Gaussian elimination acwing 883 Gauss elimination for solving linear equations

Gauss elimination AcWing 883. Gauss elimination solves linear equations

Original link

AcWing 883. Gauss elimination solves linear equations

Algorithm tags

linear algebra Gauss elimination

Ideas

Code

#include<bits/stdc++.h>
#define int long long
#define abs fabs
#define rep(i, a, b) for(int i=a;i<b;++i)
#define Rep(i, a, b) for(int i=a;i>=b;--i)
using namespace std;
const int N = 105;
double a[N][N], eps = 1e-8;
int n;
inline int read(){
   int s=0,w=1;
   char ch=getchar();
   while(ch<'0'||ch>'9'){if(ch=='-')w=-1;ch=getchar();}
   while(ch>='0'&&ch<='9') s=s*10+ch-'0',ch=getchar();
   return s*w;
}
void put(int x) {
    if(x<0) putchar('-'),x=-x;
    if(x>=10) put(x/10);
    putchar(x%10^48);
}
int gu(){//  Gauss elimination , The answer lies in a[i][n] in ,0 <= i < n
    // c Representative column  r On behalf of the line 
    int c, r;
    //  Enumerate by column 
    for(c=0, r=0; c<n; ++c){
        int t=r;
        rep(i, r, n){
            if(abs(a[i][c])>abs(a[t][c])){//  Find the row with the largest absolute value 
                t=i;
            }
        }
        if(abs(a[t][c])<eps){
            continue;
        }
        rep(i, c, n+1){//  Change the line with the largest absolute value to the top 
            swap(a[t][i], a[r][i]);
        }
        Rep(i, n, c){//  Change the first place of the current line to 1
            a[r][i]/=a[r][c];
        }
        rep(i, r+1, n){//  Use the current row to eliminate all the following columns into 0
            if(abs(a[i][c])>eps){
                Rep(j, n, c){
                    a[i][j]-=a[r][j]*a[i][c];
                }
            }
        }
        ++r;
    }
    if(r<n){
        rep(i, r, n){
            if(abs(a[i][n])>eps){
                return 2;//  unsolvable 
            }
        }
        return 1;//  There are infinite sets of solutions 
    }
    Rep(i, n-1, 0){
        rep(j, i+1, n){
            a[i][n]-=a[i][j]*a[j][n];
        }
    }
    return 0;//  There is a unique solution 
}
signed main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    n=read();
    rep(i, 0, n){
        rep(j, 0, n+1){
            scanf("%lf", &a[i][j]);
        }
    }
    int t=gu();
    if(t==2){
        puts("No solution");
    }else if(t==1){
        puts("Infinite group solutions");
    }else{
        rep(i, 0, n){
            if(abs(a[i][n])<eps){//  Remove the output  -0.00  The situation of 
                a[i][n]=0;
            }
            printf("%.2lf\n", a[i][n]);
        }
    }
    return 0;
}

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