Help with explanation

#1

prob: https://atcoder.jp/contests/abc156/tasks/abc156_c

editorial: https://img.atcoder.jp/abc156/editorial.pdf

Strictly speaking, when holding a meeting at coordinate x which can be represented as x =
R + d (d > 0) for example, the points of stamina that i-th person will spend is:
(Xi − (R + d))2 = ((R + d) − Xi)
2 = (R − Xi)
2 + d(R − Xi) + d
2
,
and since the second term of the rightmost hand side is non-negative and the third term is
positive, the points of stamina spent is strictly greater than when holding a meeting at coordinate
R. It is the same when holding a meeting at coordinate x such that x < L.

I’m not able to understand how they derived that equation among other things

#2

Let L be the smallest and R be the largest of the coordinates in which a person lives. At this time,
You don’t have to think about holding a rally at coordinates x such that x <L or R <x. I mean
Even in such cases, the physical strength consumed to participate is less than when holding a rally at coordinates L or R.
Because it never gets smaller.
Strictly speaking, if you hold a rally at coordinates x, for example x = R + d (d> 0), the i-th person attends the rally.
The physical strength consumed to do (Xi − (R + d)) 2 = ((R + d) − Xi)
2 = (R − Xi)
2 + d (R − Xi) + d
2
Since the second term on the far right side is non-negative and the third term is positive, compared to when a rally is held at coordinate R,
It really consumes more physical strength. The same is true if you hold a rally at coordinates x such that x <L.
Based on this idea, reduce the number of coordinates that need to be examined as candidates for a meeting place to at most 100
Can be done. When one meeting place is fixed, the total physical strength consumed by N people is calculated as O (N) times.

#3

I’m not able to understand what this is supposed to mean

#4

See this will be your relation
image
In this second term on the far right side is d(R − Xi)
& second term on the far right side is (R − Xi)^2
This is what i think they mean.

#5

understood that but what does the term being negative and positive have to do with the coordinates is not clear

#6

This question is also not clear to me. Can’t say much about that. Try do dry run it you will get the intuition or you can post a new thread too. As far as i think we have to calculate cost for every value between x[0…n] and cost is given by (X[j] - i) * (X[j] - i) . So there’s the use of coordinate.

#7

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