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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.

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}& \textbf{2022} & \textbf{2021-1}&\textbf{2021-2}&\textbf{2020}&\textbf{2019}&\textbf{2018}&\textbf{2017-1}&\textbf{2017-2}&\textbf{2016-1}&\textbf{2016-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count} & 2 &3&2&3&2&0&2&2&3&3&0&2.2&3
\\\hline\textbf{2 Marks Count} & 2 &3&4&4&2&4&2&3&2&3&2&2.9&4
\\\hline\textbf{Total Marks} & 6 &9&10&11&6&8&6&8&7&9&\bf{6}&\bf{8}&\bf{11}\\\hline
\end{array}}}$$

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Recent questions in Algorithms

0 votes
1 answer
2371
complexity
1.(n + a)b = $\Omega$(nb) for all real numbers a , b >0 2.na+1=theta(nb) iff a=b for all real numbers a , b>0 which is true? Acyclic graph directory structure is more flexible than simple tree structure - true or false
1.(n + a)b = $\Omega$(nb) for all real numbers a , b >02.na+1=theta(nb) iff a=b for all real numbers a , b>0which is true?Acyclic graph directory structure is more flexib...
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2 votes
2 answers
2372
time complexity
A) T(n) = 2T(root(n)) + 1 ; n>2 T(n) =1 ; 0 < n <= 2 B) f(n) =n g(n) = n(1+sin n) where n is positive integer which is true? 1.f(n) = O(g(n)) 2.f(n) = $\Omega$(g(n))
A) T(n) = 2T(root(n)) + 1 ; n>2 T(n) =1 ; 0 < n <= 2B) f(n) =ng(n) = n(1+sin n)where n is positive integerwhich is true?1.f(n) = O(g(n))2.f(n) = $\Omega$(g(n))
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1 votes
1 answer
2374
Master Theorem
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3 votes
0 answers
2375
Self Doubt ( Decrease key operation )
While going through dijkstra's algorithm, there is a term "decrease key". I am not getting the meaning when it says "we do decrease key operation". What exactly we do and what is the meaning of decrease key ?
While going through dijkstra's algorithm, there is a term "decrease key". I am not getting the meaning when it says "we do decrease key operation". What exactly we do and...
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1 votes
2 answers
2376
Aymptotic notation
Consider $\sum_{i=0}^n{}$ i3 =x.what can be X 1.theta(n4) 2.theta(n5) 3.O(n5) 4.$\Omega$(n3)
Consider $\sum_{i=0}^n{}$ i3 =x.what can be X1.theta(n4)2.theta(n5)3.O(n5)4.$\Omega$(n3)
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2 votes
1 answer
2377
Asymptotic time order
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0 votes
0 answers
2378
Spanning Tree
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2 votes
0 answers
2379
Algo doubt
Assume f(n) and g(n) are two functions such that f (n)=O(g(n)) which of the following always hold F(n) = O (f(n)2) F(n) = Ω (f(n)2) G(n) = O (f(n)2) G(n) = Ω (g(n))
Assume f(n) and g(n) are two functions such that f (n)=O(g(n))which of the following always holdF(n) = O (f(n)2)F(n) = Ω (f(n)2)G(n) = O (f(n)2)G(n) = Ω (g(n))
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1 votes
2 answers
2381
Alo doubt
Complexity of equation - T(n)=. 2T(n-1)-1 if n>0 1. Otherwise
Complexity of equation -T(n)=. 2T(n-1)-1 if n>0 1. Otherwise
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4 votes
0 answers
2382
Recursion Tree
Is this code running fine ?if yes what is the output I am getting 2 here.
Is this code running fine ?if yes what is the output I am getting 2 here.
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0 votes
0 answers
2384
self doubt
is there any problem which can be solved by top down approach of dynamic programming but can not solve by bottom up approach or vice versa?
is there any problem which can be solved by top down approach of dynamic programming but can not solve by bottom up approach or vice versa?
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0 votes
0 answers
2385
time complexity
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7 votes
0 answers
2387
Dijkstra's
I know that Dijkstra's Doesn't work for Negative weight cycle because it form a loop, Does it also true that it may or may not work for negative weight edge(without cycle) ? If it is not working for a negative weight edge(without cycle) give some example to prove it.
I know that Dijkstra's Doesn't work for Negative weight cycle because it form a loop, Does it also true that it may or may not work for negative weight edge(without cycle...
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3 votes
2 answers
2388
Time complexity
Given a 2D array X[m][n] which has m rows and n columns. The array X is row wise and column wise sorted (i.e) each individula row and column is sorted. What is the complexity to search an element in this array a)O(m*n) b)O(m2) or O(n2) c)O(log2(m*n)) d)O(m+n)
Given a 2D array X[m][n] which has m rows and n columns. The array X is row wise and column wise sorted (i.e) each individula row and column is sorted. What is the comple...
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1 votes
1 answer
2389
Long integer multiplication
Given 2 long integers having n digits , it is required to multiply them.Assuming the numbers are represented in an array of size n . The time complexity to multiply them using traditional divide and conquer is
Given 2 long integers having n digits , it is required to multiply them.Assuming the numbers are represented in an array of size n . The time complexity to multiply them ...
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2 votes
1 answer
2390
priority based scheduling
Given that ready contains at some point of time a maximum of n process , the time complexity to schedule and dispatch a process from ready queue onto CPU using priority based scheduling is a)O(n) b)O(logn) c)O(nlogn) d)O(1)
Given that ready contains at some point of time a maximum of n process , the time complexity to schedule and dispatch a process from ready queue onto CPU using priority ...
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