Recent questions tagged time-complexity

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1

UGCNET-Oct2020-II: 25
If algorithm $A$ and another algorithm $B$ take $\log_2 (n)$ and $\sqrt{n}$ microseconds, respectively, to solve a problem, then the largest size $n$ of a problem these algorithms can solve, respectively, in one second are ______ and ______. $2^{10^n}$ and $10^6$ $2^{10^n}$ and $10^{12}$ $2^{10^n}$ and $6.10^6$ $2^{10^n}$ and $6.10^{12}$

If algorithm $A$ and another algorithm $B$ take $\log_2 (n)$ and $\sqrt{n}$ microseconds, respectively, to solve a problem, then the largest size $n$ of a problem these algorithms can solve, respectively, in one second are ______ and ______. $2^{10^n}$ and $10^6$ $2^{10^n}$ and $10^{12}$ $2^{10^n}$ and $6.10^6$ $2^{10^n}$ and $6.10^{12}$

asked Nov 20, 2020 in Algorithms jothee 165 views

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2

UGCNET-Oct2020-II: 52
The running time of an algorithm is $O(g(n))$ if and only if its worst-case running time is $O(g(n))$ and its best-case running time is $\Omega(g(n)) \cdot (O= \textit{ big }O)$ its worst-case running time is $\Omega (g(n))$ and its best-case running ... $(a)$ only $(b)$ only $(c)$ only $(d)$ only

The running time of an algorithm is $O(g(n))$ if and only if its worst-case running time is $O(g(n))$ and its best-case running time is $\Omega(g(n)) \cdot (O= \textit{ big }O)$ its worst-case running time is $\Omega (g(n))$ ... , $(o = \textit{ small } o)$ Choose the correct answer from the options given below: $(a)$ only $(b)$ only $(c)$ only $(d)$ only

asked Nov 20, 2020 in Algorithms jothee 77 views

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3

NTA NET NOV2020( Big O )

asked Nov 17, 2020 in CBSE/UGC NET Sanjay Sharma 33 views

1 vote

1 answer

4

NIELIT 2016 MAR Scientist C - Section C: 51
The most efficient algorithm for finding the number of connected components in a $n$ undirected graph on $n$ vertices and $m$ edges has time complexity $\Theta (n)$ $\Theta (m)$ $\Theta (m+n)$ $\Theta (mn)$

The most efficient algorithm for finding the number of connected components in a $n$ undirected graph on $n$ vertices and $m$ edges has time complexity $\Theta (n)$ $\Theta (m)$ $\Theta (m+n)$ $\Theta (mn)$

asked Apr 2, 2020 in Algorithms Lakshman Patel RJIT 195 views

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5

NIELIT 2016 MAR Scientist C - Section C: 52
Consider the process of inserting an element into a $Max\ Heap$, where the $Max\ Heap$ is represented by an $array$. Suppose we perform a binary search on the path from the new leaf to the root to find the position for the newly inserted element, the number of $comparisons$ ... $\Theta(n\log _{2} \log_2 n)$ $\Theta (n)$ $\Theta(n\log _{2}n)$

Consider the process of inserting an element into a $Max\ Heap$, where the $Max\ Heap$ is represented by an $array$. Suppose we perform a binary search on the path from the new leaf to the root to find the position for the newly inserted element, the number of $comparisons$ performed is $\Theta(\log _{2}n)$ $\Theta(n\log _{2} \log_2 n)$ $\Theta (n)$ $\Theta(n\log _{2}n)$

asked Apr 2, 2020 in DS Lakshman Patel RJIT 627 views

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6

NIELIT 2017 OCT Scientific Assistant A (IT) - Section C: 2
An algorithm is made up pf two modules $M1$ and $M2.$ If order of $M1$ is $f(n)$ and $M2$ is $g(n)$ then the order of algorithm is $max(f(n),g(n))$ $min(f(n),g(n))$ $f(n) + g(n)$ $f(n) \times g(n)$

An algorithm is made up pf two modules $M1$ and $M2.$ If order of $M1$ is $f(n)$ and $M2$ is $g(n)$ then the order of algorithm is $max(f(n),g(n))$ $min(f(n),g(n))$ $f(n) + g(n)$ $f(n) \times g(n)$

asked Apr 1, 2020 in Algorithms Lakshman Patel RJIT 325 views

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1 answer

7

NIELIT 2017 OCT Scientific Assistant A (IT) - Section B: 14
The running time of an algorithm $T(n),$ where $’n’$ is the input size , is given by $T(n) = 8T(n/2) + qn,$ if $n>1$ $= p,$ if $n = 1$ Where $p,q$ are constants. The order of this algorithm is $n^{2}$ $n^{n}$ $n^{3}$ $n$

The running time of an algorithm $T(n),$ where $’n’$ is the input size , is given by $T(n) = 8T(n/2) + qn,$ if $n>1$ $= p,$ if $n = 1$ Where $p,q$ are constants. The order of this algorithm is $n^{2}$ $n^{n}$ $n^{3}$ $n$

asked Apr 1, 2020 in Algorithms Lakshman Patel RJIT 241 views

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3 answers

8

NIELIT 2017 OCT Scientific Assistant A (CS) - Section C: 4
The running time of an algorithm $T(n),$ where $’n’$ is the input size , is given by $T(n) = 8T(n/2) + qn,$ if $n>1$ $ = p,$ if $n = 1$ Where $p,q$ are constants. The order of this algorithm is $n^{2}$ $n^{n}$ $n^{3}$ $n$

The running time of an algorithm $T(n),$ where $’n’$ is the input size , is given by $T(n) = 8T(n/2) + qn,$ if $n>1$ $ = p,$ if $n = 1$ Where $p,q$ are constants. The order of this algorithm is $n^{2}$ $n^{n}$ $n^{3}$ $n$

asked Apr 1, 2020 in Algorithms Lakshman Patel RJIT 250 views

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9

NIELIT 2017 OCT Scientific Assistant A (CS) - Section B: 8
Consider the following C code segment: int Ls Prime(n) { int i,n; for(i=2;i<=sqrt(n);i++) if(n%i ==0) { printf( NOT Prime.\n ); return 0; } return 1; } Let $T(n)$ denote the number of times the for loop is executed by the program on input $n.$ ... $T(n) = \Omega (1)$ $T(n) = O(n)$ and $T(n) = \Omega (\sqrt{n})$ None of these

Consider the following C code segment: int Ls Prime(n) { int i,n; for(i=2;i<=sqrt(n);i++) if(n%i ==0) { printf( NOT Prime.\n ); return 0; } return 1; } Let $T(n)$ denote the number of times the for loop is executed by the program on input $n.$ ... $T(n) = O(\sqrt{n})$ and $T(n) = \Omega (1)$ $T(n) = O(n)$ and $T(n) = \Omega (\sqrt{n})$ None of these

asked Apr 1, 2020 in Algorithms Lakshman Patel RJIT 239 views

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10

NIELIT 2017 OCT Scientific Assistant A (CS) - Section B: 30
An algorithm is made up of two modules $M1$ and $M2.$ If order of $M1$ is $f(n)$ and $M2$ is $g(n)$ then he order of algorithm is $max(f(n),g(n))$ $min(f(n),g(n))$ $f(n) + g(n)$ $f(n) \times g(n)$

An algorithm is made up of two modules $M1$ and $M2.$ If order of $M1$ is $f(n)$ and $M2$ is $g(n)$ then he order of algorithm is $max(f(n),g(n))$ $min(f(n),g(n))$ $f(n) + g(n)$ $f(n) \times g(n)$

asked Apr 1, 2020 in Algorithms Lakshman Patel RJIT 231 views

3 votes

12 answers

11

NIELIT 2016 MAR Scientist B - Section C: 12
Which of the following sorting algorithms does not have a worst case running time of $O(n^2)$? Insertion sort. Merge sort. Quick sort. Bubble sort.

Which of the following sorting algorithms does not have a worst case running time of $O(n^2)$? Insertion sort. Merge sort. Quick sort. Bubble sort.

asked Mar 31, 2020 in Algorithms Lakshman Patel RJIT 1k views

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3 answers

12

NIELIT 2016 MAR Scientist B - Section C: 22
Time complexity of an algorithm $T(n)$, where $n$ is the input size is given by $\begin{array}{ll}T(n) & =T(n-1)+\frac{1}{n}, \text{ if }n>1\\ & =1, \text{ otherwise} \end{array}$ The order of this algorithm is $\log n$ $n$ $n^2$ $n^n$

Time complexity of an algorithm $T(n)$, where $n$ is the input size is given by $\begin{array}{ll}T(n) & =T(n-1)+\frac{1}{n}, \text{ if }n>1\\ & =1, \text{ otherwise} \end{array}$ The order of this algorithm is $\log n$ $n$ $n^2$ $n^n$

asked Mar 31, 2020 in Algorithms Lakshman Patel RJIT 456 views

3 votes

2 answers

13

NIELIT 2016 DEC Scientist B (IT) - Section B: 27
Complexity of Kruskal's algorithm for finding minimum spanning tree of an undirected graph containing $n$ vertices and $m$ edges if the edges are sorted is: $O(mn)$ $O(m)$ $O(m+n)$ $O(n)$

Complexity of Kruskal's algorithm for finding minimum spanning tree of an undirected graph containing $n$ vertices and $m$ edges if the edges are sorted is: $O(mn)$ $O(m)$ $O(m+n)$ $O(n)$

asked Mar 31, 2020 in Algorithms Lakshman Patel RJIT 392 views

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3 answers

14

NIELIT 2016 DEC Scientist B (CS) - Section B: 16
Two main measures for the efficiency of an algorithm are: Processor and Memory Complexity and Capacity Time and Space Data and Space

Two main measures for the efficiency of an algorithm are: Processor and Memory Complexity and Capacity Time and Space Data and Space

asked Mar 31, 2020 in Algorithms Lakshman Patel RJIT 1.8k views

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2 answers

15

NIELIT 2016 DEC Scientist B (CS) - Section B: 27
What is the solution to the recurrence $T(n)=T \bigg (\dfrac{n}{2} \bigg )+n$? $O(\log n)$ $O(n)$ $O(n\log n)$ None of these

What is the solution to the recurrence $T(n)=T \bigg (\dfrac{n}{2} \bigg )+n$? $O(\log n)$ $O(n)$ $O(n\log n)$ None of these

asked Mar 31, 2020 in Algorithms Lakshman Patel RJIT 321 views

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2 answers

16

NIELIT 2016 DEC Scientist B (CS) - Section B: 52
The concept of order Big O is important because It can be used to decide the best algorithm that solves a given problem It is the lower bound of the growth rate of algorithm It determines the maximum size of a problem that can be solved in a given amount of time Both (A) and (B)

The concept of order Big O is important because It can be used to decide the best algorithm that solves a given problem It is the lower bound of the growth rate of algorithm It determines the maximum size of a problem that can be solved in a given amount of time Both (A) and (B)

asked Mar 31, 2020 in Algorithms Lakshman Patel RJIT 311 views

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2 answers

17

NIELIT 2017 July Scientist B (IT) - Section B: 59
What is the running time of the following function (specified as a function of the input value)? void Function(int n){ int i=1; int s=1; while(s<=n){ i++; s=s+i; } } $O(n)$ $O(n^2)$ $O(1)$ $O(\sqrt n)$

What is the running time of the following function (specified as a function of the input value)? void Function(int n){ int i=1; int s=1; while(s<=n){ i++; s=s+i; } } $O(n)$ $O(n^2)$ $O(1)$ $O(\sqrt n)$

asked Mar 30, 2020 in Algorithms Lakshman Patel RJIT 440 views

1 vote

2 answers

18

NIELIT 2017 July Scientist B (CS) - Section B: 9
The worst case running times of Insertion sort, Merge sort and Quick sort, respectively, are $\Theta(n \log n),\Theta(n \log n) \text{ and } \Theta(n^2)$ $\Theta(n^2),\Theta(n^2)\text{ and } \Theta(n \log n)$ $\Theta(n^2), \Theta(n \log n)\text{ and } \Theta(n \log n)$ $\Theta(n^2),\Theta(n\log n) \text{ and } \Theta(n^2)$

The worst case running times of Insertion sort, Merge sort and Quick sort, respectively, are $\Theta(n \log n),\Theta(n \log n) \text{ and } \Theta(n^2)$ $\Theta(n^2),\Theta(n^2)\text{ and } \Theta(n \log n)$ $\Theta(n^2), \Theta(n \log n)\text{ and } \Theta(n \log n)$ $\Theta(n^2),\Theta(n\log n) \text{ and } \Theta(n^2)$

asked Mar 30, 2020 in Algorithms Lakshman Patel RJIT 272 views

5 votes

4 answers

19

TIFR2020-B-10
Among the following asymptotic expressions, which of these functions grows the slowest (as a function of $n$) asymptotically? $2^{\log n}$ $n^{10}$ $(\sqrt{\log n})^{\log ^{2} n}$ $(\log n)^{\sqrt{\log n}}$ $2^{2^{\sqrt{\log\log n}}}$

Among the following asymptotic expressions, which of these functions grows the slowest (as a function of $n$) asymptotically? $2^{\log n}$ $n^{10}$ $(\sqrt{\log n})^{\log ^{2} n}$ $(\log n)^{\sqrt{\log n}}$ $2^{2^{\sqrt{\log\log n}}}$

asked Feb 11, 2020 in Algorithms Lakshman Patel RJIT 609 views

5 votes

2 answers

20

ISRO2020-36
What is the complexity of the following code? sum=0; for(i=1;i<=n;i*=2) for(j=1;j<=n;j++) sum++; Which of the following is not a valid string? $O(n^2)$ $O(n\log\ n)$ $O(n)$ $O(n\log\ n\log\ n)$

What is the complexity of the following code? sum=0; for(i=1;i<=n;i*=2) for(j=1;j<=n;j++) sum++; Which of the following is not a valid string? $O(n^2)$ $O(n\log\ n)$ $O(n)$ $O(n\log\ n\log\ n)$

asked Jan 13, 2020 in Algorithms Satbir 1.3k views

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