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Tournament Trees
Winner trees.
Loser Trees.
Winner Trees
Complete binary tree with n external nodes
and n - 1 internal nodes.
External nodes represent tournament players.
Each internal node represents a match played
between its two children; the winner of the match
is stored at the internal node.
Root has overall winner.
Winner Tree For 16 Players
player match node
Winner Tree For 16 Players
1
1
2
3 1 2 2
3 6 1 3 2 4 2 5
4 3 6 8 1 5 7 3 2 6 9 4 5 2 5 8
Smaller element wins = min winner tree.
Winner Tree For 16 Players
1
1
2
3 1 2 2
3 6 1 3 2 4 2 5
4 3 6 8 1 5 7 3 2 6 9 4 5 2 5 8
height is log2 n (excludes player level)
Complexity of Initialize
• O(1) time to play match at each match node.
• n - 1 match nodes.
• O(n) time to initialize n player winner tree.
Applications
Sorting.
Put elements to be sorted into a winner tree.
Repeatedly extract the winner and replace by
a large value.
Sort 16 Numbers
1
1
2
3 1 2 2
3 6 1 3 2 4
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