洛谷P2455 [SDOI2006]线性方程组(高斯消元)

3
2 -1 1 1
4 1 -1 5
1 1 1 0

x1=1.00
x2=0
x3=-1.00

// luogu-judger-enable-o2
#include<cstdio>
#include<algorithm>
const double eps = 1e-9;
inline int read() {
    char c = getchar(); int x = 0, f = 1;
    while(c < '0' || c > '9') { if(c == '-')f = -1; c = getchar(); }
    while(c >= '0' && c <= '9') x = x * 10 + c - '0', c = getchar();
    return x * f;
}
const int MAXN = 101;
int N;
double a[MAXN][MAXN];
double Ans[MAXN];
double fabs(double x) {return x < 0 ? -x : x;}
void Gauss() {
    for(int i = 1; i <= N; i++) {
        int mx = i;
        for(int j = i + 1; j <= N; j++) 
            if(fabs(a[j][i]) > fabs(a[mx][i])) mx = j;
        if(mx != i) std::swap(a[mx], a[i]);
        if(fabs(a[i][i]) >= eps)
            for(int j = 1; j <= N; j++) {
                if(i == j) continue;
                double temp = a[j][i] / a[i][i];
                for(int k = 1; k <= N + 1; k++)
                    a[j][k] -= temp * a[i][k];
            }
    }
    int NoSolution = 0, ManySolution = 0;
    for(int i = 1; i <= N; i++) {
        int num = 0;
        for(int j = 1; j <= N + 1; j++) 
            if(a[i][j] == 0) num ++;
            else break;
        if(num == N + 1) ManySolution = 1;
        if(num == N && a[i][N+1] != 0) NoSolution = 1;
    }
    if(NoSolution) {printf("-1");return ;}
    if(ManySolution) {printf("0");return ;}
    for(int i = N; i >= 1; i--) {
        Ans[i] = a[i][N+1] / a[i][i];
        for(int j = i; j >= 1; j--)
            a[j][N+1] -= a[j][i] * Ans[i];
    }
    for(int i = 1; i <= N; i++)
        printf("x%d=%.2lf\n",i,Ans[i]);
}
int main() {
    #ifdef WIN32
    freopen("a.in", "r", stdin);
    #endif
    N = read();
    for(int i = 1; i <= N; i++)
        for(int j = 1; j <= N + 1; j++)
            a[i][j] = read();
    Gauss();
    return 0;
}