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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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Recent questions in Algorithms

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41
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Recurrence
Q.${Solve}$ ${Recurrence}$.$T(n) = T\left(\frac{n}{15}\right) + T\left(\frac{n}{10}\right) + 2T\left(\frac{n}{6}\right) + \sqrt{n}$ 
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1 1 vote
1 1 answer
169
169 views
GATE@Zeal Basic DSA Searching and Sorting (Q24)
You have given an array A[] = {12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1}. An inversion in an array A is a pair of array indices (i, j) such that i < j and A[i] A[j]. Assume...
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3 3 votes
1 1 answer
302
302 views
GO Classes DPP | GATE CS, DA | Algorithms | Directed Graph
Let $G$ be a directed graph with nonnegative edge weights, and let $s$ and $t$ be vertices of $G$.Consider the statement:Any shortest path from $s$ to $t$ in $G$ is also ...
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3 3 votes
1 1 answer
205
205 views
GO Classes DPP | GATE CS, DA | Algorithms | Quick Sort
During sorting, one complete processing of all elements whose final positions have not yet been determined is called a pass.Which of the following sequences cannot be the...
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3 3 votes
1 1 answer
147
147 views
GO Classes DPP | GATE CS, DA | Algorithms | Hashing
An initially empty hash table $\text{HT}$ has length $11$.The hash function is:$H(key)=key \bmod 7$Collisions are resolved using linear probing.The following keys are ins...
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3 3 votes
1 1 answer
180
180 views
GO Classes DPP | GATE CS, DA | Algorithms | Time Complexity
The algorithm $\text{ALGSORT}$ sorts an array of distinct integers using comparisons.The function $\text{MININDEX(V,i,j)}$ returns the position of the smallest element in...
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1 1 vote
1 1 answer
153
153 views
GO Classes DPP | GATE CS, DA | Algorithms | MST vs Shortest Path Tree
Consider the following statement:For every connected weighted graph $G$, there exists some vertex $v$ such that a shortest path tree rooted at $v$ is identical to a minim...
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2 2 votes
1 1 answer
147
147 views
GO Classes DPP | GATE CS, DA | Algorithms | Bellman Ford
Consider a simple version of Bellman-Ford algorithm where we initialize $\text{distTo}[s]$ to $0$ and the rest of $\text{distTo}[v]$ to $+\infty$. Then fix an order on al...
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1 1 vote
1 1 answer
138
138 views
GO Classes DPP | GATE CS, DA | Algorithms | Dijkstra's Algorithm
Consider Dijkstra's algorithm on a graph having $V$ vertices and $E$ edges.Suppose an indexed priority queue is not used.Instead, the tentative distances are stored only ...
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1 1 vote
1 1 answer
96
96 views
GO Classes DPP | GATE CS, DA | Algorithms | Edge Relaxation
Consider a directed edge $e = v \to w$ with weight $7$. Suppose that during a shortest path algorithm:$\operatorname{distTo}[v] = 16$ and $\operatorname{distTo}[w] = 25$...
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1 1 vote
1 1 answer
128
128 views
GO Classes DPP | GATE CS, DA | Algorithms | Time Complexity
Suppose Huffman coding is implemented as follows.Initially, the $n$ symbols are stored in a min priority queue according to their frequencies.The algorithm repeatedly per...
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1 1 vote
1 1 answer
136
136 views
GO Classes DPP | GATE CS, DA | Algorithms | MST
Let, $G=(V,E)$ be a connected undirected graph. Edge weights may be negative.We want to choose, $E'\subseteq E$ such that $G'=(V,E')$ is connected and: $\sum_{e\in E'}w(e...
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1 1 answer
134
134 views
GO Classes DPP | GATE CS, DA | Algorithms | Dijkstra's Algorithm
Let $G=(V,E)$ be a directed graph with positive edge weights.Given vertices $s,w,t$ we want the length of the shortest path from $s$ to $t$ that must pass through $w$.Con...
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2 2 votes
1 1 answer
112
112 views
GO Classes DPP | GATE CS, DA | Algorithms | Floyd-Warshall
What is the primary reason to use Floyd's algorithm for the all-pairs shortest-path problem instead of Dijkstra's algorithm?Faster for dense graphs. Faster for sparse gra...
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1 1 vote
1 1 answer
175
175 views
GO Classes DPP | GATE CS, DA | Algorithms | Binary Search
Which of the following cannot be a sequence of keys compared during a binary search for some target key?$500,200,450,180$ $500,450,200,180$ $180,500,200,450$ $180,200,500...
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1 1 vote
1 1 answer
105
105 views
GO Classes DPP | GATE CS, DA | Algorithms | Time Complexity
Consider,f1(N): x = 0 for i = 0 to N - 1: x++ return xand,f2(N, R): x = 0 for i = 0 to N - 1: for j = 1; j <= R; j = j + j: x = x + f1(j) return xWhat is the order of gro...
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1 1 vote
1 1 answer
155
155 views
GO Classes DPP | GATE CS, DA | Algorithms | Dijkstra's Algorithm
Let $G$ be a directed graph with nonnegative edge weights.Run Dijkstra's algorithm from source $s$. After the algorithm terminates, use the $\text{prev}$ pointers to cons...
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0 0 votes
1 1 answer
116
116 views
GO Classes DPP | GATE CS, DA | Algorithms | Minimum Spanning Tree
Consider the following statements.Let $M$ be an MST of a connected undirected graph with positive edge weights. If $7$ is added to every edge weight, $M$ is guaranteed to...
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1 1 vote
1 1 answer
112
112 views
GO Classes DPP | GATE CS, DA | Algorithms | Bellman-Ford
Consider the following directed weighted graph with source vertex $0$:Bellman-Ford performs one complete pass, relaxing edges in this exact order:$$0\rightarrow1,\quad 0\...
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2 2 votes
1 1 answer
156
156 views
GO Classes DPP | GATE CS, DA | Algorithms | Analysis of Algorithms
The following running times are observed for a program:$$\begin{array}{|c|c|}\hlineN & \text{Running time} \\\hline1000 & 0.1\text{ seconds} \\2000 & 0.3\text{ seconds} \...
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