I’m given an array $ A = [a_1, a_2, ….a_n] $ using which I construct $ n-1$ contiguous line segments by drawing a line from $ (i,a_i)$ to $ (i+1, a_{i+1})$ . Now, I’m given $ q$ queries in the form of $ x_1, x_2, y, l, r$ where $ l$ and $ r$ are the range for the array $ A$ and the rest indicate a horizontal line segment $ L$ from $ (x_1, y)$ to $ (x_2, y)$ . For each query, I want to find total intersections of $ L$ and the segments in the range $ l$ and $ r$ in $ O(n+q)$ or $ O(n + q\log{n})$ complexity.
I was able to arrive at a solution that works in $ O(nq)$ which simply traverses each range and calculates whether $ L$ intersects with the segments or not.
I believe, some pre-processing can be done on $ A$ which can reduce the complexity.
Any leads will be appreciated!
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