Segment Triplet Triangle Feasibility

Easy

You are given a table named Triangle that stores candidate segment triplets. Columns: x: length of segment 1 y: length of segment 2 z: length of segment 3 The tuple (x, y, z) is unique for each row. Task: For every row, determine whether these three segment lengths can form a valid triangle. A row is valid when all triangle-inequality checks hold: x + y > z x + z > y y + z > x Return exactly these columns in this order: x y z triangle Where triangle is: "Yes" if the row forms a valid triangle "No" otherwise Output row order is not semantically important. Supported submission environments: SQL (SQLite 3.27.2) Pandas (Python)

Input

Triangle:
| x  | y  | z  |
|----|----|----|
| 13 | 15 | 30 |
| 10 | 20 | 15 |

Output

[
  {"x":10,"y":20,"z":15,"triangle":"Yes"},
  {"x":13,"y":15,"z":30,"triangle":"No"}
]

Explanation

(13, 15, 30) fails because 13 + 15 is not greater than 30. (10, 20, 15) satisfies all three strict inequalities.

Input

Triangle:
| x | y | z |
|---|---|---|
| 5 | 5 | 5 |
| 3 | 4 | 5 |
| 1 | 1 | 2 |

Output

[
  {"x":1,"y":1,"z":2,"triangle":"No"},
  {"x":3,"y":4,"z":5,"triangle":"Yes"},
  {"x":5,"y":5,"z":5,"triangle":"Yes"}
]

Explanation

Equilateral and classic 3-4-5 rows are valid. (1, 1, 2) is degenerate because 1 + 1 equals 2.

Input

Triangle:
| x | y | z |
|---|---|---|
| 1 | 2 | 3 |
| 2 | 5 | 8 |
| 4 | 1 | 7 |

Output

[
  {"x":1,"y":2,"z":3,"triangle":"No"},
  {"x":2,"y":5,"z":8,"triangle":"No"},
  {"x":4,"y":1,"z":7,"triangle":"No"}
]

Explanation

Every row fails at least one triangle inequality, so all labels are No.

Constraints