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Data Structures Algorithms Ii
Masters Theorem Interview
Quiz 1
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Q.1
Solve the following recurrence using Master’s theorem.
a) T(n) = O(n)
b) T(n) = O(log n)
c) T(n) = O(n2log n)
d) T(n) = O(n2)
Q.2
Solve the following recurrence using Master’s theorem.
a) T(n) = O(n2)
b) T(n) = O(n2 log n)
c) T(n) = O(2n)
d) cannot be solved
Q.3
Solve the following recurrence using Master’s theorem.
a) T(n) = O(n)
b) T(n) = O(log n)
c) T(n) = O(n2log n)
d) T(n) = O(n2)
Q.4
Solve the following recurrence using Master’s theorem.
a) T(n) = O(n)
b) T(n) = O(log n)
c) T(n) = O(n2log n)
d) cannot be solved using master’s theorem
Q.5
Solve the following recurrence using Master’s theorem.
a) T(n) = O(n)
b) T(n) = O(log n)
c) T(n) = O(n2log n)
d) cannot be solved using master’s theorem
Q.6
Solve the following recurrence using Master’s theorem.
a) T(n) = O(n!)
b) T(n) = O(n! log n)
c) T(n) = O(n2log n)
d) cannot be solved using master’s theorem
Q.7
Solve the following recurrence using Master’s theorem.
a) T(n) = O(n (log n)2)
b) T(n) = O(n log n)
c) T(n) = O(n2log n)
d) cannot be solved using master’s theorem
Q.8
What will be the recurrence relation of the following code? Int sum(int n) { If(n== return else return n+sum(n-1); }
a) T(n) = T(n/2) + n
b) T(n) = T(n-1) + n
c) T(n) = T(n-1) + O(1)
d) T(n) = T(n/2) + O(1)
Q.9
What will be the recurrence relation of the following code? int xpowy(int x, int n) if (n==returnif (n==return x; if ((n %==return xpowy(x*x, n/2); else return xpowy(x*x, n/* x;
a) T(n) = T(n/2) + n
b) T(n) = T(n-1) + n
c) T(n) = T(n-1) + O(1)
d) T(n) = T(n/2) + O(1)
Q.10
What will be the time complexity of the following code? int xpowy(int x, int n) { if (n== return if (n== return x; if ((n %== return xpowy(x*x, n/2); else return xpowy(x*x, n/* x; }
a) O(log n)
b) O(n)
c) O(n log n)
d) O(n2)
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