Three matrices

2024-05-23 21:08

文章标签 three matrices

本文主要是介绍Three matrices，希望对大家解决编程问题提供一定的参考价值，需要的开发者们随着小编来一起学习吧！

点击打开链接 http://codeforces.com/contest/393/problem/B

Chubby Yang is studying linear equations right now. He came up with a nice problem. In the problem you are given an n × n matrix W, consisting of integers, and you should find two n × n matrices A and B, all the following conditions must hold:

Aij = Aji, for all i, j (1 ≤ i, j ≤ n);
Bij = - Bji, for all i, j (1 ≤ i, j ≤ n);
Wij = Aij + Bij, for all i, j (1 ≤ i, j ≤ n).

Can you solve the problem?

Input

The first line contains an integer n (1 ≤ n ≤ 170). Each of the following n lines contains n integers. The j-th integer in the i-th line is Wij(0 ≤ |Wij| < 1717).

Output

The first n lines must contain matrix A. The next n lines must contain matrix B. Print the matrices in the format equal to format of matrix Win input. It is guaranteed that the answer exists. If there are multiple answers, you are allowed to print any of them.

The answer will be considered correct if the absolute or relative error doesn't exceed 10 - 4.

Sample test(s) 
input 
2
1 4
3 2
output 
1.00000000 3.50000000
3.50000000 2.00000000
0.00000000 0.50000000
-0.50000000 0.00000000
input 
3
1 2 3
4 5 6
7 8 9
output 
1.00000000 3.00000000 5.00000000
3.00000000 5.00000000 7.00000000
5.00000000 7.00000000 9.00000000
0.00000000 -1.00000000 -2.00000000
1.00000000 0.00000000 -1.00000000
2.00000000 1.00000000 0.00000000

题目大意：给出一个矩阵w，要求构造出两个矩阵a，b；要求a是对称矩阵a[i][j] = a[j][i]，b是负对称矩阵b[i][j] = -b[j][i]，并且a[i][j] + b[i][j] = w[i][j]。

解题思路：a[i][j] + b[i][j] = w[i][j]; a[j][i] + b[j][i] = a[i][j] - b[i][j] = w[j][i];两式子相加相减除2就分别是a[i][j]和b[i][j].

这道题其实很简单，可是我却A了好几遍都没过，是在没发现有什么错误，而且测试数据都对，后来发现时这样的，数组开小了，希望大家在做题的时候可以看清题意。

#include <iostream>
#include <iomanip>
using namespace std;
int main()
{int n;double a[205][205];double flag;double b[205][205],c[205][205];while(cin>>n){for(int i=0; i<n; i++){for(int j=0; j<n; j++){cin>>a[i][j];if(i==j)b[i][j]=a[i][j];else{flag=(a[i][j]+a[j][i])/2;b[i][j]=b[j][i]=flag;c[i][j]=a[i][j]-flag;c[j][i]=-c[i][j];}}}for(int i=0; i<n; i++){for(int j=0; j<n; j++){if(j==0)cout<<fixed<<setprecision(8)<<b[i][j];elsecout<<fixed<<setprecision(8)<<" "<<b[i][j];}cout<<endl;}for(int i=0; i<n; i++){for(int j=0; j<n; j++){if(j==0)cout<<fixed<<setprecision(8)<<c[i][j];elsecout<<fixed<<setprecision(8)<<" "<<c[i][j];}cout<<endl;}}return 0;
}

这篇关于Three matrices的文章就介绍到这儿，希望我们推荐的文章对编程师们有所帮助！