Python

Used sliding window for part 3. The off-by-one difference between i and j tripped me up for a while.

def part1(data: str, mentor: str = 'A'):
    mentors = 0
    pairs = 0
    for p in data:
        if p == mentor:
            mentors += 1
        elif p == mentor.lower():
            pairs += mentors
    return pairs

assert part1("ABabACacBCbca") == 5

def part2(data: str):
    all_pairs = 0
    for mentor in 'ABC':
        all_pairs += part1(data, mentor)
    return all_pairs    

assert part2("ABabACacBCbca") == 11

from collections import defaultdict

def part3(data: str, distance_limit: int = 1000, repeat: int = 1000):
    n = len(data)
    N = len(data) * repeat

    pairs = 0
    person_count = defaultdict(int)
    curr = 0

    # initialize the first window excluding the right boundary
    for j in range(distance_limit):
        person_count[data[j % n]] += 1

    for curr in range(N):
        # move left boundary (if applicable)
        if (i := curr - distance_limit - 1) >= 0:
            person_count[data[i % n]] -= 1
        # move right boundary (if applicable)
        if (j := curr + distance_limit) < N:
            person_count[data[j % n]] += 1
        # if mentee, record pairs
        if data[curr % n].islower():
            pairs += person_count[data[curr % n].upper()]

    return pairs
    

assert (t := part3("AABCBABCABCabcabcABCCBAACBCa", 10, 1)) == 34, f"Expected 34 but got {t}"
assert (t := part3("AABCBABCABCabcabcABCCBAACBCa", 10, 2)) == 72, f"Expected 72 but got {t}"
assert (t := part3("AABCBABCABCabcabcABCCBAACBCa", 1000, 1000)) == 3442321, f"Expected 3442321 but got {t}"-