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This is no mean feat; actually no spell-checker / grammar-checker does a perfect job. Something simple you could do is just to check whether each word is in a dictionary. The data structures you use will depend on the programming language chosen, but having your dictionary in an array would definitely be slow - you may want to use something like a hashtable or a binary tree instead. However, an array can work for a proof of concept.
If you write your program this way, something like an "Ode to the Spelling Checker" should pass without errors - although it is full of errors. The "Ode to the Spelling Checker" uses words that are in the dictionary - but the wrong word in each case, for example "eye" instead if "I", and "tolled" instead of "told". I paste a copy of the Ode here, for your easy reference - you'll have to read it out loud to make sense out of it!
Eye halve a spelling chequer
It came with my pea sea
It plainly marques four my revue
Miss steaks eye kin knot sea.
Eye strike a quay and type a word
And weight four it two say
Weather eye am wrong oar write
It shows me strait a weigh.
As soon as a mist ache is maid
It nose bee fore two long
And eye can put the error rite
It's rare lea ever wrong.
Eye have run this poem threw it
I am shore your pleased two no
It's letter perfect awl the weigh
My chequer tolled me sew.
What else can I help you with?
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