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Data Structures Algorithms Ii
Data Structure Multiple Choice
Quiz 1
Solution
Q.1.
Which of the following is NOT a Catalan number?
a) 1
b) 5
c) 14
d) 43
Q.2.
Which of the following numbers is the 6th Catalan number?
a) 14
b) 429
c) 132
d) 42
Q.3.
Which of the following is not an application of Catalan Numbers?
a) Counting the number of Dyck words
b) Counting the number of expressions containing n pairs of parenthesis
c) Counting the number of ways in which a convex polygon can be cut into triangles by connecting vertices with straight lines
d) Creation of head and tail for a given number of tosses
Q.4.
Which of the following methods can be used to find the nth Catalan number?
a) Recursion
b) Binomial coefficients
c) Dynamic programming
d) Recursion, Binomial Coefficients, Dynamic programming
Q.5.
The recursive formula for Catalan number is given by Cn = ∑Ci*C(n-i).
a) arr[i] = arr[j] * arr[k];
b) arr[j] += arr[i] * arr[k];
c) arr[i] += arr[j] * arr[k].
d) arr[j] = arr[i] * arr[k];
Q.6.
Which of the following implementations of Catalan numbers has the smallest time complexity?
a) Dynamic programming
b) Binomial coefficients
c) Recursion
d) All have equal time complexity
Q.7.
Which of the following implementations of Catalan numbers has the largest space complexity(Don’t consider the stack space)?
a) Dynamic programming
b) Binomial coefficients
c) Recursion
d) All have equal space complexities
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