Chapter 11.2, Problem 26E

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.

26.

a) Use Huan coding to encode these symbols with frequencies a: 04, b: 0.2, C: 0.2, d 0.1, e: 0.1 in two different ways by breaking ties inthe aorithmdifferenUy, First. among the trees of minimum weight select two trees with the largest ntunberof vertices to

combineateachstageoftheaorithni Second, amongthe trees of mmimmweightselectreeswiththesmaflestnumberof

vertices at each stage.

b) Compute the average number of bits required to encode a symbol with each code and compute the variances of this number of bits for each code. Which tie-breaking procedure produced the smaller variance in the number of bits required to encode a symbol?