问题 C: Vector

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Given four three-dimensional vectors $A_{1}, A_{2}, A_{3}, A_{4}$ , determine whether there exist non-negative real numbers $x_{1}, x_{2}, x_{3}$ that satisfy the following equation:

$x_{1} A_{1} + x_{2} A_{2} + x_{3} A_{3} = A_{4}$

Here, $A_{i} = (a_{i 1}, a_{i 2}, a_{i 3})$ represents the components of the three-dimensional vector $A_{i}$ .

For example, $A_{1} = (3, 4, 4)$ , $A_{2} = (4, 3, 0)$ , $A_{3} = (2, 3, 2)$ , $A_{4} = (9, 10, 6)$ has a non-negative solution because $A_{1} + A_{2} + A_{3} = A_{4}$ .

The first line contains an integer $T$ $（ 1 \leq T \leq 1000 ）$ , representing the number of test cases.

Each test case consists of a single line containing $12$ integers

$a_{11}, a_{12}, a_{13}, a_{21}, a_{22}, a_{23}, a_{31}, a_{32}, a_{33}, a_{41}, a_{42}, a_{43} （ 0 \leq a_{ij} \leq 1 0^{4}, 1 \leq i \leq 4, 1 \leq j \leq 3 ）$ , representing the components of the four three-dimensional vectors $A_{1}, A_{2}, A_{3}, A_{4}$ .

For each test case, output a single line containing either "YES" or "NO", indicating whether a non-negative solution exists.

If a non-negative solution exists, output "YES"; otherwise, output "NO".

2
3 4 4 4 3 0 2 3 2 9 10 6 
0 3 1 0 1 3 4 0 4 4 1 10

YES
NO

2023“钉耙编程”中国大学生算法设计超级联赛（6）

问题 C: Vector

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问题 C: Vector

题目描述

输入格式

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输入样例 复制

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