reorg and add code for second edition
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if word_a[i] == word_b[j] then
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-- The letters match.
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cell[i][j] = cell[i - 1][j - 1] + 1
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else
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-- The letters don't match.
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cell[i][j] = math.max(cell[i - 1][j], cell[i][j - 1])
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end
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