Recursion

Abstract

Do you remember the tournament problem among n players we discussed in Chapter 4? The proposed algorithm, based on the tree of matches (Figures 4.3 and 4.4), goes from the leaves, where all the players are placed, up to the root, where the champion resides, determining and storing in each level the winners of the different rounds. However, the sequence of matches could be defined the other way around, that is, from the root to the leaves, establishing that the tournament is organized as the match between the winners of two tournaments among n / 2 players allocated to the two halves of the knockout stage; and these two tournaments are equally defined among groups of n / 4 players, down to the matches between pairs of players in the leaves (as is known, in order to simplify calculations the organizers admit a number of participants equal to a power of two).