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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.

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|}\hline \textbf{Year}& \textbf{2026 - 1}& \textbf{2026 - 2}& \textbf{2025 - 1}& \textbf{2025 - 2}& \textbf{2024 - 1}& \textbf{2024 - 2}& \textbf{2023}& \textbf{2022}& \textbf{2021 - 1}& \textbf{2021 - 2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}\\\hline \textbf{1 Mark Count}&4&4&2&2&1&2&2&2&3&2&1&2.4&4\\\hline \textbf{2 Marks Count}&6&4&3&3&4&2&2&2&3&4&2&3.3&6\\\hline \textbf{Total Marks}&16&12&8&8&9&6&6&6&9&10&\bf{6}&\bf{9}&\bf{16}\\\hline \end{array}}}$$

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a) what is the iterative equation showing the running time of the algorithm whose pseudocode is given below? b) What is this repeated equation in asymptotic notation using the Master's theorem. c) What is the same repeated equation in asymptotic notation using the recursion tree method.
a) what is the iterative equation showing the running time of the algorithm whose pseudocode is given below? b) What is this repeated equation in asymptotic notation usin...
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what is the running time of the following iterative algorithm?
1 question:a) Calculate the running time of the following iterative algorithm. For this purpose, write the working time of each row in the corresponding column of the tab...
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958
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asymptotic notation
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NIELIT 2022 April Scientist B | Section B | Question: 44
What is the time complexity of the following function?void myfun() { int a,b; for(a=1; a<=n; a++) for(b=1; b<=log(a); b++) printf(“My Function”); }$\theta (n)$$\theta (n^...
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NIELIT 2022 April Scientist B | Section B | Question: 51
Consider the directed graph shown in the figure below. There are multiple shortest paths between vertices $\text{S}$ and $\text{T}$. Which one will be reported by Dijkstr...
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696
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NIELIT 2022 April Scientist B | Section B | Question: 81
The number of distinct minimum spanning trees for the weighted graph below is ________.$4$$5$$6$$7$
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735
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NIELIT 2022 April Scientist B | Section B | Question: 86
A Young tableau is a $\text{2D}$ array of integers increasing from left to right and from top to bottom. Any unfilled entries are marked with $\infty$, and hence there ca...
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NIELIT 2022 April Scientist B | Section B | Question: 96
Suppose we are sorting an array of eight integers using heapsort, and we have just finished some heapify (either maxheapify or minheapify) operations. The array now looks...
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NIELIT 2022 April Scientist B | Section B | Question: 105
What is the time complexity of the following recursive function?int ComputFun(int n) { if(n<=2) return 1; else return (DoSomething(floor(sqrt(n)))+n); }$\Theta(n)$$\Theta...
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574
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Test Series
What is the time complexity of the below mentioned recursive function.int f(n){ if(n!=1){ return f(n/2)+f(n/2);}elsereturn 10;} O(n)O(n^2)O(log n)O(n logn)
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#Quicksort
In Quicksort of the following numbers, if the pivot is chosen as the first element, what will be the order of the numbers after the use of partition function? Assume we a...
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Time complexity using back substitution
T(n) = T(n-1) + n^4
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What is the recurrence for T(n)=2T(n/4)+sqrt(n) using the Master Theorem
How do I apply the master theorem in the above recurrence? Please give details about which case and on hiow to solve the asymptotic analysis...
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1 1 vote
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484
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CRT-2022
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Algorithm self doubt
As we know the time complexity of solving the greedy knapsack algorithm depends mainly on the sorting algorithm used, Can we use counting sort as the sorting algorithm to...
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114 114 votes
4 answers 4 answers
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GATE CSE 2022 | Question: 1
Which one of the following statements is $\text{TRUE}$ for all positive functions $f(n)?$$f(n^{2}) = \theta (f(n)^{2}),$ when $f(n)$ is a polynomial$f(n^{2}) = o (f(n)^{2...
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53 53 votes
7 answers 7 answers
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GATE CSE 2022 | Question: 6
​​​Suppose we are given $n$ keys, $m$ hash table slots, and two simple uniform hash functions $h_{1}$ and $h_{2}.$ Further suppose our hashing scheme uses $h_{1}$ for the...
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54 54 votes
4 answers 4 answers
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GATE CSE 2022 | Question: 39
Consider a simple undirected weighted graph $\textit{G},$ all of whose edge weights are distinct. Which of the following statements about the minimum spanning trees of $\...
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86 86 votes
13 answers 13 answers
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GATE CSE 2022 | Question: 48
Let $\textit{G(V,E)}$ be a directed graph, where $\textit{V} = \{ 1, 2, 3, 4, 5 \}$ is the set of vertices and $\textit{E}$ is the set of directed edges, as defined by th...
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