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

Assignment Help:

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.

#### Make adjacency matrix for un-directed graph, Q. Describe the adjacency matr...

Q. Describe the adjacency matrix and make the same for the given undirected graph.    Ans: The representation of Adjacency Matrix: This representation consists of

#### Infix expression into the postfix expression, Q. Convert the given infix ex...

Q. Convert the given infix expression into the postfix expression (also Show the steps) A ∗ (B + D)/ E - F(G + H / k ) Ans. Steps showing Infix to Post fix

#### Write a function that performs integer division, Write a function that perf...

Write a function that performs integer division. The function should take the large number in memory location 1 and divide it by the large number in memory location 2 disregarding

#### What do you mean by hash clash, What do you mean by hash clash? Hashing...

What do you mean by hash clash? Hashing is not perfect. Occasionally, a collision occurs when two different keys hash into the same hash value and are assigned to the same arra

#### What are the languages which support assertions, What are the languages whi...

What are the languages which support assertions Languages which support assertions often provide different levels of support. For instance, Java has an assert statement which t

#### If else, design algorithm and flow chart that computes the absolute differe...

design algorithm and flow chart that computes the absolute difference of two values x and y

#### The complexity of searching an element, The complexity of searching an elem...

The complexity of searching an element from a set of n elements using Binary search algorithm is   O(log n)

#### The quick sort algorithm exploit design technique, The quick sort algorithm...

The quick sort algorithm exploit design technique Divide and Conquer

#### Postorder traversal of a binary tree, Postorder traversal of a binary tree ...

Postorder traversal of a binary tree struct NODE { struct NODE *left; int value;     /* can take any data type */ struct NODE *right; }; postorder(struct NODE

#### Graph, explain the prims''s algorithm with suitable example?

explain the prims''s algorithm with suitable example?  