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Discrete Mathematics With Applicat...

5th Edition
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Publisher: Cengage Learning,
ISBN: 9781337694193

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Section
BuyFindarrow_forward

Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
Publisher: Cengage Learning,
ISBN: 9781337694193
Chapter 6.1, Problem 36ES
Textbook Problem
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Trace the action of Algorithm 6,1,1 on the variables I, j, found, and answer for m = 3, n = 3, and sets A and B represented as the arrays a [ 1 ] = u , a [ 2 ] = v , a [ 3 ] = w ; b [ 1 ] = w ; b [ 2 ] = u .

To determine

Trace the action of Algorithm 6.1.1 on the variables i, j, found, and answerfor m = 3, n = 3, and sets Aand Brepresented as the arrays. a[1]=u, a[2]=v, a[3]=w, b[1]=w, b[2]=u,andb[3] =v

Explanation of Solution

Given information:

For m = 3, n = 3, and sets A and B represented as the arrays

a[1]=u,a[2]=v,a[3]=w,b[1]=w,b[2]=u,and b[3]=v.

Calculation:

Input:

m=3

n=3

a[1]=u

a[2]=v

a[3]=w

b[1]=w

b[2]=u

b[3]=v

We also initialize i as 1 and we initialize answer as AB.

i 1
j
found
answer AB

Next, the algorithm will enter the outer while-loop.

We first assign the value 1 to j and the value “no” to found.

i 1 1
j 1
found no
answer AB AB

Since a[1]=uw=b[1], the value of found is not changed in the first iteration of the inner while-loop.

We increase the value of j by 1.

Since a[1]=u=b[2], we change the value of found to “yes”

i 1 1 1
j 1 2
found no yes
answer AB AB AB

Since found is set to “yes”, the inner while-loop stops executing and we then increase i by 1.

Next, we start the second iteration of the outer while-loop, which re-initializes j as 1 and found as no

i 1 1 1 2
j 1 2 1
found no yes no
answer AB AB AB AB

Since a[2]=vw=b[1], the value of found is not changed in the first iteration of the inner while-loop.

We increase the value of j by 1.

Since a[2]=vu=b[2], the value of found remains “no”

i 1 1 1 2 2
j 1 2 1 2
found no yes no no
answer AB AB AB AB AB

We increase the value of j by 1.

Since a[1]=u=b[3], we change the value of found to “yes”

i 1 1 1 2 2 2
j 1 2 1 2 3
found no yes no no yes
answer AB AB AB AB AB AB

Since found is set to “yes”, the inner while-loop stops executing and we then increase i by 1

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Discrete Mathematics With Applications
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