CF1767A.Cut the Triangle

入门

通过率:0%

时间限制:2.00s

内存限制:512MB

AC君温馨提醒

该题目为【codeforces】题库的题目,您提交的代码将被提交至codeforces进行远程评测,并由ACGO抓取测评结果后进行展示。由于远程测评的测评机由其他平台提供,我们无法保证该服务的稳定性,若提交后无反应,请等待一段时间后再进行重试。

题目描述

You are given a non-degenerate triangle (a non-degenerate triangle is a triangle with positive area). The vertices of the triangle have coordinates (x1,y1)(x_1, y_1), (x2,y2)(x_2, y_2) and (x3,y3)(x_3, y_3).

You want to draw a straight line to cut the triangle into two non-degenerate triangles. Furthermore, the line you draw should be either horizontal or vertical.

Can you draw the line to meet all the constraints?

Here are some suitable ways to draw the line:

However, these ways to draw the line are not suitable (the first line cuts the triangle into a triangle and a quadrangle; the second line doesn't cut the triangle at all; the third line is neither horizontal nor vertical):

给你一个非退化三角形(非退化三角形指面积为正的三角形)。该三角形的三个顶点坐标分别为 (x1,y1)(x_1, y_1)、(x2,y2)(x_2, y_2) 和 (x3,y3)(x_3, y_3)。

你想画一条直线,将该三角形分割成两个非退化三角形。此外,你所画的直线必须是水平或垂直的。

你能否画出满足所有约束条件的直线?

以下是一些合适的画线方式:

然而,以下画线方式不合适(第一条直线将三角形分割成一个三角形和一个四边形;第二条直线根本没有切割三角形;第三条直线既非水平也非垂直):

输入格式

The first line contains one integer tt (1≤t≤1041 \le t \le 10^4) — the number of test cases.

Each test case consists of four lines. The first of them is empty. The ii-th of the next three lines contains two integers xix_i and yiy_i (1≤xi,yi≤1081 \le x_i, y_i \le 10^8) — the coordinates of the ii-th vertex of the triangle.

Additional constraint on the input: in each test case, the triangle formed by three vertices has positive area (i. e. it is non-degenerate).

第一行包含一个整数 tt(1≤t≤1041 \le t \le 10^4)—— 测试用例的数量。

每个测试用例由四行组成。其中第一行为空行。接下来三行中,第 ii 行包含两个整数 xix_i 和 yiy_i(1≤xi,yi≤1081 \le x_i, y_i \le 10^8)—— 表示三角形第 ii 个顶点的坐标。

输入的附加约束:在每个测试用例中,由这三个顶点构成的三角形面积为正(即该三角形是非退化的)。

输出格式

For each test case, print YES if it is possible to cut the triangle according to the statement, or NO otherwise. You may print each letter in any case (YES, yes, Yes will all be recognized as positive answer, NO, no and nO will all be recognized as negative answer).

对于每个测试用例,如果能按照题目描述切割该三角形,则输出 YES;否则输出 NO。你可以以任意大小写形式输出每个字母(例如 YES、yes、Yes 均被视为肯定回答,NO、no、nO 均被视为否定回答)。

输入输出样例

  • 输入#1

    4
    
    4 7
    6 8
    3 5
    
    4 5
    4 7
    6 8
    
    5 8
    1 8
    2 5
    
    3 6
    6 6
    6 3

    输出#1

    YES
    YES
    YES
    NO

输入解题思路,AI测评打分。不知道怎么写?

首页