Recent questions tagged time-complexity

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IIIT BLR TEST 1 : ALGORITHMS 3
Given an array of ( both positive and negative ) integers, $a_0,a_1,….a_{n-1}$ and $l, 1<l<n$. Design a linear time algorithm to compute the maximum product subarray, whose length is atmost $l$.

asked Aug 27 in Algorithms by Shaik Masthan Veteran (62.4k points) | 116 views

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IIIT BLR TEST 1 : ALGORITHMS 1
Solve the following recursions ( in terms of Θ ). T(0) = T(1) = Θ(1) in all of the following. $T(n) = n + \frac{1}{n}\sum_{i=0}^{i=n-1}T(i)$ $T(n) = n + \frac{2}{n}\sum_{i=0}^{i=n-1}T(i)$ $T(n) = n + \frac{4}{n}\sum_{i=0}^{i=n/2}T(i)$ $T(n) = n + \frac{40}{n}\sum_{i=0}^{i=n/5}T(i)$

asked Aug 27 in Algorithms by Shaik Masthan Veteran (62.4k points) | 59 views

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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 (41.4k points) | 47 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 (41.4k points) | 22 views

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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 (41.4k points) | 13 views

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1 answer

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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 (41.4k points) | 35 views

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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 (41.4k points) | 35 views

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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 (41.4k points) | 27 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 (41.4k points) | 15 views

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2 answers

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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 (41.4k points) | 37 views

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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 (375 points) | 44 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 (233 points) | 83 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 (127 points) | 109 views

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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) | 122 views

+1 vote

3 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) | 206 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 (114k points) | 111 views

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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 (114k points) | 86 views

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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 (114k points) | 115 views

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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 (999 points) | 142 views

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20

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 (114k points) | 264 views

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1 answer

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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) | 140 views

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22

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) | 125 views

+2 votes

1 answer

23

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) | 154 views

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1 answer

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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) | 106 views

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25

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

asked Apr 19 in Algorithms by Mk Utkarsh Boss (34.9k points) | 110 views

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26

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) | 167 views

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1 answer

27

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) | 100 views

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2 answers

28

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 (155 points) | 71 views

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29

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 (811 points) | 135 views

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1 answer

30

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) | 116 views

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