点到线段距离 - 题目

#15283. 点到线段距离

统计

此題目在以下比賽中使用過：

XXII 赛前模板训练赛

给定平面上三个整点 $A, B, C$，你需要求点 $C$ 到线段 $AB$ 的距离。线段 $AB$ 可能会退化为一个点。

输入格式

每个测试点中包含多组测试数据。

输入的第一行包含一个整数 $T$，表示数据组数。对于每组数据：

输入只有一行，包含 6 个整数 $x_A, y_A, x_B, y_B, x_C, y_C$，分别描述三个点的坐标。

输出格式

对于每组测试数据，输出一行一个实数，表示最短距离。要求相对误差或绝对误差不超过 $10^{-9}$。

样例数据

样例输入

5
0 0 1 1 2 2
0 0 0 1 1 1
0 0 0 1 2 2
0 0 0 0 1 4
-1000000000 -1000000000 1000000000 1000000000 0 0

样例输出

1.4142135624
1.0000000000
2.2360679775
4.1231056256
0.0000000000

子任务

对于所有数据，$1 \le T \le 10^5$，点的每一维坐标为 $[-10^9, 10^9]$ 中的整数。点的坐标可能重合。

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