## Invitation to Computer Science 8th Edition

Published by Cengage Learning

# Chapter 3 - Exercises - Page 140: 4a

#### Answer

$$341$$ --- Let us perform the operations according to the suggested algorithm. We'll keep track of the total number of matches after each round. We start with 342 players and divide them by two, which will give us the number of winners in each given round. In case of an odd number of players, the leftovers will only play in the round after that. 1. $342 / 2=171$ matches $[171 \text { total }]$ 2. $171 / 2=85$ matches plus 1 left over $[256 \text { total }]$ 3. $86 / 2=43$ matches $[299 \text { total }]$ 4. $43 / 2=21$ matches plus 1 left over $[320 \text { total }]$ 5. $22 / 2=11$ matches $[331 \text { total }]$ 6. $11 / 2=5$ matches plus 1 left over $[336 \text { total }]$ 7. $6 / 2=3$ matches $[339 \text { total }]$ 8. $3 / 2=1$ match and 1 left over $[340 \text { total }]$ 9. $2 / 1=1$ final match between the last 2 remaining players ${ \text { total }}$ After 9 rounds we got to a total of 341 matches needed to determine a winner.

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