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You are given an array of n distinct slot positions on a one-dimensional track, and you need to place m sensors into these slots. The separation between any two sensors is defined as the absolute difference between their slot positions.
Your goal is to distribute all m sensors into the available slots such that the minimum separation between any two adjacent sensors (in terms of position, not index) is as large as possible.
Return the maximum possible value of this minimum separation that can be achieved through optimal sensor placement.
This is a classic optimization problem where you need to balance the spacing of objects across discrete positions to achieve the most even distribution possible.
position = [1,2,3,4,7]
m = 33The optimal placement is to position the 3 sensors at slots 1, 4, and 7. The separations between consecutive sensors are: |4-1| = 3 and |7-4| = 3. The minimum separation is 3. No arrangement can achieve a minimum separation greater than 3 with 3 sensors in these positions.
position = [5,4,3,2,1,1000000000]
m = 2999999999With only 2 sensors to place, the optimal strategy is to maximize the distance between them. Placing sensors at positions 1 and 1000000000 yields a separation of 999999999, which is the maximum possible.
position = [1,3,5,7,9]
m = 34The positions are evenly spaced with gaps of 2. Placing 3 sensors at positions 1, 5, and 9 gives separations of 4 and 4. The minimum separation is 4, which is optimal for this configuration.
Constraints