Questions tagged [mergesort]
The mergesort tag has no usage guidance.
61
questions
0
votes
0
answers
27
views
Recurrence for C(N+1) - C(N) of mergesort
I am reading "An Introduction to the Analysis of Algorithms" by Robert Sedgewick and Kevin Wayne. In this book, Exercise 1.4 asks to develop a recurrence for $C_{N+1} - C_{N}$ and use it to ...
- 101
1
vote
2
answers
93
views
Partition an array in two groups while keeping the relative order within groups
I came across the following problem in the book "Elements of Programming Interviews in Python".
Given an array A of n objects with Boolean-valued keys, reorder the array so that objects ...
- 111
0
votes
2
answers
64
views
merging logn + 1 sorted subarrays
given array A of size $n$ which is made of $logn + 1$ sub arrays which are sorted,
I need to sort ASAP.
example of array : $A[500,501,3,8,100,1,2,9]$ as you can see, sub arrays are :$[1:2][3:5][6:]$
...
0
votes
1
answer
145
views
Why does merge sort work for any $n$, but the basic FFT algorithm only for powers of $2$?
Merge sort and FFT are both divide and conquer algorithms that split the input in two repeatedly. While merge sort can be applied to any $n$, the FFT algorithm given in CLRS (section 30.2, third ...
- 305
1
vote
1
answer
67
views
Divide-and-Conquer Algorithms: What exactly is $a$ and $b$ here?
Chapter 2.3.2 Analysing divide-and-conquer algorithms of Introduction to Algorithms, fourth edition, by CLRS, says the following:
A recurrence for the running time of a divide-and-conquer algorithm ...
- 203
0
votes
1
answer
32
views
Applying merge sort: Would the value in the box with the red cross be $71$? Does it matter whether we start at the bottom-left or bottom-right?
I have the following diagram showing a case of merge sort:
I am trying to find the value that would be in the box with the red cross when applying merge sort in ascending order.
It seems to me that ...
- 203
0
votes
1
answer
133
views
In merge sort, what will be the time complexity if in each recursion, we break the array in two parts of size 1/4 and 3/4 respectively?
Let's say number of elements are a power of 4. Now if we break the array in parts of 1/4 and 3/4, how do we calculate the time complexity in this case?
- 101
0
votes
0
answers
69
views
How will changing the splitting point in merge sort affect the algorithm and its time complexity
Everyone knows that merge sort will continuously divide the array into halves until they are small enough to (like 2 elements per block or so) be able to be sorted quickly, hence its time complexity ...
- 1
1
vote
0
answers
132
views
Showing that for all positive integers m and n there are sorted lists with m elements and n elements such that m+n-1 comparisons are needed
I was trying to solve a discrete math question regarding the comparison needed by a merge-sort algorithm. I wanted to ask if there were a more formal way to put organize my reasoning for this problem ...
- 111
2
votes
3
answers
104
views
Number of comparisons for mergesort
In their book An introduction to the Analysis of Algorithms, Flajolet and Sedgewick analyze the number of compares performed by Mergesort along the following lines. They denote by $C_N$ the number of ...
1
vote
2
answers
532
views
Sorting an array with x sorted subarrays
I have been given two True/False questions regarding sorting an array. The questions are as following -
Question A
Given an array A with 3n keys that contains three equal parts
A[1,n], A[n+1,2n] and ...
- 231
0
votes
3
answers
193
views
Runtime of sorting algorithms given a particular input
say that we have {2,3,5,4,6} as input that we want to sort in ascending order. Then, we know that we can use any of the sorting algorithms: bubble, insertion, selection, quick, merge, heap or counting....
1
vote
2
answers
997
views
How does size of list in merge-sort, quick-sort, insertion-sort, matter?
We have been taught that:
Insertion-sort will best work if we have a small list.
Quick-sort will best work if we have a long list.
Merge-sort will best work if we have a huge list.
It is not ...
- 27
0
votes
2
answers
92
views
How to known which algorithm is the best for what situation, when sorting numbers?
Is there some kind of "universal list" of performance of different algorithms in different situations?
I have different databases that save user input (numbers). However some of these sets ...
- 111
1
vote
0
answers
60
views
Merge Sort sentinel: What if your array contains Integer.MAX_VALUE?
I'm just getting my head round Merge Sort, and I was wondering whether the use of the sentinel value was considered good practice in the real world, or mostly an algorithmic conceit?
I get that it ...
- 11
0
votes
0
answers
58
views
External Sorting - Calculate passes with different number of disks
Let suppose that we have a file with n = 10^6 records. The block size is B = 10 records and we have available main memory m = 20 blocks. (Sorting with MergeSort)
a) If we have 1 disk find minimum ...
- 19
1
vote
1
answer
978
views
Bottom-up Mergesort vs Natural Merge Sort
I ran into natural mergesort in this Wikipedia page: https://en.wikipedia.org/wiki/Merge_sort#Natural_merge_sort
However, I can't find much information regarding:
The algorithm(s) to achieve natural ...
- 23
1
vote
1
answer
409
views
Worst case running time of lexicographical sorting of a list of n strings each of length n using merge sort
This same question has been asked here so many times by several people. This is a problem which was asked in an entrance exam.
And I am having difficulties in digesting the correct answer of this ...
- 281
1
vote
1
answer
95
views
Runtime of Divide and Conquer Flavored Bogo Sort
Here we propose a way to reduce Bogo Sort's runtime from factorial to exponential using a divide and conquer approach. This is something we have likely all pondered on extensively.
https://en....
1
vote
1
answer
24
views
How can divide by 2 blocksize bubblesort followed by a final mergesort be optimized in a particular environment?
I am wondering if we had a large array to sort (let's say 1,048,576 random integers), chosen because it is a perfect power of 2, if we can just keep dividing those blocks into smaller and smaller half ...
- 134
1
vote
1
answer
872
views
Quick Sort vs Radix Sort
In an coding exam, I was once asked this question:
Assuming that you are only sorting Integers in ascending order, which algorithm do you use when you want to prioritize speed the most, but you ...
1
vote
2
answers
1k
views
Why does MergeSort have O(n) space complexity if it splits the array log(n) times?
I know this is a common algorithm with plenty of analysis, but when I searched for an answer the only one I found was "Merge Sorting has O(n) auxiliary space because it copies the array into L and R". ...
- 113
5
votes
1
answer
1k
views
How can merging two sorted arrays of N items require at least 2N - 1 comparisons in every case?
The HW question, on page 362 of Data Structures and Algorithms in C++: Fourth Editionby Mark Allen Weiss, reads as follows:
Prove that merging two sorted arrays of N items requires at least 2 * N - ...
- 155
1
vote
0
answers
528
views
Time complexity of a hybrid merge and selection sort algorithm
I'm trying to analyse the time and space complexity of the following algorithm, which is essentially a hybrid of a merge and selection sort. The algorithm is defined as follows:
...
- 111
0
votes
0
answers
552
views
Job Scheduling with deadline with $nlogn$ algorithm
We know that there is a Greedy algorithm for scheduling of $n$ jobs which each job has its own deadline and profit.
In greedy algorithm, we sort the set by their profit descendant, And if a job can ...
- 1
1
vote
1
answer
420
views
Space Complexity of Bottom-Up Merge Sort
What is the space complexity of Bottom-up merge sort?
It uses iteration rather than recursion so it will not use stack. But will an auxiliary array be used for the merge operation?
Please explain.
...
1
vote
2
answers
1k
views
number of permutation with k inversions
We are given two numbers N and K.
N <= 10^9.
K<=min{1000,(N*(N-1))/2}
We need to find numbers of permutations of ( 1 to N ) such that inversions are exactly K.
If N was <= 10^3. It would ...
user102578
1
vote
0
answers
29
views
Is there a name for the technique used in the "merge" part of MergeSort?
MergeSort has two parts, "divide" and "merge" (arguably three if you include "recurse" as its own part in the middle). I'm interested in the "merge" part, which tends to look like this:
...
- 111
2
votes
2
answers
625
views
Merge Sort Confusion - Initial Phase Missing?
Below is the solution to a merge sort exercise - "Use a merge sort to sort the list". I'm confused because I thought that there needed to be an initial phase of breaking the list in to sub-lists, yet ...
- 255
3
votes
1
answer
804
views
Worst Case Space Complexity of Merge Sort and Bubble Sort
I understand that the worst space complexity of Bubble Sort is constant O(1), since all the space we need is the array where the elements were stored. But why is Merge Sort's worst space complexity O(...
- 205
3
votes
3
answers
73
views
Why is subarray $A[p..k-1]$ empty when $k=p$?
I'm working through a proof of correctness for merge sort.
I'm given a loop invariant for a for loop, which makes reference to a subarray $A[p..k-1]$. During the initialization step of the ...
- 215
5
votes
2
answers
882
views
Complexity of Merge Sort that splits in a random position
I got a question that I don't fully understand:
Given a new algorithm to merge sort (AKA mergesort2) that instead of splitting the list in the middle it splits the list in a random number between $1$ ...
- 65
5
votes
1
answer
232
views
Merge sort in place
I don't quite understand why in-place sort merge sort isn't preferred over not-in place? Is it because theoretically in place merge sort is better because of its memory complexity tradeoff, but in ...
- 51
1
vote
1
answer
49
views
Recurrence Relation Mergesort
I was reading Algorithms 4th Edition by Sedgewick et al. and I found this statement when discussing about the analysis of mergesort:
The number of compares is at most n and no less than $\lfloor n/...
- 145
2
votes
1
answer
761
views
Merge sort: sorting and merging complexity $\Theta(n)$
So this is the Master theorem for Merge Sort:
$$ T(n) = 2T(n/2) + \Theta(n). $$
I am not able to understand why is the time complexity for sorting and merging $\Theta(n)$.
Is sorting $O(1)$ and ...
- 159
0
votes
2
answers
1k
views
Merge sort and quicksort recursion tree depth
1)
I need to determine recursion tree depth for strings composed of 10, 100 and 1000 elements when using merge sort. For the 10 elements one/I can do it on a paper, just drawing tree, but what about ...
- 101
1
vote
1
answer
85
views
MergeSort k arbitrary words in linear time
Given $k$ arbitrary words, such as $\{\text{"fjqke"}, \text{"gbqig"}, \text{"a"}\}$, is there a way to mergesort these words in linear time so that the final output would be "abefgggijkq"? I tried to ...
- 113
2
votes
1
answer
160
views
Compute the general time complexity of a merge sort algorithm with specified complexity of the merge process
The problem was from an exam, I spent much time wrapping my head up around this kind of problems, so I decided to ask for help ;(
Problem:
We implement a merge sort algorithm to sort $n$ items. The ...
- 159
0
votes
1
answer
951
views
Merge sort mxn matrix
The question is as follows:
I am new to this, and I do not understand how to apply divide and conquer to a matrix, the algorithm that I have come up with is as follows (I am not sure if I am correct)
...
- 123
2
votes
1
answer
3k
views
Merging $k$ sorted lists in $O(n\log k)$ time
This question is based on a solution of Laura Toma to a question from CLRS (#6 on the sheet).
Question: Give an $O(n\lg k)$-time algorithm to merge $k$ sorted lists into one sorted list, where $n$ is ...
- 169
1
vote
1
answer
536
views
Counting Inversions with merge-sort
I'm doing this course: Engineering: Algorithms1 - SELF PACED Algorithms: Design and Analysis, on Stanford's website. And the first assignment asked us to count the inversions in an array.
The idea ...
- 113
5
votes
1
answer
614
views
Merge sort worst case running time for lexicographical sorting?
A list of n strings each of length n is being sorted in lexicographical order using the merge sort algorithm. Since we have to take care of comparison of each character in the strings so the merge ...
- 1,195
0
votes
1
answer
236
views
What is the time complexity of MergeSort without its penultimate merge?
As in, with the two final sublists which are sorted arrays, let's say just for this example (yes it is no longer fully MergeSort but I am interested in the time complexity only), that we finish with a ...
user88835
2
votes
1
answer
355
views
Proving time-complexity analysis for merge-sort-like algorihtm
I have this algorithm, which is exactly like merge-sort, but instead of halving the array each recursion, it actually splits it into $1/4$ and $3/4$ parts. Other then that, it does exactly the same ...
- 121
0
votes
1
answer
26
views
Merge Sort meaning of a bit part of code
I am studying this part for a merge sort implementation:
...
- 103
0
votes
0
answers
113
views
2
votes
1
answer
534
views
Exact Analysis of the Merge Sort
When doing the "inexact" analysis of the Merge Sort, the literature that I have seen usually consider that the input is an array with a even quantity of numbers and the recurrence relation is:
$T(n) =...
- 144
2
votes
1
answer
3k
views
To find median of $k$ sorted arrays of $n$ elements each in less than $O(nk\log k)$
How do I efficiently find the median of $k$ sorted arrays each of length $n$? Note that the total number of elements will be $nk$. I know it can be done in $O(nk \log k)$ time using merge technique. ...
- 481
1
vote
1
answer
188
views
Sort huge file algoritm [closed]
What algorithm should be used here to solve this problem efficiently?
One file stores 5 year log of user IDs & their website visit dates in random order. There were around 1,000,000 users on the ...
- 31
3
votes
1
answer
2k
views
Radix, merge, counting sort and when to use
Okay can't figure this out. I want to make sure I understand it.
There are n random keys each being float numbers with p decimal places.
So, for example,
123.456,
343.645,
234.543,
863.238,
956....
- 51