Cod sursa(job #3220610)

Utilizator tibinyteCozma Tiberiu-Stefan tibinyte Data 4 aprilie 2024 12:52:43
Problema Algoritmul lui Gauss Scor 10
Compilator cpp-64 Status done
Runda Arhiva educationala Marime 2.06 kb
#include <bits/stdc++.h>

#define cin fin
#define cout fout

using namespace std;

ifstream fin("gauss.in");
ofstream fout("gauss.out");

typedef long double ld;

const ld eps = 1e-9;

int gauss(int n, int m, vector<vector<ld>> a, vector<ld> &ans)
{
    vector<int> wh(m + 1);
    for (int col = 1, row = 1; col <= m; ++col)
    {
        int qui = row;
        for (int i = row; i <= n; ++i)
        {
            if (abs(a[i][col]) > abs(a[qui][col]))
            {
                qui = i;
            }
        }
        swap(a[row], a[qui]);

        if (abs(a[row][col]) < eps)
        {
            continue;
        }

        wh[col] = row;

        ld clown = a[row][col];
        for (int i = col; i <= m + 1; ++i)
        {
            a[row][i] /= clown;
        }

        for (int i = 1; i <= n; ++i)
        {
            if (i != row)
            {
                ld clown = a[i][col];
                for (int j = col; j <= m + 1; ++j)
                {
                    a[i][j] -= a[row][j] * clown;
                }
            }
        }
        ++row;
    }
    ans.resize(m + 1);
    for (int i = 1; i <= m; ++i)
    {
        if (wh[i])
        {
            ans[i] = a[wh[i]][m + 1];
        }
    }
    for (int i = 1; i <= n; ++i)
    {
        ld sum = 0;
        for (int j = 1; j <= m; ++j)
        {
            sum += a[i][j] * ans[j];
        }
        if (abs(sum - a[i][m + 1]) > eps)
        {
            return 0;
        }
    }
    return 1;
}

int32_t main()
{
    cin.tie(nullptr)->sync_with_stdio(false);
    int n, m;
    cin >> n >> m;
    vector<vector<ld>> a(n + 1, vector<ld>(m + 2));
    for (int i = 1; i <= n; ++i)
    {
        for (int j = 1; j <= m + 1; ++j)
        {
            cin >> a[i][j];
        }
    }
    vector<ld> ans;
    if (gauss(n, m, a, ans))
    {
        for (int i = 1; i <= m; ++i)
        {
            cout << fixed << setprecision(10) << ans[i] << ' ';
        }
    }
    else
    {
        cout << "Imposibil\n";
    }
}