ch5: merge sort - ecpe.nu.ac.th · merge sort vscards • we have two sorted piles of a card deck....

Ch5: Merge Sort

305233, 305234

Algorithm Analysis and Design

Jiraporn PooksookNaresuan University

Merge Sort vs Cards

This photo is taken from https://www.pleasanttimes.com/images/2card-box-teak-2.jpg

Merge Sort vs Cards

• We have two sorted piles of a card deck.

Sorted Sorted

pillsSorted

pills pills

Merge Sort vs Cards

• We compare the top card of both piles and

put the smaller card on another pile.

Sorted

piles

Sorted

pilespiles piles

<

Merge Sort vs Cards

• We compare the top card of both piles and

put the smaller card on another pile. Then we

compare the next cards.

Sorted Output Sorted

piles

Sorted

piles

Output

piles

Merge Sort

2 4 175 3 2 6

divide

2 4 175 3 2 62 4 175 3 2 6

2 4 75 1 3 2 6

2 4 75 1 3 2 6

divide

divide

Merge Sort

2 2 431 5 6 7

4 5 172 2 3 6

merge

4 5 172 2 3 6

5 4 72 1 3 2 6

2 4 75 1 3 2 6

merge

merge

Merge Sort

• Divide the n element arrays to be two arrays

of size n/2

• Sort the two divided arrays using merge sort

recursivelyrecursively

• Merge the two sorted arrays to produce the

sorted answer

Psudocode: merge(A,p,q,r)N1 = q – p + 1

N2 = r – q

Create arrays L[1..N1+1] and R[1…N2+1]

For i = 1 to N1

do L[i] = A[ p + i -1]

For j = 1 to N2

do R[j] = A[q + j]do R[j] = A[q + j]

L[N1+1] =

R[N2+1] =

i = 1

j = 1

For k=p to r

do if L[ i ] <= R[ j ]

then A[k] = L[ i ]

i = i+1

else A[k] = R[ j ]

j = j+1

∞

∞

Practice: Merge(A,p,q,r)

4 5 172 2 3 6… …

4 5 172 2 3 6L R

K

∞4 5 172 2 3 6L R

i j

∞ ∞


4 5 171 2 3 6… …

4 5 172 2 3 6L R

K

∞

1 < 2

4 5 172 2 3 6L R

i j

∞ ∞


4 5 171 2 3 6… …

4 5 172 2 3 6L R

i j

K

∞ ∞

i j

2 5 171 2 3 6… …

4 5 172 2 3 6L R

i j

K

∞ ∞

2 <= 2


2 5 171 2 3 6… …

4 5 172 2 3 6L R

i j

K

∞ ∞

i j

2 2 171 2 3 6… …

4 5 172 2 3 6L R

i j

K

∞ ∞

2 < 4


2 2 171 2 3 6… …

4 5 172 2 3 6L R

i j

K

∞ ∞

i j

2 2 131 2 3 6… …

4 5 172 2 3 6L R

i j

K

∞ ∞

3 < 4


2 2 131 2 3 6… …

4 5 172 2 3 6L R

i j

K

∞ ∞

i j

2 2 431 2 3 6… …

4 5 172 2 3 6L R

i j

K

∞ ∞

4 < 6


2 2 431 2 3 6… …

4 5 172 2 3 6L R

i j

K

∞ ∞

i j

2 2 431 5 3 6… …

4 5 172 2 3 6L R

i j

K

∞ ∞

5 < 6


2 2 431 5 3 6… …

4 5 172 2 3 6L R

i j

K

∞ ∞

i j

2 2 431 5 6 6… …

4 5 172 2 3 6L R

i j

K

∞ ∞

6 < 7


2 2 431 5 6 6… …

4 5 172 2 3 6L R

i j

K

∞ ∞

i j

2 2 431 5 6 7… …

4 5 172 2 3 6L R

i j

K

∞ ∞

7 < ∞


2 2 431 5 6 7… …

4 5 172 2 3 6L R

i j

K

∞ ∞

i j

Psudocode: merge-sort (A,p,r)

If p < r

then q = L(p+r)/2

merge-sort(A, p, q)

merge-sort(A, q+1, r)merge-sort(A, q+1, r)

merge(A, p, q, r)

Practice: merge-sort (A,1,8)

If p < r

then q = L(p+r)/2

round 1 , q= 4

round 2 , q= 2

merge-sort(A, p, q)merge-sort(A, p, q)

round 1 , merge-sort(A,1,4)

merge-sort(A, q+1, r)


merge(A, p, q, r)

round 1 , merge(A,1,4,8)


If p < r

then q = L(p+r)/2

round 2 , q= 2

merge-sort(A, p, q)

round 1 , merge-sort(A,1,4)round 1 , merge-sort(A,1,4)




round 2, merge-sort(A,3,4)

merge(A, p, q, r)




If p < r

then q = L(p+r)/2

round 2 , q= 2

merge-sort(A, p, q)

round 1 , merge-sort(A,1,4)round 1 , merge-sort(A,1,4)





merge(A, p, q, r)




If p < r

then q = L(p+r)/2

round 3 , q= 1

merge-sort(A, p, q)



round 3, merge-sort(A,1,1)round 3, merge-sort(A,1,1)





merge(A, p, q, r)



round 3, merge(A,1,1,2)


If p < r

then q = L(p+r)/2

round 3 , q= 3

merge-sort(A, p, q)



round 3, merge-sort(A,3,3)round 3, merge-sort(A,3,3)





merge(A, p, q, r)



round 3, merge(A,3,3,4)

Practice: Merge-sort(A,p,r)

2 4 175 3 2 6

2 4 175 3 2 6L R

Merge-sort(A,1,8)

2 4 175 3 2 6L R

2 4 75

Merge-

sort(A,1,4)

1 3 2 6

Merge-

sort(A,5,8)

2 4 75 1 3 2 6

Merge-

sort(A,1,2)

Merge-

sort(A,3,4)

Merge-

sort(A,5,6)

Merge-

sort(A,7,8)

Practice: Merge-sort(A,p,r)

2 4 175 3 2 6

2 4 175 3 2 6L R

Merge-sort(A,1,8) Merge

(A,1,4,8)

2 4 175 3 2 6L R

2 4 75

Merge-

sort(A,1,4)

1 3 2 6

Merge-

sort(A,5,8)

2 4 75 1 3 2 6

Merge-

sort(A,1,2)

Merge-

sort(A,3,4)

Merge-

sort(A,5,6)

Merge-

sort(A,7,8)

Merge

(A,1,2,4)

Merge

(A,5,6,8)

Merge

(A,1,1,2)

Merge

(A,3,3,4)

Merge

(A,5,5,6)Merge

(A,7,7,8)

Exercise merge-sort

Input = [9,5,7,4,2,8]

ch5: merge sort - ecpe.nu.ac.th · merge sort vscards • we have two sorted piles of a card deck....

Documents

UNIT 5C Merge Sort - cs.cmu.edu15110-n15/lectures/unit05-3-MergeSort.pdf · Merge Sort Input: List a of n elements. Output: Returns a new list containing the same elements in sorted

Pills & News

initially Treat data as N sorted collections that are each one datum long. merge Merge each consecutive pair of collections to form sorted collections

DIET PILLS Jennifer Qing. What are diet pills? Pills that claim to make you lose weight

Insertion Sort Merge Sort · Merge two sorted arrays MERGE (A, B, m, n) T(m, n) i=1, j=1 1 while i

zEnterprise The Ideal Platform For Smarter Computing · SORT Job: Sort a 3 GB transaction file ... MERGE Job: Merge 30 sorted files into a 90 GB master file ... More performance!**

SIGNZ Mail Merge / E-mail Merge / Labels SIGNZ Mail Merge / E-mail Merge / Labels

PROGRAMMING FOR PROBLEM SOLVING LABORATORY LAB … · Write a C program to merge two sorted arrays into another array in a sorted order. e. Write a C program to find the frequency

5. Divide-and-Conquer 5.1 Mergesort - cs.princeton.edu · 5 Mergesort Mergesort.! Divide array into two halves.! Recursively sort each half.! Merge two halves to make sorted whole

1 101418193716172325211 Counting Inversions Merge and count step. n Given two sorted halves, count number of inversions where a i and a j are in different

Semester - 1panducollege.org/uploadfiles/file/Syllabi/TDC-Computer... · 2018-06-16 · Write a program to merge two sorted arrays. 29. Write a program to implement selection sort

On the Nature of Merge: External Merge, Internal …home.uni-leipzig.de/muellerg/citko05.pdfOn the Nature of Merge: External Merge, Internal Merge, and Parallel Merge Barbara Citko

Ch5: Merge Sort...Merge Sort vsCards •We compare the top card of both piles and put the smaller card on another pile. Sorted piles Sorted piles < Merge Sort •Divide the n element

1 101418193716172325211 Merge and Count Merge and count step. n Given two sorted halves, count number of inversions where a i and a j are in different

Diabetes and pills

Princeton University Computer Science › courses › archive › ...facts recursive merging is the main operation performance merging 2-sorted arrays takes lir time merge sort tree

Microelectronic Pills

English in pills

Merge Strategies for Merge-and-Shrink Heuristicsai.cs.unibas.ch/papers/theses/federau-master-17.pdf · Merge Strategies for Merge-and-Shrink Heuristics Master’s Thesis ... merge

Stanford ProCoYou are given two sorted arrays of integers. Write a program that will merge both arrays into a single, sorted, output array. The merge algorithm is as follows: compare

Knowledge Pills Catalog

Mindfulness Pills

Micro Pills

merge demo merge-and-count demo · Merge-and-count demo Given two sorted lists A and B, ・Count number of inversions (a, b) with a ∈ A and b ∈ B. ・Merge A and B into sorted

Penelope Pills - Tessuti

Happy Pills

Confrontation Pills

Chapter 1 Triplet Merge Trees - MIT CSAILThe merge tree of this function is a path, with vertices assigned the input values in sorted order. 4 Dmitriy Smirnov and Dmitriy Morozov The

Novelon Contraceptive Pills

Male Enhancement Pills

Lecture 21: Searching and Sorting - longbaonguyen.github.io · •merge sort: recursively divide the array in half and sort it • heap sort : place the values into a sorted tree

Taking Medications Pills

Worst Pills, Best Pills News Now Available Online!

Pills 2011

Swallowing Pills