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Searching, Sorting, Hashing, Asymptotic worst case time and Space complexity, Algorithm design techniques: Greedy, Dynamic programming, and Divide‐and‐conquer, Graph search, Minimum spanning trees, Shortest paths.

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}&\textbf{2024-1} & \textbf{2024-2} & \textbf{2023} & \textbf{2022} & \textbf{2021-1}&\textbf{2021-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count} & 1&2&2& 2 &3&2&1&2&3
\\\hline\textbf{2 Marks Count} &4&2&2& 2 &3&4&2&2.83&4
\\\hline\textbf{Total Marks} &9&6&6& 6 &9&10&\bf{6} & \bf{7.67}&\bf{10}\\\hline
\end{array}}}$$

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Recent questions in Algorithms

#3481
506
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1 answers
0 votes
Is logloglogx same as log^3(x) same as (logx)^3?
It is given in CLRS book chapter 3, page no. 56 that lg^k(n) = (lg n)^k. Can somebody please give me an example or check if my example is correct? Shoudn't lg^k(n) be { lg lg lg..... k times (n) }?
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#3482
4.4k
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4 answers
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UGC NET CSE | Junet 2015 | Part 2 | Question: 48
Which of the following algorithms sort $n$ integers, having the range $0$ to $(n^2 -1)$, in ascending order in $O(n)$ time?Selection sortBubble sortRadix sortInsertion sort
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#3483
6.2k
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1 answers
2 votes
UGC NET CSE | Junet 2015 | Part 2 | Question: 25
To determine the efficiency of an algorithm the time factor is measured byCounting micro secondsCounting number of key operationsCounting number of statementsCounting kilobytes of algorithm
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#3484
1.5k
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1 answers
3 votes
UGC NET CSE | Junet 2015 | Part 2 | Question: 24
The average case occurs in Linear Search Algorithm whenThe item to be searched is in some where middle of the ArrayThe item to be searched is not in the arrayThe ... arrayThe item to be searched is either in the last or not in the array
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#3485
693
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2 answers
2 votes
merge sort
is there any swap operation done in merge sort?
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#3486
1.0k
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1 answers
1 votes
heap sort
The number of elements that can be sorted in time using heap sort ?
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#3487
2.5k
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1 answers
3 votes
UGC NET CSE | Junet 2015 | Part 2 | Question: 4
Consider the following statements:Depth-first search is used to traverse a rooted treePre-order, Post-order and Inorder are used to list the vertices of an ordered rooted tree.Huffman's ... $\text{i, ii, iii, and iv}$
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#3488
581
views
1 answers
1 votes
Open addressing hashing
What are the advantages of open addressing hashing scheme?In this, we need the size of the table greater than number of keys. In that case, why we ... technique for large datasets, then why we bear the overhead in computing hash functions?
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#3489
729
views
2 answers
2 votes
Time complexity
What is the answer to the following equation?$T(n) = T(\sqrt n)+ \log \log n$
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#3490
1.3k
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4 answers
8 votes
Recursion Tree
How to solve this equation by the recursion tree method?$T(n)=5T(\frac{n}{5})+\sqrt{n}$
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#3491
2.5k
views
4 answers
1 votes
UGC NET CSE | December 2014 | Part 3 | Question: 35
Consider the problem of a chain $\langle A_{1}, A_{2}, A_{3}\rangle$ ... $10$20$100$
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#3492
3.4k
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1 answers
1 votes
UGC NET CSE | December 2014 | Part 3 | Question: 34
Dijkstra algorithm, which solves the single-source shortest--paths problem, is a _______, and the Floyd-Warshall algorithm, ... Greedy algorithmGreedy algorithm, Dynamic programming algorithmDynamic programming algorithm, Greedy algorithm
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#3493
3.7k
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1 answers
1 votes
UGC NET CSE | December 2014 | Part 3 | Question: 33
We can show that the clique problem is $NP$-hard by proving thatCLIQUE $\leq$ P 3-CNF_SATCLIQUE $\leq$ P VERTEX_COVERCLIQUE $\leq$ P SUBSET_SUMNone of the above
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#3494
2.2k
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1 answers
1 votes
UGC NET CSE | December 2014 | Part 3 | Question: 32
Match the following $:$\begin{array}{} & \textbf{List - I} & & \textbf{List - II} \\ \text{a.} & \text{Bucket sort} & \text{i.} & O(n^3\lg n) \\ \text{b.} & \text{ ... $\text{a-iii, b-ii, c-iv, d-i}$
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#3495
2.0k
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2 answers
3 votes
UGC NET CSE | December 2014 | Part 3 | Question: 31
Any decision tree that sorts $n$ elements has height$\Omega(n)$\Omega(\text{lg}n)$\Omega(n \text{lg} n)$\Omega(n^2)$
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#3496
323
views
0 answers
1 votes
heapsort
I have read that for heapify, t(n) = t(2n/3) +o(1) and i know the no. of nodes in the subtree will be 2n/3(worst case) but the algo actually be applied to ... it should be t(log n) instead of t(2n/3)?if anybody know then plz clear my doubt
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#3497
1.2k
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2 answers
1 votes
asymptotic notation
iff(n) ≠ O(g(n)) then, g(n) ≠ O(f(n)) state true or false with explanation.
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#3498
3.5k
views
3 answers
2 votes
Asymptotic Notation
Given that, f(n) = O(g(n)) then it implies that h(f(n)) = O(h(g(n)). State TRUE/FALSE with proper Explanation/Examples.Please provide mathematical proof,don't just prove by giving a counter example
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#3499
2.1k
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2 answers
2 votes
UGC NET CSE | December 2013 | Part 3 | Question: 38
Assuming there are n keys and each key is in the range [0, m-1]. The run time of bucket sort isO(n)O(n lgn)O(n lgm)O(n+m)
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#3500
5.8k
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2 answers
3 votes
UGC NET CSE | December 2013 | Part 3 | Question: 37
The longest common subsequence of the sequences $X=<A, B, C, B, D, A, B>$ and $Y=<B, D, C, A, B, A>$ has length$2$3$4$5$
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