题目描述
Sasha grew up and went to first grade. To celebrate this event her mother bought her a multiplication table MM with nn rows and nn columns such that Mij=ai⋅ajMij=ai⋅aj where a1,…,ana1,…,an is some sequence of positive integers.
Of course, the girl decided to take it to school with her. But while she was having lunch, hooligan Grisha erased numbers on the main diagonal and threw away the array a1,…,ana1,…,an. Help Sasha restore the array!
Input
The first line contains a single integer nn (3⩽n⩽1033⩽n⩽103), the size of the table.
The next nn lines contain nn integers each. The jj-th number of the ii-th line contains the number MijMij (1≤Mij≤1091≤Mij≤109). The table has zeroes on the main diagonal, that is, Mii=0Mii=0.
Output
In a single line print nn integers, the original array a1,…,ana1,…,an (1≤ai≤1091≤ai≤109). It is guaranteed that an answer exists. If there are multiple answers, print any.
Examples
input
5
0 4 6 2 4
4 0 6 2 4
6 6 0 3 6
2 2 3 0 2
4 4 6 2 0
output
2 2 3 1 2
input
3
0 99990000 99970002
99990000 0 99980000
99970002 99980000 0
output
9999 10000 9998
题解
题意
给你一个n*n的矩阵，其中M[i][j]=a[i]*a[j],求出a[1],…,a[n]。
题解
易知a[1]=sqrt(m[1][2]*m[1][3]/m[2][3])，可以求出a[1]；
a[2]=m[1][2]/a[1];
a[3]=m[2][3]/a[2];
…
代码
#include<algorithm>
#include<iostream>
#include<cmath>
using namespace std;
typedef long long ll;
ll m[1010][1010],a[1010];
int main()
{
int n;
cin>>n;
for(int i=1;i<=n;i++)
for(int j=1;j<=n;j++)
cin>>m[i][j];
a[1]=sqrt(m[1][2]*m[1][3]/m[2][3]);
cout<<a[1]<<' ';
for(int i=1;i<n;i++){
a[i+1]=m[i][i+1]/a[i];
cout<<a[i+1]<<' ';
}
}