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Search results for recurrence
24
votes
7
answers
1
GATE CSE 2021 Set 1 | Question: 30
Consider the following recurrence relation. $T\left ( n \right )=\left\{\begin{array} {lcl} T(n ∕ 2)+T(2n∕5)+7n & \text{if} \; n>0\\1 & \text{if}\; n=0 \end{array}\right.$ Which one of the following options is correct? $T(n)=\Theta (n^{5/2})$ $T(n)=\Theta (n\log n)$ $T(n)=\Theta (n)$ $T(n)=\Theta ((\log n)^{5/2})$
Consider the following recurrence relation.$$T\left ( n \right )=\left\{\begin{array} {lcl} T(n ∕ 2)+T(2n∕5)+7n & \text{if} \; n>0\\1 & \text{if}\; n=0 \end{array}\r...
Arjun
23.9k
views
Arjun
asked
Feb 18, 2021
Algorithms
gatecse-2021-set1
algorithms
recurrence-relation
time-complexity
2-marks
+
–
67
votes
10
answers
2
GATE CSE 2016 Set 1 | Question: 27
Consider the recurrence relation $a_1 =8 , a_n =6n^2 +2n+a_{n-1}$. Let $a_{99}=K\times 10^4$. The value of $K$ is __________.
Consider the recurrence relation $a_1 =8 , a_n =6n^2 +2n+a_{n-1}$. Let $a_{99}=K\times 10^4$. The value of $K$ is __________.
Sandeep Singh
29.4k
views
Sandeep Singh
asked
Feb 12, 2016
Combinatory
gatecse-2016-set1
combinatory
recurrence-relation
normal
numerical-answers
+
–
74
votes
9
answers
3
GATE IT 2008 | Question: 44
When $n = 2^{2k}$ for some $k \geqslant 0$, the recurrence relation $T(n) = √(2) T(n/2) + √n$, $T(1) = 1$ evaluates to : $√(n) (\log n + 1)$ $√(n) \log n$ $√(n) \log √(n)$ $n \log √n$
When $n = 2^{2k}$ for some $k \geqslant 0$, the recurrence relation$T(n) = √(2) T(n/2) + √n$, $T(1) = 1$evaluates to :$√(n) (\log n + 1)$$√(n) \log n$$√(n) \log...
Ishrat Jahan
17.4k
views
Ishrat Jahan
asked
Oct 28, 2014
Algorithms
gateit-2008
algorithms
recurrence-relation
normal
+
–
62
votes
12
answers
4
GATE CSE 2015 Set 2 | Question: 11
Consider the following C function. int fun(int n) { int x=1, k; if (n==1) return x; for (k=1; k<n; ++k) x = x + fun(k) * fun (n-k); return x; } The return value of $fun(5)$ is ______.
Consider the following C function.int fun(int n) { int x=1, k; if (n==1) return x; for (k=1; k<n; ++k) x = x + fun(k) * fun (n-k); return x; }The return value of $fun(5)$...
go_editor
21.3k
views
go_editor
asked
Feb 12, 2015
Algorithms
gatecse-2015-set2
algorithms
identify-function
recurrence-relation
normal
numerical-answers
+
–
30
votes
7
answers
5
GATE CSE 1994 | Question: 1.7, ISRO2017-14
The recurrence relation that arises in relation with the complexity of binary search is: $T(n) = 2T\left(\frac{n}{2}\right)+k, \text{ k is a constant }$ $T(n) = T\left(\frac{n}{2}\right)+k, \text{ k is a constant }$ $T(n) = T\left(\frac{n}{2}\right)+\log n$ $T(n) = T\left(\frac{n}{2}\right)+n$
The recurrence relation that arises in relation with the complexity of binary search is:$T(n) = 2T\left(\frac{n}{2}\right)+k, \text{ k is a constant }$$T(n) = T\left(\fra...
Kathleen
18.1k
views
Kathleen
asked
Oct 4, 2014
Algorithms
gate1994
algorithms
recurrence-relation
easy
isro2017
+
–
47
votes
7
answers
6
GATE CSE 2002 | Question: 2.11
The running time of the following algorithm Procedure $A(n)$ If $n \leqslant 2$ return ($1$) else return $(A( \lceil \sqrt{n} \rceil))$; is best described by $O(n)$ $O(\log n)$ $O(\log \log n)$ $O(1)$
The running time of the following algorithmProcedure $A(n)$If $n \leqslant 2$ return ($1$) else return $(A( \lceil \sqrt{n} \rceil))$;is best described by$O(n)$$O(\log ...
Kathleen
17.9k
views
Kathleen
asked
Sep 15, 2014
Algorithms
gatecse-2002
algorithms
recurrence-relation
normal
+
–
58
votes
7
answers
7
GATE CSE 2006 | Question: 51, ISRO2016-34
Consider the following recurrence: $ T(n)=2T\left ( \sqrt{n}\right )+1,$ $T(1)=1$ Which one of the following is true? $ T(n)=\Theta (\log\log n)$ $ T(n)=\Theta (\log n)$ $ T(n)=\Theta (\sqrt{n})$ $ T(n)=\Theta (n)$
Consider the following recurrence:$ T(n)=2T\left ( \sqrt{n}\right )+1,$ $T(1)=1$Which one of the following is true?$ T(n)=\Theta (\log\log n)$$ T(n)=\Theta (\log n)$$ T(n...
Rucha Shelke
28.6k
views
Rucha Shelke
asked
Sep 26, 2014
Algorithms
algorithms
recurrence-relation
isro2016
gatecse-2006
+
–
45
votes
8
answers
8
GATE CSE 1999 | Question: 2.21
If $T_1 = O(1)$, give the correct matching for the following pairs: $\begin{array}{l|l}\hline \text{(M) $T_n = T_{n-1} + n$} & \text{(U) $T_n = O(n)$} \\\hline \text{(N) $T_n = T_{n/2} + n$} & \text{(V) $T_n = O(n \log n)$ ... $\text{M-W, N-U, O-X, P-V}$ $\text{M-V, N-W, O-X, P-U}$ $\text{M-W, N-U, O-V, P-X}$
If $T_1 = O(1)$, give the correct matching for the following pairs:$$\begin{array}{l|l}\hline \text{(M) $T_n = T_{n-1} + n$} & \text{(U) $T_n = O(n)$} \\\hline \text{(...
Kathleen
15.1k
views
Kathleen
asked
Sep 23, 2014
Algorithms
gate1999
algorithms
recurrence-relation
asymptotic-notation
normal
match-the-following
+
–
7
votes
4
answers
9
GATE CSE 2023 | Question: 5
The Lucas sequence $L_{n}$ is defined by the recurrence relation: \[ L_{n}=L_{n-1}+L_{n-2}, \quad \text { for } \quad n \geq 3, \] with $L_{1}=1$ and $L_{2}=3$ ... $L_{n}=\left(\frac{1+\sqrt{5}}{2}\right)^{n}-\left(\frac{1-\sqrt{5}}{2}\right)^{n}$
The Lucas sequence $L_{n}$ is defined by the recurrence relation:\[L_{n}=L_{n-1}+L_{n-2}, \quad \text { for } \quad n \geq 3,\]with $L_{1}=1$ and $L_{2}=3$.Which one of t...
admin
8.0k
views
admin
asked
Feb 15, 2023
Combinatory
gatecse-2023
combinatory
recurrence-relation
1-mark
+
–
34
votes
4
answers
10
GATE CSE 2020 | Question: 2
For parameters $a$ and $b$, both of which are $\omega(1)$, $T(n) = T(n^{1/a})+1$, and $T(b)=1$. Then $T(n)$ is $\Theta (\log_a \log _b n)$ $\Theta (\log_{ab} n$) $\Theta (\log_{b} \log_{a} \: n$) $\Theta (\log_{2} \log_{2} n$)
For parameters $a$ and $b$, both of which are $\omega(1)$, $T(n) = T(n^{1/a})+1$, and $T(b)=1$. Then $T(n)$ is$\Theta (\log_a \log _b n)$ $\Theta (\log_{ab} n$)$\Thet...
Arjun
19.6k
views
Arjun
asked
Feb 12, 2020
Algorithms
gatecse-2020
algorithms
recurrence-relation
1-mark
+
–
14
votes
5
answers
11
How to find the complexity of T(n)=T(sqrt(n)) + 1 ?
Please tell me the complete steps how to solve this problem. $ T(n) = T ( \sqrt n )+ 1$
Please tell me the complete steps how to solve this problem.$ T(n) = T ( \sqrt n )+ 1$
Jonathan Decosta
47.3k
views
Jonathan Decosta
asked
Jun 10, 2015
Algorithms
algorithms
recurrence-relation
+
–
3
votes
4
answers
12
GATE CSE 2024 | Set 2 | Question: 5
Let $\text{T(n)}$ be the recurrence relation defined as follows: \[ \begin{array}{l} T(0)=1, \\ T(1)=2, \text { and } \\ T(n)=5 T(n-1)-6 T(n-2) \text { for } n \geq 2 \end{array} \] Which one of the following statements is TRUE? $T(n)=\Theta\left(2^{n}\right)$ $T(n)=\Theta\left(n 2^{n}\right)$ $T(n)=\Theta\left(3^{n}\right)$ $T(n)=\Theta\left(n 3^{n}\right)$
Let $\text{T(n)}$ be the recurrence relation defined as follows:\[\begin{array}{l}T(0)=1, \\T(1)=2, \text { and } \\T(n)=5 T(n-1)-6 T(n-2) \text { for } n ...
Arjun
2.4k
views
Arjun
asked
Feb 16
Algorithms
gatecse2024-set2
algorithms
recurrence-relation
asymptotic-notation
+
–
15
votes
6
answers
13
GATE CSE 2022 | Question: 41
Consider the following recurrence: $\begin{array}{} f(1) & = & 1; \\ f(2n) & = & 2f(n) - 1, & \; \text{for}\; n \geq 1; \\ f(2n+1) & = & 2f(n) + 1, & \; \text{for}\; n \geq 1. \end{array}$ Then, which of the following statements is/are $\text{TRUE}?$ ... $f(2^{n}) = 1$ $f(5 \cdot 2^{n}) = 2^{n+1} + 1$ $f(2^{n} + 1) = 2^{n} + 1$
Consider the following recurrence:$$\begin{array}{} f(1) & = & 1; \\ f(2n) & = & 2f(n) – 1, & \; \text{for}\; n \geq 1; \\ f(2n+1) & = & 2f(n) + 1, & \; \text...
Arjun
7.8k
views
Arjun
asked
Feb 15, 2022
Combinatory
gatecse-2022
combinatory
recurrence-relation
multiple-selects
2-marks
+
–
60
votes
5
answers
14
GATE CSE 2015 Set 3 | Question: 39
Consider the following recursive C function. void get(int n) { if (n<1) return; get (n-1); get (n-3); printf("%d", n); } If $get(6)$ function is being called in $main()$ then how many times will the $get()$ function be invoked before returning to the $main()$? $15$ $25$ $35$ $45$
Consider the following recursive C function.void get(int n) { if (n<1) return; get (n-1); get (n-3); printf("%d", n); }If $get(6)$ function is being called in $main()$ th...
go_editor
18.2k
views
go_editor
asked
Feb 15, 2015
Algorithms
gatecse-2015-set3
algorithms
recurrence-relation
normal
+
–
6
votes
2
answers
15
GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 56
The coefficient of $x^6$ in the expansion of $A(x)$ is, where $ A(x)=\frac{x(1+x)}{(1-x)^3} $
The coefficient of $x^6$ in the expansion of $A(x)$ is, where$$A(x)=\frac{x(1+x)}{(1-x)^3}$$
GO Classes
571
views
GO Classes
asked
Feb 5
Combinatory
goclasses2024-mockgate-14
numerical-answers
combinatory
recurrence-relation
2-marks
+
–
1
votes
1
answer
16
Recurrence relation
What is the returned value by the given function below. Algo fun(n) { If(x<=2) return 1; Else { Return fun(n1/2) + n; } } Note : Assume that all the syntax and data type constraints are valid and just check algorithm.
What is the returned value by the given function below.Algo fun(n){ If(x<=2) return 1; Else { Return fun(n1/2) + n; }}Note : Assume that all...
jenilS7
138
views
jenilS7
asked
Mar 18
Algorithms
recurrence-relation
algorithms
sequence-series
+
–
7
votes
2
answers
17
GO Classes Test Series 2024 | Mock GATE | Test 11 | Question: 44
Acceptable input for a certain pocket calculator is a finite sequence of characters each of which is either a digit or a sign. The first character must be a digit, the last character must be a digit, and any character that is a sign must be followed by a digit. There ... by $N_k=a N _{k-1}+b N _{k-2}$, for $k \geq 3$. What is $a+ b?$
Acceptable input for a certain pocket calculator is a finite sequence of characters each of which is either a digit or a sign. The first character must be a digit, the la...
GO Classes
560
views
GO Classes
asked
Jan 13
Combinatory
goclasses2024-mockgate-11
goclasses
numerical-answers
combinatory
recurrence-relation
2-marks
+
–
3
votes
3
answers
18
GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 54
Of the following, which gives the best upper bound for the value of $f(N)$ where $f$ is a solution to the recurrence $ f(2 N+1)=f(2 N)=f(N)+\log N \text { for } N \geq 1, $ with $f(1)=0?$ $O(\log N)$ $O(N \log N)$ $O\left((\log N)^2\right)$ $O(N)$
Of the following, which gives the best upper bound for the value of $f(N)$ where $f$ is a solution to the recurrence$$f(2 N+1)=f(2 N)=f(N)+\log N \text { for } N \geq 1,$...
GO Classes
901
views
GO Classes
asked
Jan 21
Algorithms
goclasses2024-mockgate-12
goclasses
algorithms
recurrence-relation
time-complexity
2-marks
+
–
1
votes
0
answers
19
Memory Based GATE DA 2024 | Question: 19
Consider the function \(f(n)\), which represents the maximum number of comparisons in binary search on a sorted array of size \(n\). Which of the following recursive relationships correctly defines \(f(n)\)? \(f(n) = f\left(\lfloor \frac{n}{2} \rfloor\right) ... \rfloor\right)\) \(f(n) = f\left(\lfloor \frac{n}{2} \rfloor\right) + 1\) None of the above
Consider the function \(f(n)\), which represents the maximum number of comparisons in binary search on a sorted array of size \(n\). Which of the following recursive rela...
GO Classes
178
views
GO Classes
asked
Feb 4
Algorithms
gate2024-da-memory-based
goclasses
algorithms
binary-search
recurrence-relation
+
–
52
votes
7
answers
20
GATE CSE 2003 | Question: 35
Consider the following recurrence relation $T(1)=1$ $T(n+1) = T(n)+\lfloor \sqrt{n+1} \rfloor$ for all $n \geq 1$ The value of $T(m^2)$ for $m \geq 1$ is $\frac{m}{6}\left(21m-39\right)+4$ $\frac{m}{6}\left(4m^2-3m+5\right)$ $\frac{m}{2}\left(3m^{2.5}-11m+20\right)-5$ $\frac{m}{6}\left(5m^3-34m^2+137m-104\right)+\frac{5}{6}$
Consider the following recurrence relation$T(1)=1$$T(n+1) = T(n)+\lfloor \sqrt{n+1} \rfloor$ for all $n \geq 1$The value of $T(m^2)$ for $m \geq 1$ is$\frac{m}{6}\left(21...
Kathleen
13.8k
views
Kathleen
asked
Sep 16, 2014
Algorithms
gatecse-2003
algorithms
time-complexity
recurrence-relation
difficult
+
–
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