Problem C
Goat Rope
You have a fence post located at the point $(x, y)$ in the plane, to which a goat is tethered by a rope. You also have a house, which you model as an axis-aligned rectangle with diagonally opposite corners at the points $(x_1, y_1)$ and $(x_2, y_2)$. You want to pick a length of rope that guarantees the goat cannot reach the house.
Determine the minimum distance from the fence post to the house, so that you can make sure to use a shorter rope.
Input
The input consists of a single line containing six space-separated integers $x$, $y$, $x_1$, $y_1$, $x_2$, and $y_2$, each in the range $[-999, 999]$.
It is guaranteed that $x_1 < x_2$ and $y_1 < y_2$, and that $(x, y)$ is strictly outside the axis-aligned rectangle with corners at $(x_1, y_1)$ and $(x_2, y_2)$.
Output
Print the minimum distance from the goat’s post to the house, with a relative or absolute error no more than $0.001$.
| Sample Input 1 | Sample Output 1 |
|---|---|
7 3 0 0 5 4 |
2.0 |
| Sample Input 2 | Sample Output 2 |
|---|---|
6 0 0 2 7 6 |
2.0 |
| Sample Input 3 | Sample Output 3 |
|---|---|
3 -4 -3 -1 -1 2 |
5.0 |
