# 3D空間で点を直線距離でソートする

1. You have a cubic 3D space `x,y,z` of size
`S` integer units, such as ```0 <= x,y,z <= S```.
2. You get from
default input methods
an array of points `P`
represented as `x,y,z` integer coordinates, in any
reasonable format as you like, for example:
`[x1,y1,z1],[x2,y2,z2],[x3,y3,z3] ... [xn,yn,zn]`.
3. All the `P` values will be in the above said cubic
3D space, such as `0 <= x,y,z <= S`.
4. The possible total number of `P` will be ```1 <= P <= S3```.
5. You also get as input the `x,y,z` integer
coordinates of the base point `B` and the 3D
cube size `S`.

タスク

あなたの目標は、基点 `B` から直線（ユークリッド）距離でソートされたポイント
`P` を好みのフォーマットで出力することです。

Rules

1. If you find more than one point `P` that are
equidistant from `B` you must output all of the
equidistant `P`‘s in your preferred order.
2. It is possible that a point `P` will coincide with
`B`, so that their distance is `0`, you must
output that point.
3. This is a challenge, so the shortest code wins.

4. Standard loopholes
are forbidden.
5. Code explanations are appreciated.

テストケース

``````Input:
S (size), [B (base point x,y,z)], [P1 (x,y,z)], [P2], [P3], [P4], [P5], [...], [Pn]
10, [5,5,5], [0,0,0], [10,10,10], [2,0,8], [10,3,1], [4,4,5], [5,5,5], [5,5,4]

Output:
[5,5,5], [5,5,4], [4,4,5], [2,0,8], [10,3,1], [0,0,0], [10,10,10]

- - -

Input:
5, [2, 3, 3], [3, 0, 4], [5, 0, 3], [0, 2, 4], [0, 3, 5], [4, 2, 1], [2, 2, 2], [3, 1, 2], [3, 1, 0], [1, 3, 2], [2, 3, 1], [3, 1, 5], [4, 0, 0], [4, 3, 1], [0, 5, 5], [1, 5, 1], [3, 1, 4], [2, 2, 2], [0, 2, 5], [3, 3, 5], [3, 3, 0], [5, 4, 5], [4, 1, 3], [5, 1, 1], [3, 5, 3], [1, 5, 3], [0, 5, 2], [4, 3, 3], [2, 1, 1], [3, 3, 0], [5, 0, 4], [1, 5, 2], [4, 2, 3], [4, 2, 1], [2, 5, 5], [3, 4, 0], [3, 0, 2], [2, 3, 2], [3, 5, 1], [5, 1, 0], [2, 4, 3], [1, 0, 5], [0, 2, 5], [3, 4, 4], [2, 4, 0], [0, 1, 5], [0, 5, 4], [1, 5, 1], [2, 1, 0], [1, 3, 4], [2, 2, 2], [4, 2, 4], [5, 5, 4], [4, 4, 0], [0, 4, 1], [2, 0, 3], [3, 1, 5], [4, 4, 0], [2, 5, 1], [1, 2, 4], [4, 3, 1], [0, 2, 4], [4, 5, 2], [2, 0, 1], [0, 0, 2], [4, 1, 0], [5, 4, 3], [2, 5, 2], [5, 4, 4], [4, 4, 3], [5, 5, 1], [4, 0, 2], [1, 3, 5], [4, 2, 0], [0, 3, 1], [2, 2, 0], [0, 4, 5], [3, 2, 0], [0, 2, 1], [1, 2, 2], [2, 5, 3], [5, 5, 2], [5, 2, 4], [4, 5, 5], [2, 1, 2], [5, 4, 3], [4, 5, 4], [2, 3, 1], [4, 4, 4], [3, 0, 0], [2, 4, 5], [4, 3, 3], [3, 5, 3], [4, 0, 0], [1, 1, 1], [3, 1, 3], [2, 5, 5], [0, 0, 5], [2, 0, 2], [1, 0, 3], [3, 1, 4], [1, 2, 5], [4, 1, 3], [1, 4, 5], [3, 1, 4], [3, 5, 1], [5, 1, 4], [1, 0, 4], [2, 2, 0], [5, 2, 1], [0, 5, 3], [2, 1, 1], [0, 3, 0], [4, 5, 5], [3, 4, 2], [5, 3, 3], [3, 1, 1], [4, 0, 1], [5, 0, 5], [5, 0, 4], [1, 4, 3], [5, 4, 2], [5, 4, 0], [5, 1, 0], [0, 0, 1], [5, 3, 0]

Output:
[2, 4, 3], [2, 3, 2], [1, 3, 4], [1, 3, 2], [2, 2, 2], [1, 4, 3], [2, 2, 2], [2, 2, 2], [1, 2, 2], [3, 4, 2], [1, 2, 4], [3, 4, 4], [2, 5, 3], [4, 3, 3], [2, 3, 1], [4, 3, 3], [2, 3, 1], [1, 3, 5], [4, 4, 3], [2, 5, 2], [3, 1, 3], [1, 5, 3], [4, 2, 3], [2, 1, 2], [3, 5, 3], [2, 4, 5], [3, 3, 5], [3, 5, 3], [3, 1, 4], [0, 2, 4], [0, 2, 4], [1, 2, 5], [3, 1, 2], [3, 1, 4], [3, 1, 4], [4, 2, 4], [1, 4, 5], [4, 4, 4], [1, 5, 2], [4, 3, 1], [0, 5, 3], [2, 1, 1], [4, 1, 3], [4, 3, 1], [2, 5, 5], [0, 3, 5], [4, 1, 3], [2, 5, 1], [2, 1, 1], [0, 3, 1], [2, 5, 5], [1, 1, 1], [0, 4, 5], [4, 5, 4], [4, 5, 2], [0, 2, 1], [1, 5, 1], [5, 3, 3], [0, 5, 2], [3, 5, 1], [3, 5, 1], [0, 2, 5], [1, 5, 1], [4, 2, 1], [3, 1, 5], [3, 1, 1], [0, 2, 5], [4, 2, 1], [0, 5, 4], [0, 4, 1], [2, 0, 3], [3, 1, 5], [2, 4, 0], [2, 2, 0], [2, 0, 2], [3, 3, 0], [3, 3, 0], [5, 4, 3], [1, 0, 3], [5, 4, 3], [2, 2, 0], [3, 0, 2], [5, 4, 4], [5, 4, 2], [1, 0, 4], [3, 0, 4], [5, 2, 4], [3, 2, 0], [3, 4, 0], [0, 1, 5], [0, 5, 5], [4, 5, 5], [4, 5, 5], [0, 3, 0], [2, 0, 1], [2, 1, 0], [4, 4, 0], [5, 1, 4], [5, 5, 4], [5, 2, 1], [3, 1, 0], [5, 4, 5], [4, 4, 0], [1, 0, 5], [4, 2, 0], [0, 0, 2], [4, 0, 2], [5, 5, 2], [4, 1, 0], [5, 5, 1], [0, 0, 1], [5, 1, 1], [4, 0, 1], [0, 0, 5], [5, 0, 3], [5, 3, 0], [5, 4, 0], [3, 0, 0], [5, 0, 4], [5, 0, 4], [5, 1, 0], [4, 0, 0], [4, 0, 0], [5, 0, 5], [5, 1, 0]

- - -

Input:
10, [1, 9, 4], [4, 6, 2], [7, 5, 3], [10, 5, 2], [9, 8, 9], [10, 5, 10], [1, 5, 4], [8, 1, 1], [8, 6, 9], [10, 4, 1], [3, 4, 10], [4, 7, 0], [7, 10, 9], [5, 7, 3], [6, 7, 9], [5, 1, 4], [4, 3, 8], [4, 4, 9], [6, 9, 3], [8, 2, 6], [3, 5, 1], [0, 9, 0], [8, 4, 3], [0, 1, 1], [6, 7, 6], [4, 6, 10], [3, 9, 10], [8, 3, 1], [10, 1, 1], [9, 10, 6], [2, 3, 9], [10, 5, 0], [3, 2, 1], [10, 2, 7], [8, 4, 9], [5, 2, 4], [0, 8, 9], [10, 1, 6], [0, 8, 10], [5, 10, 1], [7, 4, 5], [4, 5, 2], [0, 2, 0], [8, 3, 3], [6, 6, 6], [3, 0, 2], [0, 1, 1], [10, 10, 8], [6, 2, 8], [8, 8, 6], [5, 4, 7], [10, 7, 4], [0, 9, 2], [1, 6, 6], [8, 5, 9], [3, 7, 4], [5, 6, 6], [3, 1, 1], [10, 4, 5], [1, 5, 7], [8, 6, 6], [4, 3, 7], [2, 1, 0], [6, 4, 2], [0, 7, 8], [8, 3, 6], [9, 2, 0], [1, 3, 8], [4, 4, 6], [5, 8, 9], [9, 4, 4], [0, 7, 3], [8, 3, 4], [6, 7, 9], [8, 7, 0], [0, 7, 7], [8, 10, 10], [10, 2, 5], [6, 9, 5], [6, 2, 7], [0, 9, 6], [1, 4, 1], [4, 3, 1], [5, 7, 3], [9, 6, 8], [4, 1, 7], [4, 0, 8], [3, 4, 7], [2, 3, 6], [0, 0, 7], [5, 3, 6], [7, 3, 4], [6, 7, 8], [3, 7, 9], [1, 9, 10], [2, 1, 2], [2, 8, 2], [0, 3, 0], [1, 1, 9], [3, 5, 2], [10, 5, 3], [5, 2, 9], [6, 9, 0], [9, 5, 0], [7, 1, 10], [3, 3, 8], [2, 5, 1], [3, 10, 10], [6, 2, 2], [10, 7, 2], [4, 3, 1], [4, 2, 1], [4, 2, 8], [6, 8, 5], [3, 10, 0], [1, 1, 7], [6, 9, 6], [6, 2, 4], [5, 5, 7], [5, 4, 5], [9, 8, 1], [9, 8, 1], [0, 10, 6], [1, 1, 9], [3, 8, 8], [3, 1, 5], [5, 7, 4], [4, 3, 6], [5, 4, 7], [6, 0, 8], [7, 8, 1], [9, 8, 4], [2, 10, 0], [3, 4, 5], [9, 3, 10], [7, 4, 1], [2, 1, 9], [10, 8, 1], [10, 3, 7], [2, 0, 6], [3, 8, 4], [10, 0, 2], [9, 9, 10], [8, 9, 5], [4, 10, 2], [8, 3, 4], [4, 2, 10], [9, 1, 6], [6, 1, 3], [4, 1, 3], [2, 9, 0], [5, 6, 5], [8, 8, 3], [5, 5, 0], [7, 6, 9], [1, 1, 5], [3, 0, 4], [1, 10, 6], [8, 0, 2], [0, 7, 3], [8, 9, 8], [2, 1, 8], [3, 1, 10], [4, 5, 9], [7, 6, 10], [3, 6, 10], [5, 9, 8], [9, 3, 3], [2, 2, 3], [9, 9, 0], [7, 2, 2], [0, 0, 9], [8, 7, 4], [9, 2, 9], [0, 6, 4], [9, 4, 3], [10, 1, 3], [5, 9, 10], [5, 10, 6], [6, 3, 10],

Output:
[1, 10, 6], [3, 8, 4], [0, 9, 6], [0, 9, 2], [2, 8, 2], [0, 7, 3], [0, 7, 3], [0, 10, 6], [3, 7, 4], [0, 6, 4], [1, 6, 6], [0, 7, 7], [4, 10, 2], [1, 5, 4], [0, 9, 0], [2, 9, 0], [2, 10, 0], [5, 7, 4], [5, 7, 3], [5, 10, 6], [5, 7, 3], [0, 7, 8], [3, 10, 0], [3, 8, 8], [4, 6, 2], [3, 5, 2], [1, 5, 7], [5, 10, 1], [6, 9, 3], [6, 9, 5], [5, 6, 5], [2, 5, 1], [0, 8, 9], [6, 8, 5], [5, 6, 6], [6, 9, 6], [4, 5, 2], [4, 7, 0], [3, 5, 1], [3, 4, 5], [5, 9, 8], [6, 7, 6], [3, 7, 9], [1, 4, 1], [1, 9, 10], [4, 4, 6], [0, 8, 10], [6, 6, 6], [3, 4, 7], [3, 9, 10], [5, 5, 7], [3, 10, 10], [2, 3, 6], [6, 9, 0], [5, 8, 9], [5, 4, 5], [6, 7, 8], [7, 8, 1], [5, 5, 0], [4, 3, 6], [3, 6, 10], [8, 9, 5], [5, 4, 7], [4, 5, 9], [5, 4, 7], [2, 2, 3], [8, 8, 3], [1, 3, 8], [5, 9, 10], [0, 3, 0], [7, 5, 3], [8, 7, 4], [4, 3, 1], [8, 8, 6], [6, 4, 2], [4, 3, 7], [6, 7, 9], [4, 6, 10], [4, 3, 1], [6, 7, 9], [3, 3, 8], [5, 3, 6], [4, 4, 9], [4, 3, 8], [8, 6, 6], [3, 2, 1], [7, 4, 5], [7, 10, 9], [2, 3, 9], [5, 2, 4], [1, 1, 5], [3, 4, 10], [8, 9, 8], [9, 8, 4], [0, 2, 0], [4, 2, 1], [3, 1, 5], [2, 1, 2], [8, 7, 0], [9, 10, 6], [7, 4, 1], [7, 6, 9], [7, 3, 4], [1, 1, 7], [0, 1, 1], [4, 2, 8], [9, 8, 1], [0, 1, 1], [4, 1, 3], [6, 2, 4], [9, 8, 1], [8, 4, 3], [3, 1, 1], [6, 2, 2], [5, 1, 4], [9, 9, 0], [7, 6, 10], [2, 1, 0], [2, 1, 8], [4, 1, 7], [8, 6, 9], [6, 2, 7], [8, 3, 4], [8, 3, 4], [10, 7, 4], [3, 0, 4], [8, 3, 3], [8, 10, 10], [2, 0, 6], [9, 6, 8], [10, 7, 2], [1, 1, 9], [8, 3, 6], [1, 1, 9], [7, 2, 2], [3, 0, 2], [9, 4, 4], [8, 5, 9], [2, 1, 9], [6, 1, 3], [6, 2, 8], [5, 2, 9], [9, 4, 3], [9, 8, 9], [0, 0, 7], [10, 8, 1], [4, 2, 10], [8, 3, 1], [9, 5, 0], [6, 3, 10], [10, 10, 8], [10, 5, 3], [8, 4, 9], [9, 9, 10], [10, 5, 2], [9, 3, 3], [8, 2, 6], [3, 1, 10], [4, 0, 8], [0, 0, 9], [10, 4, 5], [10, 5, 0], [10, 4, 1], [8, 1, 1], [6, 0, 8], [10, 3, 7], [9, 2, 0], [10, 2, 5], [9, 1, 6], [10, 5, 10], [8, 0, 2], [9, 3, 10], [7, 1, 10], [9, 2, 9], [10, 2, 7], [10, 1, 3], [10, 1, 6], [10, 1, 1], [10, 0, 2]

- - -

Input:
10000, [8452, 3160, 6109], [7172, 5052, 4795], [9789, 4033, 2952], [8242, 213, 3835], [177, 7083, 908], [3788, 3129, 3018], [9060, 464, 2701], [6537, 8698, 291], [9048, 3860, 6099], [4600, 2696, 4854], [2319, 3278, 9825]

Output:
[9048, 3860, 6099], [7172, 5052, 4795], [9789, 4033, 2952], [8242, 213, 3835], [4600, 2696, 4854], [9060, 464, 2701], [3788, 3129, 3018], [2319, 3278, 9825], [6537, 8698, 291], [177, 7083, 908]
``````
ベストアンサー

# 05AB1E, 4 bytes

``````ΣαnO
``````

オンラインで試してみてください！

``````Σ        # sort by
O     # sum of
n      # square of
α       # absolute difference between current value and second input
``````