Invitation to Computer Science 8th Edition

Published by Cengage Learning
ISBN 10: 1337561916
ISBN 13: 978-1-33756-191-4

Chapter 3 - Exercises - Page 141: 6


First, we search for Sherman in the list. Since it's the first element of the list, it takes just one comparison to get to it. To find Jane we perform 2 comparisons. To find Ted, which is the third on the list, we need 3 comparisons. It's easy to notice that for each n-th name we need n comparisons. The average of the comparisons is the sum $1+2+3+4+5+6+7$ divided by $7 .$ We can use the formula $\frac{n *(n+1)}{2}$ for the sum. Dividing the sum by $n$ (7 in our case) gives us $\frac{n+1}{2},$ in our case $\frac{7+1}{2}=4$ We have reached the expression that we have used previously $\frac{n+1}{2}$

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