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Edit On second thoughts, and after reading the answers, I realised that I had misinterpreted the statement from the book. As such, in hindsight, this wasn't a good example for the question. Regardless, my original question is still not answered, so I will try with a new example.

Is it correct to connect a question with a statement (as in below example), and if so, should the sentence end with a question mark or a full stop?

Do you want to have some ice cream and your English homework is due tomorrow?

The point I am trying to make is that "question part" has no connection to the statement which follows.

I found this question/statement in a book.

What is the running time of BFS if we represent its input graph by an adjacency matrix and modify the algorithm to handle this form of input? This connects a question (What is the running time of BFS if we represent its input graph by an adjacency matrix) and a statement (modify the algorithm to handle this form of input). Is it correct to place the question mark at the end?

Note: Despite the similar sounding title, this question is different from Question and a sentence in the same sentence.

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    I think we can read it as What is the running time of BFS [if we represent its input graph by an adjacency matrix and modify the algorithm to handle this form of input]? This reduces it to "What is X if Y?" – Damkerng T. Jan 28 '14 at 9:03
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It's just a question with an embedded conditional clause. The conditional clause is subordinate to the main clause, and the main clause is a question, so it gets a the question mark at the end. There's no statement. Compare this shorter sentence with comparable syntax:

"What is the running time if we have no legs?"

Would you question putting a question mark at the end of this sentence?

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The question does not consist a statement.

It is instead a conditional question with two conditions. You should read them as (if we represent its input graph by an adjacency matrix) plus (modify the algorithm to handle this form of input).

2 conditions in one question, and hence there is definite requirement of a question mark at the end.

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