约旦-高斯消元法

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <cmath>

#define LL long long
#define DB double

using namespace std;

const int kN = 105;
const DB kEps = 1e-16;

int n, sum;
DB a[kN][kN], ans[kN];

signed main() {
	scanf("%d", &n);
	for (int i = 1; i <= n; ++i) {	
		for (int j = 1;j <= n + 1; ++j) {
			scanf("%lf", &a[i][j]);
		}
	}
	for (int i = 1; i <= n; ++i) {
		int p = i;
		for (int j = i + 1; j <= n; ++j) {
			if(fabs(a[j][i]) > fabs(a[p][i])) {
				swap(p, j);
			}
		}
		if(fabs(a[p][i]) < kEps) {continue;}
		if (p != i) {	
			for (int j = i; j <= n + 1; ++j) {
				swap(a[p][j], a[i][j]);
			}
		}
		DB div = a[i][i]; 
		for (int j = i; j <= n + 1; ++j) {
			a[i][j] /= div;
		}
		for (int j = 1; j <= n; ++j) {
			if(j != i) {
				DB w = a[j][i] / a[i][i];
				for (int k = i; k <= n + 1; ++k) {
					a[j][k] -= a[i][k] * w;
				}
			}
		}
		sum++;
	}
	for (int i = 1; i <= n; ++i) {
		ans[i] = a[i][n + 1];
	}
	if(sum < n) {
		for (int i = 1; i <= n; ++i) {
			if(fabs(ans[i]) < kEps && fabs(a[i][n + 1]) > kEps) {
				printf("-1\n");return 0;
			}
		}
		printf("0\n");return 0;
	}
	for (int i = 1; i <= n; ++i) {
		printf("x%d=", i);
		printf("%.2lf\n", ans[i]);
	}
	return 0;
}
/*
2
0 2 3
0 0 0
*/