# lec7 - Outline D-way merge a variation of mergesort...

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Outline D-way merge — a variation of mergesort Lowerbound proof A summary (see additional slides) Applications of sorting ADT: symbol table Lecture 7, Lowerbound and ADT Symbol Table p. 1

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Lowerbound: comparison-based model, lower- bound Relative order is determined by a compara- tor We may not inspect the values Decision tree: A decision tree is a full binary tree that rep- resents the comparisons between elements that are performed by a particular sorting algorithm Lecture 7, Lowerbound and ADT Symbol Table p. 2
Lowerbound on sorting for the worst case Number of possible outcomes — the num- ber of permutations: n ! The number of leaves in the decision tree — the number of permutations The worst-case running time of an algo- rithm — the longest root-to-leaf path The minimum height of a binary tree with n ! leaves — Θ( n log n ) Conclusion — no comparison-based sort- ing algorithm runs in o ( n log n ) time; Ω( n log n ) time bound for

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