Recent questions tagged time-complexity

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Cormen Edition 3 Exercise 7.4 Question 4 (Page No. 184)
Show that RANDOMIZED-QUICKSORT’s expected running time is $\Omega(n\ lg\ n)$.

asked Jun 28 in Algorithms by akash.dinkar12 Boss (40.9k points) | 11 views

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Cormen Edition 3 Exercise 7.4 Question 2 (Page No. 184)
Show that quicksort’s best-case running time is $\Omega(n\ lg\ n)$.

asked Jun 28 in Algorithms by akash.dinkar12 Boss (40.9k points) | 9 views

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3

Cormen Edition 3 Exercise 7.2 Question 3 (Page No. 178)
Show that the running time of QUICKSORT is $\Theta(n^2)$ when the array $A$ contains distinct elements and is sorted in decreasing order.

asked Jun 27 in Algorithms by akash.dinkar12 Boss (40.9k points) | 7 views

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4

Cormen Edition 3 Exercise 7.2 Question 2 (Page No. 178)
What is the running time of QUICKSORT when all elements of the array $A$ have the same value?

asked Jun 27 in Algorithms by akash.dinkar12 Boss (40.9k points) | 20 views

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5

Cormen Edition 3 Exercise 2.3 Question 3 (Page No. 39)
Use mathematical induction to show that when $n$ is an exact power of $2$, the solution of the recurrence $T(n) = \begin{cases} 2 \text{, if n=2, } \\2T(n/2)+n \text{, if n=$2^k$,for k >1} \end{cases}$ is $T(n) = n\ lg\ n$.

asked Jun 26 in Algorithms by akash.dinkar12 Boss (40.9k points) | 18 views

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6

Cormen Edition 3 Exercise 2.3 Question 4 (Page No. 38)
We can express the insertion sort as a recursive procedure as follows.In order to sort $A[1\dots n]$, we recursively sort $A[1 \dots n-1]$ and then insert $A[n]$ into the sorted array $A[1 \dots n-1]$. Write a recurrence for the running time of this recursive version of insertion sort.

asked Jun 26 in Algorithms by akash.dinkar12 Boss (40.9k points) | 14 views

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Cormen Edition 3 Exercise 2.2 Question 2 (Page No. 29)
Consider sorting $n$ numbers stored in an array $A$ by first finding the smallest element of $A$ and exchanging it with the element in $A[1]$. Then find the second smallest element of $A$ ... , rather than for all n elements? Give the best-case and worst-case running times of selection sort in $\Theta$-notation

asked Jun 25 in Algorithms by akash.dinkar12 Boss (40.9k points) | 7 views

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8

Cormen Edition 3 Exercise 2.2 Question 1 (Page No. 29)
Express the function $n^3/1000 -100n^2-100n+3$ in terms of $\Theta$ notation.

asked Jun 25 in Algorithms by akash.dinkar12 Boss (40.9k points) | 14 views

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9

Is each and every NP complete problem (polynomially) reduced to each and every another NP complete problem?

asked Jun 13 in Theory of Computation by commenter commenter (179 points) | 38 views

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Master's Theorem: Validity of Format
How to check if a given recurrence relation is in a format that is valid to apply Master’s Theorem? Also, how to distinguish between Master’s Theorem and extended Master’s Theorem?

asked Jun 12 in Algorithms by lolster (223 points) | 67 views

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GATE-1999
Consider the following algorithms. Assume, procedure $A$ and procedure $B$ take $O(1)$ and $O(1/n)$ unit of time respectively. Derive the time complexity of the algorithm in $O$ -notation. algorithm what (n) begin if n = 1 then call A else begin what (n-1); call B(n ... $c$ So complexity should be $O(1)$. But answer is $O(n)$.What I am doing wrong?

asked Jun 4 in Algorithms by kshitij (105 points) | 94 views

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12

Asymptotic Notation theta property
If $T1(n) = \Theta(f(n))$ & $T2(n) = \Theta(f(n))$ Then, Is $T1(n) + T2(n) = O(f(n))$ If yes, then how?

asked May 26 in Algorithms by shubhojit1412 (5 points) | 101 views

+1 vote

2 answers

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Made easy Workbook 2020
Question: $T(1)=1$ $T(n) = 2 T(n - 1) + n$ evaluates to? Can anyone solve it by substitution method? Given answer $T(n) = 2^{n+1} - (n+2)$ How?

asked May 25 in Algorithms by Jyoti Kumari97 (181 points) | 136 views

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Made Easy Test Series:Algorithm-Time Complexity
Consider a procedure $find()$ which take array of $n$ integers as input, and produce pair of element of array whose difference is not greater than the difference of any other pair of element of that array. Which of the following represent ... Here we need to sort first and then need to compare adjacent element right?? Then what will be complexity??

asked May 18 in Algorithms by srestha Veteran (112k points) | 87 views

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15

Made Easy Test Series: Algorithm-Reverse Polish Notation
Consider the new-order strategy for traversing a binary tree: Visit the root Visit the right subtree using new-order Visit the left subtree using new-order The new-order traversal of expression tree corresponding to the reverse polish expression 3 4 * 5 – 2 ^ 6 7 * 1 + – What will be expression, any procedure for it??

asked May 16 in Compiler Design by srestha Veteran (112k points) | 77 views

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16

Made Easy Test Series:Algorithm-Recurrence Relation
What is the solution of recurrence relation $T\left ( n \right )=T\left ( n-1 \right )+n$

asked May 10 in Algorithms by srestha Veteran (112k points) | 96 views

+1 vote

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17

GO screening test
Which one of the following notations is most relevant for finding the best algorithm for a problem? (A) $o(f(n))$ (B) $O(f(n))$ (C) $\omega (f(n))$ (D) $ \Omega (f(n))$

asked May 9 in Algorithms by toxicdesire Junior (855 points) | 128 views

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18

Made Easy Test Series:Time Complexity
Consider the following program: int Bar(int n){ if(n<2) return; } else{ int sum=0; int i,j; for(i=1;i<=4;i++) Bar(n/2); for(i=1;i<=n;i++){ for(j=1;j<=i;j++){ sum=sum+1; } } } Now consider the following ... $Bar\left ( n \right )$ is $O \left ( n^{3}logn^{2} \right )$ How many statements are correct________________

asked May 7 in Algorithms by srestha Veteran (112k points) | 220 views

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19

IIIT PGEE 2019
What is the time complexity to delete an arbitrary node from binary heap? O(n) O(log n) O(1) O(n log n)

asked Apr 29 in Programming by manikgupta123 (75 points) | 127 views

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20

IIIT PGEE 2019
Which of the following gives O(1) complexity if we want to check whether an edge exists between two given nodes in a graph? Adjacency List Adjacency Matrix Incidence Matrix None of these

asked Apr 29 in DS by manikgupta123 (75 points) | 114 views

+2 votes

1 answer

21

IIIT PGEE 2019
What is the time complexity for insertion in binary tree in worst case? O(1) O(log n) O(n) O(n log n)

asked Apr 29 in Programming by manikgupta123 (75 points) | 137 views

+1 vote

1 answer

22

If there is an $\rm NP$-complete language $L$ whose complement is in $\rm NP$, then...

asked Apr 20 in Theory of Computation by Rhythm (189 points) | 99 views

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23

Find Asymptotic upper bound (http://www.csd.uwo.ca/~moreno/CS433-CS9624/Resources/master.pdf)

asked Apr 19 in Algorithms by Mk Utkarsh Boss (34.5k points) | 98 views

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24

Algorithm Time Complexity-Self Doubt
What is the best case and worst case of the algorithm? And when will best case and worst case will happen?? int main() { for(i=1 ; i<=n ; i++) { if(n%i == 0) { for(j=1 ; j<=n ; j++) { printf("Hello"); } } } }

asked Apr 10 in Algorithms by sumitr (235 points) | 147 views

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25

Time complexity
Please help to find the time complexity of this loop. void main() { int n; while(n>=1) { n=n-2; } }

asked Mar 19 in Algorithms by Devshree Dubey Boss (13.7k points) | 90 views

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26

Self doubt
O(n-1)+O(n)=O(n) O(n/2)+O(n)=O(n) but O(1)+O(2)+O(3)+...+O(n)=O(n(n+1)/2)=O(n^2) why?

asked Mar 19 in Algorithms by Tanuj Guha Thakurta (151 points) | 61 views

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27

Time complexity
Is this the correct way to solve ? Q) int algorithm(int n) { int sum =0;k,j; for (k=0;k<n/2;k++) for(j=0;j<10;j++) sum++; return 4*algorithm(n/2)*algorithm(n/2)+algorithm(n/2)*algorithm(n/2) }

asked Mar 15 in Algorithms by syncronizing Junior (789 points) | 122 views

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28

JEST Sample Question 1-d
T (n) = T (n/2) + 2; T (1) = 1 When n is a power of 2, the correct expression for T (n) is: (A) 2(log n + 1) (B) 2 log n (C) log n + 1 (D)2 log n + 1

asked Feb 15 in Algorithms by sripo Active (2.3k points) | 110 views

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29

JEST Sample Question-4
A tournament is a directed graph in which there is exactly one directed edge between every pair of vertices. Let Tn be a tournament on n vertices. (a) Use induction to prove the following statement: Tn has a directed hamiltonian path (a directed ... or a simple description of the steps in the algorithm, will suffice. What is the worst case time complexity of your algorithm?

asked Feb 15 in Algorithms by sripo Active (2.3k points) | 61 views

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30

JEST Sample Question-5
Describe two different data structures to represent a graph. For each such representation, specify a simple property about the graph that can be more efficiently checked in that representation than in the other representation. Indicate the worst case time required for verifying both of your properties in either representation.

asked Feb 15 in Algorithms by sripo Active (2.3k points) | 33 views

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