Interview Question for Software Engineering Intern at Google:

Sort all left endpoints of your intervals into array a, sort all right endpoints into array b. Go along your left endpoints (array a) till you overstep the first element in the array b. If it happens => there is no common overlap for the set of all intervals. It means, that you found an interval with left endpoint being to the right of the right endpoint of another interval => these two do not overlap! Basically you have to check that all right endpoints are on the right (=less) than the minimal left endpoint.