某石油公司计划建造一条由东向西的主输油管道。该管道要穿过一个有 n 口油井的油田。从每口油井都要有一条输油管道沿最短路经(或南或北)与主管道相连。如果给定 n口油井的位置,即它们的 x 坐标(东西向)和 y 坐标(南北向),应如何确定主管道的最优位置,即使各油井到主管道之间的输油管道长度总和最小的位置?证明可在线性时间内确定主管道的最优位置,使得给定n口油井的位置,编程计算各油井到主管道之间的输油管道最小长度总和。
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