Help with explanation

[raghav007 (Raghav Sharma)]

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

[aman212yadav (Aman Yadav)]

hello @raghav007

once leave this expression for some time and try to think logically.

let say u have n person living at n distinct locations and u have to organise a party a some location such that total distance they need to travel is minimised then where u will organise the party?

u will try to organise somewhere closer to center right?

say u have only two person one at 0 and one at n .
where u will organise the pary ?

[raghav007 (Raghav Sharma)]

@aman212yadav

u will try to organise somewhere closer to center right?

yeah towards the center

[aman212yadav (Aman Yadav)]

@aman212yadav

say u have only two person one at 0 and one at n .
where u will organise the pary ?

and in this case . . . . ?

[raghav007 (Raghav Sharma)]

here also in the center

[aman212yadav (Aman Yadav)]

right …

@raghav007

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.

so through this statement they just want to say the same thing.
i,e if leftmost person is at L and righmost person is at R then u only have to care about [L…R] location rest all location are useless (take more stamina).

now just run a brute force and find answer from each location [L…R] and print which consume less stamina

[raghav007 (Raghav Sharma)]

thanks, so does this mean that it is not necessary to understand the equations

[aman212yadav (Aman Yadav)]

@raghav007

so does this mean that it is not necessary to understand the equations

whatever works for you.
if u r able think logically thats fine .otherwise math and proofs are necessary

[aman212yadav (Aman Yadav)]

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