Coordinate Reflection Pairs

Medium

You are given a table of 2D integer coordinates: Table: Coordinates X: integer x-axis value Y: integer y-axis value Rows may repeat, and duplicate coordinates are allowed. A coordinate pair (x1, y1) has a reflection partner when another row (x2, y2) exists such that: x1 = y2 y1 = x2 Your task is to return all unique coordinate pairs (x, y) that satisfy one of the following: x < y and (y, x) exists in the table. x = y and the coordinate (x, x) appears at least twice. Output requirements: Return columns in this exact order: x, y Return only unique rows Sort result by x ASC, then y ASC Supported submission environments: SQL (SQLite 3.27.2) Pandas (Python)

Example 1

Input

Coordinates:
| X  | Y  |
|----|----|
| 20 | 20 |
| 20 | 20 |
| 20 | 21 |
| 21 | 20 |
| 23 | 22 |
| 22 | 23 |

Output

[
  {"x":20,"y":20},
  {"x":20,"y":21},
  {"x":22,"y":23}
]

Explanation

(20,20) is included because it appears at least twice. (20,21) and (21,20) form a reflected pair, so only the canonical row with x < y is kept. Likewise, (22,23) is kept from the pair (23,22) and (22,23).

Example 2

Input

Coordinates:
| X | Y |
|---|---|
| 5 | 5 |
| 4 | 7 |
| 9 | 1 |

Output

[]

Explanation

(5,5) appears only once, so it does not qualify. Neither (4,7) nor (9,1) has a reverse partner.

Example 3

Input

Coordinates:
| X  | Y  |
|----|----|
| -3 | 8  |
| 8  | -3 |
| 0  | 0  |
| 0  | 0  |
| 10 | 1  |
| 10 | 1  |

Output

[
  {"x":-3,"y":8},
  {"x":0,"y":0}
]

Explanation

Negative values are valid. The pair (-3,8) has reverse (8,-3), and (0,0) appears twice. Duplicates of (10,1) do not help because (1,10) is missing.

Constraints

1 <= number of rows in Coordinates <= 100000
-1000000000 <= X, Y <= 1000000000
Duplicate rows are allowed
Result must include each valid pair only once
For non-diagonal pairs, keep only canonical orientation x < y
For diagonal pairs (x = y), include only when frequency >= 2
Return exactly two columns: x, y
Sort output by x ASC, y ASC
Use SQLite 3.27.2 semantics for SQL submissions
For Pandas submissions, return a DataFrame with columns [x, y]