Algorithms & Data Structures
the bound is a claim, and it is checkable
Concept

Ordered code — where it appears

A prefix code whose code words sort in the same order as the symbols they stand for, so a tree built from it has its leaves in the alphabet's order. An operation reading a descent's output as sorted needs one, and a frequency-shaped code is not one.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

bits heldbalanced49,593huffman41,589the answer comes backbalanced: sorted · 26 operationshuffman: sorted · 24 operations32 documents · zipf lengths83.9% of the ordered tree

The smaller tree hands it back unsorted

A frequency-shaped tree is sixteen per cent smaller and returns its documents in code order. A balanced one is larger and returns them sorted. The trade is d log d comparisons against a saving, which is not close — until the answer is truncated.

practice · Index a fixed-length codeleaves in order␣acdefghilmnoprstuvwythe best ordered treeleaves in order␣acdefghilmnoprstuvwythe best tree of any shapeleaves in frequency order␣eahnrstdiloucfgmpvwythe symbols, in the order the descent reports them21 symbols in 2,048 positionsone set, 2 of 3 sorted

One set, three orders

The symbols an interval holds do not depend on the tree's shape. The order they come out in does, and a search that accumulates a running count as it reads them computes a plausible number that is wrong on eighty per cent of queries.

wrong · Symbol

Named alongside it

The objects these essays reach for when they reach for this one.

CorrectnessDescentHuffman codeWavelet treeBidirectional indexCheckDocument arrayDocument listingIndex sizeInterval symbols

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