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This is a quick description of the viterbi aka dynamic programing
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algorthm.
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Its reason for existence is that wikipedia has become very poor on
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describing algorithms in a way that makes it useable for understanding
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them or anything else actually. It tends now to describe the very same
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algorithm under 50 different names and pages with few understandable
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by even people who fully understand the algorithm and the theory behind.
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Problem description: (that is what it can solve)
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assume we have a 2d table, or you could call it a graph or matrix if you
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prefer
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    O   O   O   O   O   O   O
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    O   O   O   O   O   O   O
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    O   O   O   O   O   O   O
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    O   O   O   O   O   O   O
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That table has edges connecting points from each column to the next column
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and each edge has a score like: (only some edge and scores shown to keep it
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readable)
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    O--5--O-----O-----O-----O-----O
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     2   / 7   / \   / \   / \   /
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      \ /   \ /   \ /   \ /   \ /
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    O7-/--O--/--O--/--O--/--O--/--O
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     \/ \/ 1/ \/ \/ \/ \/ \/ \/ \/
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     /\ /\ 2\ /\ /\ /\ /\ /\ /\ /\
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    O3-/--O--/--O--/--O--/--O--/--O
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      / \   / \   / \   / \   / \
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     1   \ 9   \ /   \ /   \ /   \
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    O--2--O--1--O--5--O--3--O--8--O
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Our goal is to find a path from left to right through it which
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minimizes the sum of the score of all edges.
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(and of course left/right is just a convention here it could be top down too)
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Similarly the minimum could be the maximum by just fliping the sign,
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Example of a path with scores:
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    O   O   O   O   O   O   O
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>---O.  O   O  .O-2-O   O   O
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      5.     .7      .
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    O   O-1-O   O   O 8 O   O
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                       .
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    O   O   O   O   O   O-1-O---> (sum here is 24)
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The viterbi algorthm now solves this simply column by column
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For the previous column each point has a best path and a associated
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score:
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    O-----5     O
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     \
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      \
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    O  \  1     O
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        \/
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        /\
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    O  /  2     O
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      /
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     /
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    O-----2     O
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To move one column forward we just need to find the best path and associated
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scores for the next column
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here are some edges we could choose from:
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    O-----5--3--O
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     \      \8
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      \       \
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    O  \  1--9--O
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        \/  \3
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        /\     \
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    O  /  2--1--O
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      /     \2
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     /        \
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    O-----2--4--O
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Finding the new best pathes and scores for each point of our new column is
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trivial given we know the previous column best pathes and scores:
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    O-----0-----8
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     \
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      \
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    O  \  0----10
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        \/
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        /\
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    O  /  0-----3
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      /     \
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     /        \
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    O     0     4
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the viterbi algorthm continues exactly like this column for column until the
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end and then just picks the path with the best score (above that would be the
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one with score 3)
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Author: Michael niedermayer
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Copyright LGPL
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