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Questions by Debashish Deka
User Debashish Deka
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User Debashish Deka
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+3
votes
1
answer
1
Series Summation
Series summation of $S_n$ in closed form? $\begin{align*} &S_n = \frac{1}{1.2.3.4} + \frac{1}{2.3.4.5} + \frac{1}{3.4.5.6} + \dots + \frac{1}{n.(n+1).(n+2).(n+3)} \end{align*}$
asked
Jun 11
in
Set Theory & Algebra

40
views
numbertheory
summation
discretemathematics
0
votes
0
answers
2
Recursive fork()
The pid_t data type is a signed integer type which is capable of representing a process ID. getpid() returns the process ID of the current process The wait() system call suspends execution of the calling process until one of its children ... : some of the system call and macro definitions are simplified for the sake of the QS as well as for simplicity.
asked
Jun 2
in
Operating System

105
views
fork
operatingsystem
+1
vote
1
answer
3
Finding best time complexity
$\begin{align*} & a[n] = \{x_1,x_2,x_3,x_4,....,x_n\} \text{ is an array of integers where } n,x_i > 0. \\ & A = \left [ \text{min}\left ( x_i,x_j \right ) \right ] \cdot \left ( ji \right ) \text{ where } j ... } i,j \leq n \\ & \text{What is the best time complexity to find out the value of } A_{\bf max} \; ? \end{align*}$
asked
May 27
in
Algorithm Challenges

114
views
algorithms
timecomplexity
0
votes
1
answer
4
$a_n = 4^n + 6^n$
If $a_n = 4^n + 6^n$ Find the value of $a_{40} \text { mod } 25$
asked
May 19
in
Set Theory & Algebra

45
views
binomialdistribution
+1
vote
1
answer
5
2  connected graph
For a regular graph how much large the value of degree (for each vertices) should be such that the graph is $2$  connected. (vertex wise). I did in this way : $\begin{align*} &\quad \kappa(G) \leq \frac{2\cdot e}{n} \ ... regular and not 2 connected although $d \geq 2$ is satisfied. Why this $d \geq 2$ is trivial and not working in some cases ?
asked
May 19
in
Graph Theory

106
views
graphtheory
graphconnectivity
0
votes
1
answer
6
Placing rooks in nXn chess board
asked
May 4
in
Algorithms

83
views
nongate
recursion
game
combinatory
+2
votes
1
answer
7
C programming  Output ?
Assume sizeof int as 4 #include <stdio.h> unsigned int L = (sizeof(unsigned int)) << 3; int foo(unsigned int m,unsigned int start,unsigned int length) { length = length >> 1; if(!length) { return m&(1<<start)?1:0; } ... length,length); return n1+n2; } } int main() { int m = 100; printf("%d\n",foo(m,0,L)); }
asked
Apr 29
in
Programming

206
views
programminginc
output
0
votes
1
answer
8
C programming
int main() { int n = 3,i,count=0; for(i=0;i<1<<n;i++) { int p = i; while(p) { int k = p & p; p = p  k; count++; } } } The value of count variable after execution of the above code? The value of count variable when $n = m$ ? [EDITED]
asked
Apr 20
in
Programming

78
views
programminginc
bitwise
+2
votes
4
answers
9
C programming  Output ?
#include <stdio.h> int main() { unsigned char a = 5; a = (1<<((sizeof(char)<<3)1)); char b = a; printf("%d %d\n",b,a); printf("%u %u\n",b,a); } If the size of a char datatype is 1 Byte, then what will be the output? [Edited]
asked
Apr 10
in
Programming

191
views
programminginc
0
votes
2
answers
10
No of spanning Trees
Let $K_n$ denote the complete undirected graph with $n$ vertices where n is an even number. Find the maximum number of spanning trees of $K_n$ that can be formed in such a way that no two of these spanning trees have a common edge.
asked
Mar 19
in
Graph Theory

154
views
spanningtree
graphtheory
0
votes
0
answers
11
Recurrence relation and generating function
asked
Mar 19
in
Combinatory

78
views
generatingfunctions
combinatory
recurrenceeqation
+1
vote
2
answers
12
c programming
#include <stdio.h> int K = 4; int a[2]; unsigned int m; int* check(unsigned int n) { int res = 1; int count = 0; for(int i=0;i<K;i++) if(!(n&(1<<i))) { count++; res = 0; } a[0] = res; a[1] = count; return a; } int foo( ... = x[1]; foo(mi,i+1); return count; } int main() { int x = foo(0,0); printf("%d\n",x); } value of x ___ ?
asked
Mar 19
in
Programming

117
views
programminginc
+1
vote
0
answers
13
Kenneth Rosen 6.444 advanced counting
asked
Mar 15
in
Combinatory

54
views
discretemathematics
generatingfunctions
recurrence
0
votes
1
answer
14
Generating function
Let $h_n$ denote the number of nonnegative integral solutions of the equation $3x_1 + 4x_2 + 2x_3 + 5x_4 = n$ Find the generating function $g(x)$ for $h_0,h_1,h_2,h_3 ... h_n$
asked
Mar 15
in
Combinatory

63
views
generatingfunctions
combinatory
+1
vote
1
answer
15
False sharing in cache Line
Here is pseudo code for a multiprocessing purpose: set_num_threads(NUM_THREADS); double sum=0.0; sum_local[NUM_THREADS]; parallel region { int this_thread_id = get_thread_number(); // returns 0 to (no_of_threads1) sum_local[this_thread_id] ... DRAM write back causing the problem, but not very clear, though. please explain a bit. @Arjun Sir
asked
Mar 6
in
CO & Architecture

79
views
co&architecture
cachememory
nongate
descriptive
0
votes
2
answers
16
Discrete math
The following is a sequence of formula, $$\begin{align*} \begin{matrix} & 9*1+2 &= &11 \\ & 9*12+3 &= &111 \\ & 9*123+4 &= &1111 \\ & 9*1234+5 &= &11111 \\ \end{matrix} \\ ... align*}$$ Here numbers are in base $10$. (a) Establish a formula in $\sum$ notation. (b) Generalize that formula in for any base $b$..
asked
Feb 26
in
Set Theory & Algebra

65
views
discretemathematics
descriptive
nongate
+2
votes
2
answers
17
Manipulation of sum
Prove the identity: $$\begin{align*} &\sum_{i=0}^{n}\sum_{j=0}^{i} a_ia_j = \frac{1}{2}\left ( \left ( \sum_{i=0}^{n}a_i \right )^2 + \left ( \sum_{i=0}^{n}a_i^2 \right )\right ) \end{align*}$$
asked
Feb 25
in
Combinatory

131
views
discretemathematics
summation
0
votes
2
answers
18
Discrete Math
Prove or disprove: $\begin{align*} \log_8x = \frac{1}{2}.\log_{2}x \end{align*}$.
asked
Feb 25
in
Set Theory & Algebra

79
views
discretemathematics
descriptive
nongate
0
votes
0
answers
19
Discrete math
Let $w \in \sum$$*$ be a string, with $\sum$ being the alphabet. Let $w^R$ be the reversal of string $w$, using induction prove that $(w^R)(w^R). . .(\text{for k times}) = (ww . . .(\text{for k times}))^R.$
asked
Feb 22
in
Set Theory & Algebra

48
views
descriptive
iitg_math
discretemathematics
0
votes
2
answers
20
Discrete Math
Prove or disprove the following: for finite sets A and B, $\overline{(A  B) \cup (B  A)} = A \cap B$ . If the proposition is incorrect, do minimal modifications to the same and prove.
asked
Feb 22
in
Set Theory & Algebra

78
views
discretemathematics
iitg_math
nongate
descriptive
0
votes
1
answer
21
Discrete math
Prove the following: $3 \;  \;\left ( a^2+b^2 \right )$ if and only if $3 \;  \;a$ and $3 \;  \;b$.
asked
Feb 22
in
Set Theory & Algebra

88
views
discretemathematics
iitg_math
descriptive
nongate
+1
vote
2
answers
22
Stable sorting algorithms
Show that any comparison based sorting algorithm can be made stable without increasing its complexity beyond a constant factor.
asked
Feb 21
in
Algorithms

110
views
algorithms
descriptive
timecomplexity
nongate
+2
votes
1
answer
23
C programming
int a[20]; unsigned int m; // global variable int foo(int a[]) { int i=0,count = 0; while(i < 20) m = 1<<(a[i++]1); i = (sizeof(int)<<3)1; while(i>=0) if(m&(1<<(i))) count++; return ... in a[] which are more than $20$ B No of distinct elements in a[] which less than $20$ C No of distinct elements in a[] D None of these
asked
Feb 18
in
Programming

140
views
programminginc
output
+2
votes
1
answer
24
Probability
Three $N$ bit binary strings $S_1$,$S_2$,$S_3$ are selected in random. What is the probability that result of bitwise XOR among them contains $k$ $1$'s.i.e. $S_1\oplus S_2\oplus S_3$ = $S$ , No of set bits in $S$ = $k$ is it $\binom{n}{k}\left ( \frac{1}{2} \right )^k\left ( \frac{1}{2} \right )^{nk}$ ??
asked
Feb 8
in
Probability

102
views
probability
+3
votes
1
answer
25
Balanced tree Minimum no of nodes for height h
asked
Feb 8
in
Algorithms

143
views
algorithms
+1
vote
1
answer
26
dfa gatebook QS
asked
Feb 7
in
Theory of Computation

63
views
theoryofcomputation
dfa
+1
vote
1
answer
27
Asynchronous counter circuit with feedback input GATEBOOK QS
asked
Feb 7
in
Digital Logic

146
views
counter
digitallogic
digitalcounter
+1
vote
2
answers
28
C programming
char *x[5] = {"abc","def","ghi","jkl","mno"}; char *y[5] = {"123","456","789","101","102"}; struct hcode { char *word; }hcodes[5]; struct key { int id; char *word; ... ; return 0; } $A.$ 456,hi,01,no $B.$ 456,ghi,101,mno $C.$ 56,hi,01,no $D.$ 456,ef,01,no
asked
Feb 3
in
Programming

138
views
programminginc
output
pointers
+3
votes
2
answers
29
Higher normal form decomposition
asked
Feb 1
in
Databases

304
views
databasenormalization
databases
decomposition
erdiagram
0
votes
0
answers
30
Encoding manchester and differential manchester
asked
Jan 27
in
Computer Networks

393
views
manchesterencoding
computernetworks
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