.
building and running
 set up rust the raw way or install nix and start a
nixshell

cargo run  help
for example:
cargo run  from common to coming matrix
You can of course just run the executable directly as well.
explanation
The minimum edit distance for two strings is the minimum number of insertion, deletion, or replacement operations required to convert the first string to the second. It is generally calculated using a grid, where each value in the cells is the minimum edit distance for the substring that ends at that column and row. For example:
In this case, 4 is the minimum edit distance.
steps to build the grid
 first, the initial cells for header column and row (
grid[header_row][1]
andgrid[first_row][0]
) represent an empty string,""
, or#
in NLP lingo. the cost for these is 0.  from the initial 0 cell, for each word, add the accumulating insertion cost for each character (i.e. 1, 2, 3, 4...length of word).
 for each of the empty cells, the cost of each operation is found in adjascent cells: