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Fix minor typos in README (#211)

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Ocn 2018-09-20 17:23:17 +04:00 committed by Oleksii Trekhleb
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10
src/algorithms/string/levenshtein-distance/README.md
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@ -50,7 +50,7 @@ to assist natural language translation based on translation memory.
Let’s take a simple example of finding minimum edit distance between Let’s take a simple example of finding minimum edit distance between
strings `ME` and `MY`. Intuitively you already know that minimum edit distance strings `ME` and `MY`. Intuitively you already know that minimum edit distance
here is `1` operation and this operation. And it is a replacing `E` with `Y`. But here is `1` operation and this operation. And it is replacing `E` with `Y`. But
let’s try to formalize it in a form of the algorithm in order to be able to let’s try to formalize it in a form of the algorithm in order to be able to
do more complex examples like transforming `Saturday` into `Sunday`. do more complex examples like transforming `Saturday` into `Sunday`.
@ -75,12 +75,12 @@ to transform an empty string to `MY`. And it is by inserting `Y` and `M`.
- Cell `(1:1)` contains number 0. It means that it costs nothing - Cell `(1:1)` contains number 0. It means that it costs nothing
to transform `M` into `M`. to transform `M` into `M`.
- Cell `(1:2)` contains red number 1. It means that we need 1 operation - Cell `(1:2)` contains red number 1. It means that we need 1 operation
to transform `ME` to `M`. And it is be deleting `E`. to transform `ME` to `M`. And it is by deleting `E`.
- And so on... - And so on...
This looks easy for such small matrix as ours (it is only `3x3`). But here you This looks easy for such small matrix as ours (it is only `3x3`). But here you
may find basic concepts that may be applied to calculate all those numbers for may find basic concepts that may be applied to calculate all those numbers for
bigger matrices (let’s say `9x7` one, for `Saturday → Sunday` transformation). bigger matrices (let’s say a `9x7` matrix for `Saturday → Sunday` transformation).
According to the formula you only need three adjacent cells `(i-1:j)`, `(i-1:j-1)`, and `(i:j-1)` to According to the formula you only need three adjacent cells `(i-1:j)`, `(i-1:j-1)`, and `(i:j-1)` to
calculate the number for current cell `(i:j)`. All we need to do is to find the calculate the number for current cell `(i:j)`. All we need to do is to find the
@ -97,13 +97,13 @@ Let's draw a decision graph for this problem.
You may see a number of overlapping sub-problems on the picture that are marked You may see a number of overlapping sub-problems on the picture that are marked
with red. Also there is no way to reduce the number of operations and make it with red. Also there is no way to reduce the number of operations and make it
less then a minimum of those three adjacent cells from the formula. less than a minimum of those three adjacent cells from the formula.
Also you may notice that each cell number in the matrix is being calculated Also you may notice that each cell number in the matrix is being calculated
based on previous ones. Thus the tabulation technique (filling the cache in based on previous ones. Thus the tabulation technique (filling the cache in
bottom-up direction) is being applied here. bottom-up direction) is being applied here.
Applying this principles further we may solve more complicated cases like Applying this principle further we may solve more complicated cases like
with `Saturday → Sunday` transformation. with `Saturday → Sunday` transformation.
![Levenshtein distance](https://cdn-images-1.medium.com/max/1600/1*fPEHiImYLKxSTUhrGbYq3g.jpeg) ![Levenshtein distance](https://cdn-images-1.medium.com/max/1600/1*fPEHiImYLKxSTUhrGbYq3g.jpeg)