Over the past 35 years a series of unmanned radar-mapping missions have produced a very detailed topographic map of the moon’s surface. This information has been digitized and is available in a gridlike format known as a Mercator projection. The topographical data for the next unmanned landing area is contained in a 100 × 100 array of grid points denoting the height above (or below) the average moon surface level for that 10 km × 10 km region. This particular landing region was chosen for its gradually changing topography; you may assume that linearly interpolating between any two adjacent grid-points will accurately describe the landscape between the grid points. Upon the rocket landing somewhere within the designated 10 km × 10 km region, it will discharge a number of autonomous robots. They will conduct a detailed exploration of the region and report their results back to the rocket via a line-of-sight lightwave communications link (flashes of light emitted by the robots and detected by the rocket). Once its exploration is complete, it is essential that a robot be able to find quickly the nearest location from which lineof-sight communication can occur, since it will have only a short battery life. The rocket designers have assured us that their receiving antenna will be 20 m above the site of the landing; the transmitting antenna on the robot will be 1 m above its site, wherever that may be in the region. Thus, given only the 100 × 100 array and the grid-point locations of the rocket and a robot, your job is to determine the grid point nearest the robot that will permit line-of-sight communication with the rocket. You may assume that the topographical data array contains only heights in integer values between +100 m and −100 m, and that both the rocket and the robots will be located on grid points when accessing your program.
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