Optimize bag_distance by calling bag_difference only once - #15475
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Assisted by: Antigravity CLI : Gemini Flash 3.5
Provides around 25% speedup for short inputs.
String.bag_distance/2only needs one bag-difference pass.The old code computed:
diff1 = bag_difference(bag1, bag2)
diff2 = bag_difference(bag2, bag1)
max(diff1, diff2)
For each grapheme count pair {count1, count2}:
max(count1 - count2, 0) - max(count2 - count1, 0) == count1 - count2
Summing over the bags gives:
diff1 - diff2 == length1 - length2
diff2 == diff1 - length1 + length2
So max(diff1, diff2) can be derived from diff1 and the two lengths:
if length1 >= length2, do: diff1, else: diff1 - length1 + length2
This preserves the exact same numerator passed to the final distance calculation while avoiding the second bag_difference/2 traversal.