Recent questions tagged sorting

1 vote
3 answers
1
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
2 votes
5 answers
2
Merge sort uses : Divide-and-conquer Backtracking Heuristic approach Greedy approach
2 votes
3 answers
3
Given two sorted list of size '$m$' and '$n$' respectively. The number of comparisons needed in the worst case by the merge sort algorithm will be : $m^{*}n$ minimum of $m, n$ maximum of $m, n$ $m+n-1$
3 votes
12 answers
4
Which of the following sorting algorithms does not have a worst case running time of $O(n​^2​)$? Insertion sort. Merge sort. Quick sort. Bubble sort.
0 votes
3 answers
5
Selection sort, quick sort is a stable sorting method True,True False,False True,False False,True
1 vote
2 answers
6
Which of the following sorting procedures is the slowest? Quick Sort Merge Sort Shell Sort Bubble Sort
1 vote
3 answers
7
The running time of Quick sort algorithm depends heavily on the selection of: No. of inputs Arrangement of elements in an array Size of elements Pivot Element
4 votes
5 answers
8
If an array $A$ contains the items $10,4,7,23,67,12$ and $5$ in that order, what will be the resultant array $A$ after third pass of insertion sort? $67,12,10,5,4,7,23$ $4,7,10,23,67,12,5$ $4,5,7,67,10,12,23$ $10,7,4,67,23,12,5$
1 vote
4 answers
9
Of the following sort algorithms, which has execution time that is least dependant on initial ordering of the input? Insertion sort Quick sort Merge sort Selection sort
5 votes
3 answers
10
Which of the following is best running time to sort $n$ integers in the range $0$ to $n^2-1$? $O(\text{lg } n)$ $O(n)$ $O(n\text { lg }n)$ $O(n^2)$
0 votes
0 answers
11
A probability distribution function $P(x)$ for a random variable $X$ is defined by $P(x) =Pr\{X\leq x\}$.Suppose that we draw a list of $n$ random variables $X_1,X_2,…,X_n$ from a continuous probability distribution function $P$ that is computable in $O(1)$ time. Give an algorithm that sorts these numbers in linear averagecase time.
0 votes
0 answers
12
We are given $n$ points in the unit circle, $P_i=(x_i,y_i)$, such that $0<x_i^2+y_i^2<1$ for $i=1,2, .,n$.Suppose that the points are uniformly distributed; that is, the probability of finding a point in any region of the circle is proportional to the ... from the origin. (Hint: Design the bucket sizes in BUCKET-SORT to reflect the uniform distribution of the points in the unit circle.)
0 votes
1 answer
13
Let $X$ be a random variable that is equal to the number of heads in two flips of a fair coin. What is $E[X^2]$? What is $E^2[X]$?
1 vote
1 answer
14
Explain why the worst-case running time for bucket sort is $\Theta(n^2)$. What simple change to the algorithm preserves its linear average-case running time and makes its worst-case running time $O(n\ lg\ n)$?
0 votes
1 answer
15
BUCKET-SORT(A) 1 let B[0...n-1] be a new array 2 n = A.length 3 for i – 0 to n – 1 4 make B[i] an empty list 5 for i = 1 to n 6 insert A[i] into list B[nA[i]] 7 for i = 0 to n – 1 8 sort list B[i] with insertion sort 9 concatenate the lists B[0] , B[1] , ….,B[n-1] together in order illustrate the operation of BUCKET-SORT on the array $A=\langle .79,.13,.16,.64,.39,.20,.89,.53,.71,.42\rangle$
1 vote
2 answers
16
Show how to sort $n$ integers in the range $0$ to $n^3-1$ in $O(n)$ time.
0 votes
0 answers
17
Use induction to prove that radix sort works. Where does your proof need the assumption that the intermediate sort is stable?
0 votes
2 answers
18
Which of the following sorting algorithms are stable: insertion sort, merge sort, heapsort, and quicksort? Give a simple scheme that makes any sorting algorithm stable. How much additional time and space does your scheme entail?
0 votes
1 answer
19
RADIX-SORT(A, d) 1 for i = 1 to d 2 use a stable sort to sort array A on digit i illustrate the operation of RADIX-SORT on the following list of English words: COW, DOG, SEA, RUG, ROW, MOB, BOX, TAB, BAR, EAR, TAR, DIG, BIG, TEA, NOW, FOX.
0 votes
2 answers
20
Describe an algorithm that, given $n$ integers in the range $0$ to $k$ preprocesses its input and then answers any query about how many of the $n$ integers fall into the range $[a..b]$ in $O(1)$ time.Your algorithm should use $\Theta(n+k)$ preprocessing time.
0 votes
0 answers
21
Suppose that we were to rewrite the for loop header in line $10$ of the COUNTINGSORT as 10 for j = 1 to A.length Show that the algorithm still works properly. Is the modified algorithm stable?
0 votes
1 answer
22
Prove that COUNTING-SORT is stable.
0 votes
0 answers
23
COUNTING-SORT(A, B, k) 1 let C[0, ,k] be a new array 2 for i = 0 to k 3 C[i] = 0 4 for j = 1 to A.length 5 C[A[j]] = C[A[j]] + 1 6 // C[i] now contains the number of elements equal to i . 7 for i =1 to k 8 C[i] = C[i] + C[i-1] 9 // C[i] now contains the ... [C[A[j]]] = A[j] 12 C[A[j]] = C[A[j]] - 1 illustrate the operation of COUNTING-SORT on the array $A=\langle 6,0,2,0,1,3,4,6,1,3,2 \rangle$
0 votes
0 answers
24
Suppose that you are given a sequence of $n$ elements to sort.The input sequence consists of $n/k$ subsequences, each containing $k$ elements.The elements in a given subsequence are all smaller than the elements in the succeeding subsequence and larger than the ... this variant of the sorting problem. (Hint: It is not rigorous to simply combine the lower bounds for the individual subsequences.)
0 votes
0 answers
25
Show that there is no comparison sort whose running time is linear for at least half of the $n!$ inputs of length $n$.What about a fraction of $1/n$ inputs of length $n$? What about a fraction $1/2^n$?
0 votes
1 answer
26
What is the smallest possible depth of a leaf in a decision tree for a comparison sort?