Today I read the following problem that makes all elements in a sequence the same, using the minimum number of steps. Where each step increments or decrements an element by a constant integer d. And I know the minimum number of steps is the number of steps that make all elements the median of all elements. But I don't know how to prove it. please can someone help me prove it. Thanks for taking the time to read this blog,
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If you think of it like finding a point which minimises the sum of Manhattan distance from a point x SUM( |Xi-Xm| )
https://cs.stackexchange.com/questions/61090/proof-that-median-of-an-array-is-the-number-that-minimizes-the-sum-of-manhattan