Optimize Dice's Coefficient

Dice's Coefficient is a simple statistic that measures the similarities of two strings. A Dice's Coefficient of 1 means the strings are exactly the same, and 0 means they have no similarities at all.

Computing Dice's Coefficient is really easy. It goes like this:

1. For string1, turn it into a set of trigrams trigrams1
2. For string2, turn it into a set of trigrams trigrams2
3. Calculate the size of the intersection of those two sets (number of trigrams)
4. Multiply the intersection size by two and divide it by the sum of the sizes of trigrams1 and trigrams2 (in triagrams)

Example:

For string1 = "hello" and string2 = "help":

1. trigrams1 = {"hel", "ell", "llo"} (size 3)
2. trigrams2 = {"hel", "elp"} (size 2)
3. Intersection: {"hel"} (size 1)
4. Dice's Coefficient: (2 * 1) / (3 + 2) = 0.4

This problem is available in two languages — pick whichever you prefer:

Language	Directory	Baseline file	File to fix	Run benchmark
JavaScript	js/	dice_baseline.js	dice_fast.js	node js/bench.js
C++	c++/	dice_baseline.cpp	dice_fast.cpp	cd c++ && make run

Windows (C++): Use make -f Makefile.win run instead of make run.

The baseline file contains a gold-standard implementation of Dice's Coefficient. The only problem is that it's slow. The dice_fast file contains a hacky attempt to speed it up by approximating the answer. It succeeds in speeding up the result, but fails by returning an incorrect answer - the result is 14.1% off from the baseline on one of the test cases.

Your job is to fix dice_fast - make the function as fast as possible, while returning a result within 5% of the baseline.

Get the % of baseline number as low as possible while not failing the tests.

Test data lives in test_data.json at the project root and is shared between both implementations. The C++ build downloads nlohmann/json on first run, so you'll need network access the first time you build.

Feel free to google things and/or use a profiler, but don't use any AI.

It shouldn't be too hard to get to ~50% of baseline with 0% degradation.

This is what Ivo's Head of Engineering got:

(index)	length	Baseline	Baseline ms	fastDice	fastDice ms
0	5	'0.40'	'0.01'	'✅'	'0.00 (67.2%) 🚀🚀🚀'
1	61183	'0.98'	'12.40'	'✅'	'0.79 (6.4%) 🚀🚀🚀🚀🚀🚀🚀🚀🚀'
2	360606	'0.99'	'22.09'	'✅'	'2.20 (10.0%) 🚀🚀🚀🚀🚀🚀🚀🚀🚀'
3	145169	'0.23'	'56.47'	'✅ (0.24: 3.0% off)'	'2.59 (4.6%) 🚀🚀🚀🚀🚀🚀🚀🚀🚀'

Total elapsed (baseline): 90.97ms
Total elapsed (fastDice): 5.59ms
Runtime (fastDice): 6.1% of baseline 🚀🚀🚀🚀🚀🚀🚀🚀🚀
✅ All test cases passed