits in x and y in Karatsuba's recursive multiplication algorithm?
$n$
How many recursive calls are made in Karatsuba's algorithm to obtain quadratic running time?
$3$
What is the value of p in the Recursive-Multiply(x,y) algorithm if n=1?
$x * y$
What is the primary strategy used in the divide and conquer algorithm design?
Divide a problem into sub-problems and combine the solutions
Which algorithm is an example of a recursive implementation of the divide and conquer strategy?
Merge sort
What is the number of bits in x and y in Karatsuba's recursive multiplication algorithm?
4
Which auxiliary function helps in merging two ordered vectors in the merge sort algorithm?
Heapify
What does the concept of 'Divide and Conquer' refer to outside of algorithm design?
Breaking up existing power structures to prevent smaller power groups from linking up
What is the value of p in the Recursive-Multiply(x,y) algorithm if n=1?
$y$
What is the time complexity of the merge sort algorithm?
O(nlogn)
What did Anatolii Karatsuba disprove with his algorithm?
Andrey Kolmogorov's 1956 conjecture that Ω(n^2) operations would be required to multiply n-digit numbers
What is the value of p in the Recursive-Multiply(x,y) algorithm if n=1?
x * y
What is the base case for the recursive multiplication of binary numbers in Karatsuba's algorithm?
$n = 1$
Which auxiliary function helps in merging two ordered vectors in the merge sort algorithm?
merge()
Who developed a fast algorithm for multiplying n-digit numbers with complexity O(nlg3)?
Anatolii Karatsuba
How many recursive calls are made in Karatsuba's algorithm to obtain quadratic running time?
$4$
What is the main strategy of the divide and conquer algorithm design?
Combine and Conquer
Which algorithm is NOT listed as a notable example of the divide and conquer strategy?
Insertion sort
What is a common characteristic of the sub-problems in the divide and conquer strategy?
They are homogeneous in content
Test your knowledge of divide and conquer algorithms with this quiz focused on algorithm design strategies, including insertion sort, Dijkstra's algorithm, merge sort, quicksort, and all-pairs-shortest-path. This quiz covers concepts from Chapter 3 of the book 'Algorithms Illuminated'.
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