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lec05 - Tournament Trees Winner trees Loser Trees Winner...

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Tournament Trees Winner trees. Loser Trees.
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Winner Tree – Definition 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.
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Winner Tree For 16 Players player match node
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Winner Tree For 16 Players 4 3 6 8 1 5 7 3 2 6 9 4 5 2 5 8 Smaller element wins => min winner tree . 3 6 1 3 2 4 2 5 3 1 2 2 1 2 1
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Winner Tree For 16 Players 4 3 6 8 1 5 7 3 2 6 9 4 5 2 5 8 3 6 1 3 2 4 2 5 3 1 2 2 1 2 1
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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.
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Winner Tree Operations Initialize O(n) time Get winner O(1) time Replace winner and replay O(log n) time More precisely Theta(log n) Tie breaker (player on left wins in case of a tie).
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Replace Winner And Replay 4 3 6 8 1 5 7 3 2 6 9 4 5 2 5 8 3 6 1 3 2 4 2 5 3 1 2 2 1 2 1 Replace winner with 6 .
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Replace Winner And Replay 4 3 6 8 6 5 7 3 2 6 9 4 5 2 5 8 3 6 1 3 2 4 2 5 3 1 2 2 1 2 1 Replay matches on path to root.
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Replace Winner And Replay 4 3 6 8 6 5 7 3 2 6 9 4 5 2 5 8 3 6 1 3 2 4 2 5 3 1 2 2 1 2 1 Replay matches on path to root.
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