K (ngn/k), 19 bytes

1+?{*(++,\x)?,x}',\ 

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Modeled after @Jonah's J answer.

• {...}',\ for each prefix of the (implicit) input...
• (++,\x) expand each prefix (of the current passed-in prefix) to the full length of that prefix (e.g., transform 1 1 2 from (1;1 1;1 1 2) into (1 1 1;1 1 1;1 1 2))
• *(...)?,x get the index of the first transformed prefix that matches the prefix itself
• 1+?{...} add one to the distinct indices