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I also think its the best way and probably the simplest logic too.

I think hash tables is not good in this situation. The restriction over the load factor cannot be reserved here, resulting in a big list of words on each key.

Please will you provide a detail steps
Thanks in advance :)

Following link gives you better understanding.
en.wikipedia.org/wiki/Trie
In leaf node you can put count(occurrences of the word).
So once you construct a trie, you can easily tell number of occurrences of word(Time Complexity for searching = size of word)

What can be more optimal than iterating over the document character only once?

I think the solution is to iterate over each word from the beginning, while adding each word to the Trie. When we try to add a word that already in, then we update the $->counter of that word to be $->counter=$->counter+1.

Note: $ is the closing character of each word on the Trie. To $ we add a field called counter that count each occurrence of that word.

As voora suggested, reading about Trie might help you understand the solution.

I like your comment :-)