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Recent questions tagged algorithms

1 vote
1 answer
1
The weight of minimum spanning tree in graph $G$, calculated using Kruskal’s algorithm is: $14$ $15$ $17$ $18$
asked May 12 in Others soujanyareddy13 128 views
6 votes
4 answers
2
Let $G$ be a connected undirected weighted graph. Consider the following two statements. $S_1$: There exists a minimum weight edge in $G$ which is present in every minimum spanning tree of $G$. $S_2$: If every edge in $G$ has distinct weight, then $G$ has a unique minimum spanning ... $S_1$ is true and $S_2$ is false $S_1$ is false and $S_2$ is true Both $S_1$ and $S_2$ are false
asked Feb 18 in Algorithms Arjun 2k views
3 votes
3 answers
3
What is the worst-case number of arithmetic operations performed by recursive binary search on a sorted array of size $n$? $\Theta ( \sqrt{n})$ $\Theta (\log _2(n))$ $\Theta(n^2)$ $\Theta(n)$
asked Feb 18 in Algorithms Arjun 1.4k views
3 votes
2 answers
4
Consider the following $\text{ANSI C}$ function: int SomeFunction (int x, int y) { if ((x==1) || (y==1)) return 1; if (x==y) return x; if (x > y) return SomeFunction(x-y, y); if (y > x) return SomeFunction (x, y-x); } The value returned by $\textrm{SomeFunction(15, 255)}$ is __________
asked Feb 18 in Algorithms Arjun 844 views
3 votes
2 answers
5
Consider the string $\textrm{abbccddeee}$. Each letter in the string must be assigned a binary code satisfying the following properties: For any two letters, the code assigned to one letter must not be a prefix of the code assigned to the other letter. For any two letters ... assignments which satisfy the above two properties, what is the minimum length of the encoded string? $21$ $23$ $25$ $30$
asked Feb 18 in Algorithms Arjun 1.6k views
5 votes
3 answers
6
For constants $a \geq 1$ and $b>1$, consider the following recurrence defined on the non-negative integers: $T(n) = a \cdot T \left(\dfrac{n}{b} \right) + f(n)$ Which one of the following options is correct about the recurrence $T(n)$? If $f(n)$ is $n \log_2(n)$, then $T(n)$ ... $\Theta(n^{\log_b(a)})$ If $f(n)$ is $\Theta(n^{\log_b(a)})$, then $T(n)$ is $\Theta(n^{\log_b(a)})$
asked Feb 18 in Algorithms Arjun 1.2k views
3 votes
2 answers
7
Consider the following directed graph: Which of the following is/are correct about the graph? The graph does not have a topological order A depth-first traversal starting at vertex $S$ classifies three directed edges as back edges The graph does not have a strongly connected component For each pair of vertices $u$ and $v$, there is a directed path from $u$ to $v$
asked Feb 18 in Algorithms Arjun 1.1k views
4 votes
2 answers
8
Consider the following $\text{ANSI C}$ program #include <stdio.h> int foo(int x, int y, int q) { if ((x<=0) && (y<=0)) return q; if (x<=0) return foo(x, y-q, q); if (y<=0) return foo(x-q, y, q); return foo(x, y-q, q) + foo(x-q, y, q); } int main( ) { int r = foo(15, 15, 10); printf(“%d”, r); return 0; } The output of the program upon execution is _________
asked Feb 18 in Algorithms Arjun 960 views
4 votes
2 answers
9
In a directed acyclic graph with a source vertex $\textsf{s}$, the $\textit{quality-score}$ of a directed path is defined to be the product of the weights of the edges on the path. Further, for a vertex $v$ other than $\textsf{s}$, the quality-score of $v$ is ... quality-score of $\textsf{s}$ is assumed to be $1$. The sum of the quality-scores of all vertices on the graph shown above is _______
asked Feb 18 in Algorithms Arjun 1.1k views
4 votes
4 answers
10
Consider the following three functions. $f_1=10^n\quad f_2=n^{\log n}\quad f_3=n^{\sqrt {n}}$ Which one of the following options arranges the functions in the increasing order of asymptotic growth rate? $f_3, f_2, f_1$ $f_2, f_1, f_3$ $f_1, f_2,f_3$ $f_2, f_3, f_1$
asked Feb 18 in Algorithms Arjun 1.2k views
3 votes
3 answers
11
Consider the following array.$\begin{array}{|l|l|l|l|l|l|} \hline 23&32&45&69&72&73&89&97 \\ \hline\end{array}$ Which algorithm out of the following options uses the least number of comparisons (among the array elements) to sort the above array in ascending order? Selection sort Mergesort Insertion sort Quicksort using the last element as pivot
asked Feb 18 in Algorithms Arjun 1.4k views
1 vote
3 answers
12
6 votes
5 answers
13
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? $T(n)=\Theta (n^{5/2})$ $T(n)=\Theta (n\log n)$ $T(n)=\Theta (n)$ $T(n)=\Theta ((\log n)^{5/2})$
asked Feb 18 in Algorithms Arjun 2.8k views
2 votes
2 answers
14
Define $R_n$ to be the maximum amount earned by cutting a rod of length $n$ meters into one or more pieces of integer length and selling them. For $i>0$, let $p[i]$ denote the selling price of a rod whose length is $i$ meters. Consider the array of prices: ... $R_7$? $R_7=18$ $R_7=19$ $R_7$ is achieved by three different solutions $R_7$ cannot be achieved by a solution consisting of three pieces
asked Feb 18 in Algorithms Arjun 1.3k views
3 votes
1 answer
15
Consider a $\textit{dynamic}$ hashing approach for $4$-bit integer keys: There is a main hash table of size $4$. The $2$ least significant bits of a key is used to index into the main hash table. Initially, the main hash table entries are empty. Thereafter, when more keys are hashed into it, to resolve ... in decimal notation)? $5,9,4,13,10,7$ $9,5,10,6,7,1$ $10,9,6,7,5,13$ $9,5,13,6,10,14$
asked Feb 18 in Algorithms Arjun 845 views
2 votes
3 answers
16
Consider the following $\text{ANSI C}$ function: int SimpleFunction(int Y[], int n, int x) { int total = Y[0], loopIndex; for (loopIndex=1; loopIndex<=n-1; loopIndex++) total=x*total +Y[loopIndex]; return total; } Let $\textsf{Z}$ be an array of $10$ elements with $\textsf{Z}[i]=1$, for all $i$ such that $0 \leq i \leq 9$. The value returned by $\textsf{SimpleFunction(Z},10,2)$ is __________
asked Feb 18 in Algorithms Arjun 627 views
1 vote
2 answers
17
Consider the following program. Assume that $x$ and $y$ are integers. f(x, y) { if (y != 0) return (x * f(x,y-1)); else return 1; } What is $f(6,3)?$ $243$ $729$ $125$ $216$
asked Jan 29 in Algorithms soujanyareddy13 181 views
1 vote
1 answer
18
For any string $\text{str, length(str)}$ returns the length of the string, $\text{append(str1, str2)}$ concatenates $\text{str1}$ with another string $\text{str2}$, and $\text{trim(str)}$ removes any spaces that exist at the end of the string $\text{str}$. The function $\text{reverse(str, i, j)}$ ... n; i=i+1) { if(str[i] is ' ') { reverse(str, j, i-1); j = i + 1; } } trim(str); return str; }
asked Jan 29 in Algorithms soujanyareddy13 98 views
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