    def train(self, text, vocab_size, verbose=False):
        assert vocab_size >= 256
        num_merges = vocab_size - 256

        # input text preprocessing
        text_bytes = text.encode("utf-8") # raw bytes
        ids = list(text_bytes) # list of integers in range 0..255

        # iteratively merge the most common pairs to create new tokens
        merges = {} # (int, int) -> int
        vocab = {idx: bytes([idx]) for idx in range(256)} # int -> bytes
        for i in range(num_merges):
            # count up the number of times every consecutive pair appears
            stats = get_stats(ids)
            # find the pair with the highest count
            pair = max(stats, key=stats.get)
            # mint a new token: assign it the next available id
            idx = 256 + i
            # replace all occurrences of pair in ids with idx
            ids = merge(ids, pair, idx)
            # save the merge
            merges[pair] = idx
            vocab[idx] = vocab[pair[0]] + vocab[pair[1]]
…
    def encode(self, text):
        # given a string text, return the token ids
        text_bytes = text.encode("utf-8") # raw bytes
        ids = list(text_bytes) # list of integers in range 0..255
        while len(ids) >= 2:
            # find the pair with the lowest merge index
            stats = get_stats(ids)
            pair = min(stats, key=lambda p: self.merges.get(p, float("inf")))
            # subtle: if there are no more merges available, the key will
            # result in an inf for every single pair, and the min will be
            # just the first pair in the list, arbitrarily
            # we can detect this terminating case by a membership check
            if pair not in self.merges:
                break # nothing else can be merged anymore
            # otherwise let's merge the best pair (lowest merge index)
            idx = self.merges[pair]
            ids = merge(ids, pair, idx)
        return ids
The problem
