Naive Approach
In a simple case, the intervals do not overlap and they can be inserted into a simple binary search tree and queried in O(log n) time. However, with arbitrarily overlapping intervals, there is no way to compare two intervals for insertion into the tree since orderings sorted by the beginning points or the ending points may be different. A naive approach might be to build two parallel trees, one ordered by the beginning point, and one ordered by the ending point of each interval. This allows discarding half of each tree in O(log n) time, but the results must be merged, requiring O(n) time. This gives us queries in O(n + log n) = O(n), which is no better than brute-force.
Interval trees solve this problem. This article describes two alternative designs for an interval tree, dubbed the centered interval tree and the augmented tree.
Read more about this topic: Interval Tree
Famous quotes containing the words naive and/or approach:
““The days have outnumbered
my fingers and toes.
What can I count with now?”
Saying this,
the naive girl cries.”
—Hla Stavhana (c. 50 A.D.)
“The white man regards the universe as a gigantic machine hurtling through time and space to its final destruction: individuals in it are but tiny organisms with private lives that lead to private deaths: personal power, success and fame are the absolute measures of values, the things to live for. This outlook on life divides the universe into a host of individual little entities which cannot help being in constant conflict thereby hastening the approach of the hour of their final destruction.”
—Policy statement, 1944, of the Youth League of the African National Congress. pt. 2, ch. 4, Fatima Meer, Higher than Hope (1988)