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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

#3501
2.9k
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2 answers
3 votes
UGC NET CSE | December 2013 | Part 3 | Question: 36
The recurrence relation $T(n) =mT(\frac{n}{2}) + tan^2$ is satisfied byO(n$^2$)O(n$^{lg \, m}$)O(n$^2 \: lg \:n)$O(n lg n)
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#3502
2.6k
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1 answers
2 votes
UGC NET CSE | December 2013 | Part 3 | Question: 35
Let $A$ and $B$ be two $n$ $\times$n$ matrices. The efficient algorithm to multiply the two matrices has the time complexity$O(n^3)$O(n^{2.81})$O(n^{2.67})$O(n^2)$
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#3503
25.9k
views
2 answers
7 votes
time complexity
find TC : $T(n)= 2T(\sqrt{n}) + 1$
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#3504
518
views
2 answers
1 votes
can someone clear my doubt....
I think Dijkstra algo. works fine with negative weight in connected graphs but not with negative cycle..if we have -ve weight but no cycle then it will give the shortest ... tells there is -ve wt. cycle and never gives wrong result....????
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#3505
691
views
0 answers
1 votes
Ace Practice booklet
T(n)=sqrt(2T(n/2))+logn
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#3506
5.0k
views
1 answers
7 votes
master theorem
T(n)=4T(n/2)+n/lognthis can be solved by master theorem but whyt(n)=2t(n/2)+n/logn can't be solved by master theorem ?
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#3507
388
views
1 answers
2 votes
Cormen third edition 4-3 d
$T(n)=3T(n/3-2)+n/2$Find the tightest bound.
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#3508
530
views
0 answers
1 votes
Solve the recurrence equation
Consider the recurrence T(n)=2T(n/2)+nlogn Find complexity
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#3509
3.3k
views
2 answers
2 votes
UGC NET CSE | December 2013 | Part 2 | Question: 35
Big-O estimate for $f(x)=(x+1) \log(x^2 +1) + 3x^2 $ is given as$O(x \log x)$O(x^2)$O(x^3)$O(x^2 \log x)$
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#3510
469
views
0 answers
1 votes
Test serise qn=2
Here I have doubt which one is stronger ans option(A) or (D)?.According to question op(A) & (D) gives same output.I think op(D) is stronger ans why bez |v| ... ) but |E| not always |V|-1.-Plz give the correct reason by Arjun Suresh sir-
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#3511
8.6k
views
2 answers
4 votes
UGC NET CSE | December 2013 | Part 2 | Question: 25
Given two sorted list of size 'm' and 'n' respectively. The number of comparisons needed in the worst case by the merge sort algorithm will bem $\times$ nmax(m, n)min(m, n)m+n-1
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#3512
4.0k
views
1 answers
1 votes
UGC NET CSE | December 2013 | Part 2 | Question: 24
For any B-tree of minimum degree t $\geq$ 2, every node other than the root must have at least ____ keys and every node can have at most ____ keys.t-1, 2t+1t+1, 2t+1t-1, 2t-1t+1, 2t-1
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#3513
1.9k
views
1 answers
1 votes
DFS
Consider the following graph G modified DFS on G is as folows:starting vertex is 'a'vertex is visited on alphabetic ordervertices are visited in order a,c,d,.....it works same as DFS except the ... on G?(a) {f,b}(b) {e,a}(c){d,a}(d){c,a}
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#3514
18.4k
views
2 answers
3 votes
BFS
Consider two vertices a and b that are simultaneously on the FIFO queue at same point during the execution of breadth first search from s in an undirected graph.Which of the following is true ... 1 and 2 only c. 2 only d. 1, 2 and 3
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#3515
611
views
1 answers
1 votes
quick sort
is it quick sort is inplace algorithm. according to me it takes o(logn) space in best case and as i know any algo takes more then 0(1) spcae count as not inplace algo then why quick sort is inplace plz explain clearly
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#3516
643
views
2 answers
1 votes
Sorting
What is the Worst Case Space Complexity of Quick Sort?
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#3517
1.1k
views
2 answers
1 votes
Binary Search
What is the worst case complexity for searching for a key in a sorted array using Binary Search??
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#3518
7.2k
views
2 answers
1 votes
UGC NET CSE | September 2013 | Part 3 | Question: 42
Given 0-1 knapsack problem and fractional knapsack problem and the following statements:$S_1$: 0-1 knapsack is efficiently solved using Greedy algorithm.$S_2$: Fractional ... $S_2$ are not correct$S_1$ is not correct and $S_2$ is correct
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#3519
1.4k
views
1 answers
0 votes
UGC NET CSE | September 2013 | Part 3 | Question: 39
The number of possible paranthesizations of a sequence of n matrices isO(n)$\theta$(n Ig n)$\Omega(2^n)$None of the above
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#3520
1.2k
views
1 answers
1 votes
UGC NET CSE | September 2013 | Part 3 | Question: 37
The time complexity of reccurence relation T(n) = T(n/3) + T(2n/3) +O(n) isO(Ig n)O(n)O(n Ig n)O(n$^2$)
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