turbopascal | Web-based Turbo Pascal compiler | Interpreter library

The algorithm in this answer attempts to arrange rectangles inside a fixed-width bounding box. Input to the algorithm is an array of rectangles whose topY and bottomY are specified. The algorithm computes the leftX and rightX for each rectangle. Rectangles are sized and positioned to avoid overlap. For example, the image below shows 7 rectangles that have been arranged by the algorithm. In region 1, the maximum overlap is 2, so the rectangles are drawn half width. Region 2 has no overlap, so the rectangle is full width. And region 3 has overlap 3, and therefore rectangles are one-third the width of the bounding box.

The algorithm has three major steps:

1. Fill the eventQueue based on the information in the input array. Each rectangle spawns two events: an EVENT_START with the topY, and an EVENT_STOP with the bottomY. The eventQueue is a priority queue, where the priority is based on the three values that define an event (evaluated in the order shown):
   • y: lower y values have priority.
   • type: EVENT_STOP has priority over EVENT_START.
   • rectID: lower rectID values have priority.
2. Search for the end of a region while:
   • storing the events into a regionQueue. The regionQueue is a simple FIFO, which allows the events to be processed a second time, after the extent of the region has been determined.
   • keeping track of the maxOverlap (which is limited by a function parameter). The maxOverlap determines the width of all rectangles within the region.
3. Drain the regionQueue while computing the X values for each rectangle in the region. This part of the algorithm employs an array called usedColumns. Each entry in that array is either -1 (indicates that the column is not in use) or a rectID (indicates which rectangle is using the column). When an EVENT_START is popped from the regionQueue, a column is assigned to the rectangle. When an EVENT_STOP is popped from the regionQueue, the column is returned to the unused (-1) state.

The input to the algorithm is an array of rectangles. The topY and bottomY values of those rectangles must be filled by the caller. The leftX and rightX values must be initialized to -1. If the X values are still -1 when the algorithm finishes, the rectangle could not be assigned a location because the overlapLimit was exceeded. All the other rectangles have a full set of coordinates, and are ready to be drawn.