An energy company needs a control center to manage a distributed wind farm. Due to terrain and other ...

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An energy company needs a control center to manage a distributed wind farm. Due to terrain and other considerations, the cost to reach a group of windmills is specific to each location. Locate the control center to minimize the cost, and return the minimum cost. The control center is located at integral coordinates (cx, cy). Wind farm i is located at integral coordinates (x[i], y[i]). The distance to farm i is the Manhattan distance, distance[i] = |x[i] - cx| + |y[i] - cy|. The cost to connect farm i is premium[i] * distance[i], and the total cost is the sum of the cost to connect each farm. Determine the minimum cost to connect all the farms to the control center, and design an efficient algorithm for it.