2018.3.4【 AtCoder - 3867 】解题报告（矩阵知识，数学）

C - Takahashi's Information

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Time limit : 2sec / Memory limit : 256MB

Score: 300 points

Problem Statement

We have a 3×3 grid. A number ci,j is written in the square (i,j), where (i,j) denotes the square at the i-th row from the top and the j-th column from the left.
According to Takahashi, there are six integers a1,a2,a3,b1,b2,b3 whose values are fixed, and the number written in the square (i,j) is equal to ai+bj.
Determine if he is correct.

Constraints

• ci,j (1≤i≤3,1≤j≤3) is an integer between 0 and 100 (inclusive).

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Input

Input is given from Standard Input in the following format:

c1,1 c1,2 c1,3
c2,1 c2,2 c2,3
c3,1 c3,2 c3,3

Output

If Takahashi's statement is correct, print Yes; otherwise, print No.

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Sample Input 1

Copy

1 0 1
2 1 2
1 0 1

Sample Output 1

Copy

Yes

Takahashi is correct, since there are possible sets of integers such as: a1=0,a2=1,a3=0,b1=1,b2=0,b3=1.

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Sample Input 2

Copy

2 2 2
2 1 2
2 2 2

Sample Output 2

Copy

No

Takahashi is incorrect in this case.

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Sample Input 3

Copy

0 8 8
0 8 8
0 8 8

Sample Output 3

Copy

Yes

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Sample Input 4

Copy

1 8 6
2 9 7
0 7 7

Sample Output 4

Copy

No

【题目大意】

给一个3*3的矩阵，要求该矩阵元素可以表示成 ci,j=ai+bj，即9个元素是由a1，a2，a3，b1，b2，b3，交叉相加得到的。

【解题思路】

由于不用找出 a1，a2，a3，b1，b2，b3，判断存在即可。三斜线和相等即可。

【解题代码】

#include 
#include 
#include 
#include 
#include 
#include 

【收获与反思】