Gauss.cpp

/*******************************************************************************

    Gauss method of solving system of linear algebraic equation.
    Works in O(n ^ 3) (more precisely - O(min(n, m) * n * m))

    Based on problem 198 from acmp.ru:
    http://acmp.ru/index.asp?main=task&id_task=198

*******************************************************************************/

#include <iostream>
#include <fstream>
#include <cmath>
#include <algorithm>
#include <vector>
#include <set>
#include <map>
#include <stack>
#include <queue>
#include <cstdlib>
#include <cstdio>
#include <string>
#include <cstring>
#include <cassert>
#include <utility>
#include <iomanip>

using namespace std;

const int MAXN = 150;
const int INF = 1 << 20;
const double eps = 1e-6;

int n, m;
double a[MAXN][MAXN];
double ans[MAXN];

// returns the number of solutions: 0, 1 or infinity 
// in case of any solution, it is written in the ans[] array
int gauss(int n, int m, double a[MAXN][MAXN], double ans[MAXN]) {
    int pos[MAXN];
    memset(pos, 0, sizeof(pos));

    bool parameters = false;
    int row = 1, col = 1;

    for (; row <= n && col <= m; col++) {
        int pivot = row; 
        for (int i = row; i <= n; i++) 
            if (abs(a[i][col]) > abs(a[pivot][col]))
                pivot = i;

        if (abs(a[pivot][col]) < eps) {
            parameters = true;
            continue;
        }

        for (int i = 1; i <= m + 1; i++)
            swap(a[row][i], a[pivot][i]);

        pos[col] = row;

        double div = a[row][col];
        for (int i = 1; i <= m + 1; i++)
            a[row][i] /= div;

        for (int i = 1; i <= n; i++) {
            if (i == row) 
                continue;
            div = a[i][col];
            for (int j = 1; j <= m + 1; j++)
                a[i][j] -= a[row][j] * div;
        }

        row++;
    }

    for (int i = 1; i <= m; i++)
        if (pos[i] != 0)
            ans[i] = a[pos[i]][m + 1];
        else
            ans[i] = 0;

    for (int i = 1; i <= n; i++) {
        double sum = 0;
        for (int j = 1; j <= m; j++)
            sum += ans[j] * a[i][j];
        if (abs(sum - a[i][m + 1]) > eps)
            return 0;
    }

    if (parameters)
        return INF;

    return 1;
}

int main() {
    freopen("input.txt","r",stdin);
    freopen("output.txt","w",stdout);

    scanf("%d", &n);
    m = n;

    for (int i = 1; i <= n; i++) 
        for (int j = 1; j <= m + 1; j++)
            scanf("%lf", &a[i][j]);

    if (gauss(n, m, a, ans) == 1) {
        for (int i = 1; i <= m; i++) {
            ans[i] = floor(ans[i] + 0.5);
            printf("%.0lf ", ans[i]);
        }
    }

    return 0;
}