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The Knuth–Plass algorithm is a line-breaking algorithm designed for use in Donald Knuth's typesetting program TeX.It integrates the problems of text justification and hyphenation into a single algorithm by using a discrete dynamic programming method to minimize a loss function that attempts to quantify the aesthetic qualities desired in the finished output.
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𝟕 𝟖 𝟗 𝟘 𝟙 𝟚 𝟛 𝟜 𝟝 𝟞 𝟟 U+1D7Ex 𝟠 𝟡 𝟢 𝟣 𝟤 𝟥 𝟦 𝟧 𝟨 𝟩 𝟪 𝟫 𝟬 𝟭 𝟮 𝟯 U+1D7Fx 𝟰 𝟱 𝟲 𝟳 𝟴 𝟵 𝟶 𝟷 𝟸 𝟹 𝟺 𝟻 𝟼 𝟽 𝟾 𝟿 Notes 1. ^ As of Unicode version 16.0 2. ^ Grey areas indicate non-assigned code points
In the case of our word, 11 such patterns can be matched, namely 1 c 4 l 4, 1 cy, 1 d 4 i 3 a, 4 edi, e 3 dia, 2 i 1 a, ope 5 d, 2 p 2 ed, 3 pedi, pedia 4, y 1 c. For each position in the word, TeX will calculate the maximum value obtained among all matching patterns, yielding en 1 cy 1 c 4 l 4 o 3 p 4 e 5 d 4 i 3 a 4.
Moreover, the positions of the zeroes in the inversion table give the values of left-to-right maxima of the permutation (in the example 6, 8, 9) while the positions of the zeroes in the Lehmer code are the positions of the right-to-left minima (in the example positions the 4, 8, 9 of the values 1, 2, 5); this allows computing the distribution ...
For example, summation of [1, 2, 4, 2] is denoted 1 + 2 + 4 + 2, and results in 9, that is, 1 + 2 + 4 + 2 = 9. Because addition is associative and commutative , there is no need for parentheses, and the result is the same irrespective of the order of the summands.
Express each term of the final sequence y 0, y 1, y 2, ... as the sum of up to two terms of these intermediate sequences: y 0 = x 0, y 1 = z 0, y 2 = z 0 + x 2, y 3 = w 1, etc. After the first value, each successive number y i is either copied from a position half as far through the w sequence, or is the previous value added to one value in the ...
This screenshot shows the formula E = mc 2 being edited using VisualEditor.The window is opened by typing "<math>" in VisualEditor. The visual editor shows a button that allows to choose one of three offered modes to display a formula.