The tournament sort is a sorting algorithm that works by building an ordered binary tree. We represent the elements to be sorted by vertices that sill become the leaves. We build up the tree one level at a time we would construct the tree representing the winners of matches in a tournament Working left to right, we compare pairs of consecutive elements, adding a parent vertex labeled with the larger of the two elements under comparison. We make similar comparisons between labels of vertices at each level until we reach the root of the tree that is labeled with the largest element. The tree constructed by the tournament sort of , 8.14,17,3,9,27,11 is ilinstrated in part(a)ef the figure. Once the argestelementhbeendetermined. The leaf with this labelisrelabeled by -s,which is definedtobelessthanevery element The labels of all vertices on the path from this vertex up to the root of the tree are recalculated, as shown in part (b) of the figure.
This produces the second largest element This process continues until the entire list has been sorted.
19. Which of these codes are prefix codes?
a) a: 11, e: 00, t: 10, s: 01
b) a: o,e: l,t: ol,s: 001
c) a: 101, e: 11, t: 001, s: Oil, n: 010
d) a: 010, e: 11, t: O11,s: 1011, n: 1001, j: 10101
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Chapter 11 Solutions
Discrete Mathematics and Its Applications
- Taylor's baseball team played a full 9-inning game. The team scored 4 runs in every inning, and for every 2 runs it scored, it had 5 hits. What is an appropriate process for finding how many total hits the team had? Make a tree diagram with 1 inning as the starting point. Draw 4 branches to represent the runs. Connect every 2 runs to a single node and draw 5 branches to represent the hits. Multiply the number of hits by 9 to find the number of hits in the full 9-inning game. Make a table with one column for runs and one for hits. Start with 4 runs and 2 hits, then increase each column by 5 for 9 rows to find the number of hits in the full 9-inning game. Make a graph with the number of hits on the x-axis and the number of runs on the y-axis. Start at 0 hits and 0 runs, then add 5 hits for every 4 runs. Continue this pattern 9 times to find the number of hits in the full 9-inning game. Make two tape diagrams, one with 4 rectangles to represent the number of runs, and one with 5…arrow_forwardDraw an ordered stemplot of these scores: 22, 32, 34, 30, 28, 19, 26, 18, 19, 20. List the 'leaves' on the second row in this stemplot in their correct order.arrow_forwardWhat is the two possible routes, the greedy and edge-picking algorithm, what are the difference of these routes. Can you also help me understand what are the difference of the processarrow_forward
- Create a tree diagram to show the possible answer combinations of the first three questions on the take-home assignment.arrow_forwardWhat is the total weight of the edge-picking grapharrow_forwardUse the critical path algorithm to create a priority list for the digraph below. T1 (2) T4 (12) Т6 (5) End T2 (7) T5 (4) T7 (11) Т3 (9) Priority list: Give the priority as a list of task numbers. For example, you'd enter something like: 1,2,3,4,5,6,7,8,9,10arrow_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
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