Generate a single sorted list of all n elements, Data Structure & Algorithms

Q. Assume that we have separated n elements in to m sorted lists. Explain how to generate a single sorted list of all n elements in time O (n log m )?                                                   

Ans.

The list can be developed using Merge sort. Following is the method for it. Assume A is a sorted list with r elements and B is a sorted list with s elements. The operation that combines the elements of A and B into the single sorted list C with n = r +s elements is known as merging.

Procedure 1

MERGING(A, R, B, S, C)

Let A and B be the sorted arrays with R and S elements respectively. The

algorithm merges A and B into an array C with N= R + S elements.

1. [Initialize.] Set NA := 1, NB := 1 and PTR := 1.

2. [Compare.] Repeat while NA <=  R and NB <=  S : If A[NA] < B[NB], then ;

(a)  [Assign element from A to C.] Set C[PTR] := A[NA].

(b)  [Update pointers.] Set PTR := PTR + 1 and

NA := NA + 1. Else:

(a)   [Assign element from B to C.] Set C[PTR]

:= B[NB].

(b)   [Update pointers.] Set PTR := PTR + 1 and

NB := NB + 1.

[End of If structure.] [End of loop.]

3. [Assign remaining elements to C.] If NA > R, then:

Repeat for K = 0, 1, 2,...,S-NB:

Set C[PTR + K] := B[NB + K]. [End of loop.]

Else:

Repeat for K = 0, 1, 2, ..., R - NA:

Set C[PTR + K] := A[NA + K]. [End of loop.]

[End of If structure.]

4. Exit.

Procedure 2:

MERGE(A, R, LBA, S, LBB, C, LBC)

This procedure merges the sorted arrays A

and B into the array C.

1. Set NA := LBA, NB := LBB, PTR := LBC, UBA:= LBA + R - 1, UBB :=     LBB + S - 1.

2. call merging (A,UBA,B,UBB,C)

3. Return.

Procedure 3:

MERGEPASS(A, N, L, B)

The N-element array A consists of sorted subarrays where each subarray has L elements apart from possibly the last subarray, which can have fewer than L elements. The procedure merges the pairs of subarrays of A and assigns them to the array B.

1.   Set Q := INT(N/(2*L)), S:= 2*L*Q and R := N - S.

2.  [Use procedure2 to merge the Q pairs of subarrays.] Repeat for J = 1, 2, . . ., Q:

(a) Set LB := 1 + (2*J - 2) * L. [Finds lower bound of first array.]

(b) Call MERGE(A, L, LB, A, L, LB + L, B, LB). [End of loop.]

3.  [Only one subarray left ?] If R ?  L, then: Repeat for J = 1, 2, . . ., R: Set B(S + J) := A(S+J).

[End of loop.]

Else :

CALL MERGE(A, L, S + 1, A, R, L + S + 1, B, S + 1).

[End of If structure.]

4.   Return.

Procedure 4 MERGESORT( A, N)

This particular algorithm sorts the Nth element array A using an auxiliary array B.

1.   Set L:=1 . [ Initiliazes the number of elements in the subarrays.]

2.   Repeat Steps 3 to 6 while L

3.            Call MERGEPASS(A,N,L,B)

4.            Call MERGEPASS(B,N,2*L,A).

5.             Set L:= 4*L.

[End of Step 2 loop].

6.   Exit.

Posted Date: 7/13/2012 2:58:57 AM | Location : United States







Related Discussions:- Generate a single sorted list of all n elements, Assignment Help, Ask Question on Generate a single sorted list of all n elements, Get Answer, Expert's Help, Generate a single sorted list of all n elements Discussions

Write discussion on Generate a single sorted list of all n elements
Your posts are moderated
Related Questions
an electrical student designed a circuit in which the impedence in one part of a series circuit is 2+j8 ohms and the impedent is another part of the circuit is 4-j60 ohm mm program

Question 1. How can you find out the end of a String? Write an algorithm to find out the substring of a string. 2. Explain the insertion and deletion operation of linked lis

Elaborate the symbols of abstract data type length(a)-returns the number of characters in symbol a. capitalize(a)-returns the symbol generated from a by making its first cha

create a flowchart that displays the students average score for these quizzes

Determine the types of JAVA Java has two parts... 1. Core language -- variables, arrays, objects o Java Virtual Machine (JVM) runs the core language o Core language is

Explain the Abstract data type assertions Generally, ADT assertions translate into assertions about the data types which implement ADTs, which helps insure that our ADT impleme


Define container in terms of  object-oriented terms A Container is a broad category whose instances are all more specific things; there is never anything which is just a Contai

algorithm for multiplication of two sparse matrices using link list

Construct a B+ tree for the following keys, starting with an empty tree.  Each node in the tree can hold a maximum of 2 entries (i.e., order d = 1). Start with an empty root nod