Cod sursa(job #3213220)

Utilizator sandry24Grosu Alexandru sandry24 Data 12 martie 2024 18:48:06
Problema Algoritmul lui Gauss Scor 100
Compilator cpp-64 Status done
Runda Arhiva educationala Marime 2.25 kb
#include <bits/stdc++.h>
using namespace std;
 
//#pragma GCC optimize("O3,unroll-loops")
//#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
typedef long long ll;
typedef vector<int> vi;
typedef pair<int, int> pi;
#define pb push_back
#define mp make_pair
#define f first
#define s second
 
const double EPS = 1e-9;
const int INF = 2; // it doesn't actually have to be infinity or a big number

int gauss (vector < vector<long double> > a, vector<long double> & ans) {
    int n = (int) a.size();
    int m = (int) a[0].size() - 1;

    vector<int> where (m, -1);
    for (int col=0, row=0; col<m && row<n; ++col) {
        int sel = row;
        for (int i=row; i<n; ++i)
            if (abs (a[i][col]) > abs (a[sel][col]))
                sel = i;
        if (abs (a[sel][col]) < EPS)
            continue;
        for (int i=col; i<=m; ++i)
            swap (a[sel][i], a[row][i]);
        where[col] = row;

        for (int i=0; i<n; ++i)
            if (i != row) {
                long double c = a[i][col] / a[row][col];
                for (int j=col; j<=m; ++j)
                    a[i][j] -= a[row][j] * c;
            }
        ++row;
    }

    ans.assign (m, 0);
    for (int i=0; i<m; ++i)
        if (where[i] != -1)
            ans[i] = a[where[i]][m] / a[where[i]][i];
    for (int i=0; i<n; ++i) {
        long double sum = 0;
        for (int j=0; j<m; ++j)
            sum += ans[j] * a[i][j];
        if (abs (sum - a[i][m]) > EPS)
            return 0;
    }

    for (int i=0; i<m; ++i)
        if (where[i] == -1)
            return INF;
    return 1;
}
 
void solve(){
    int n, m;
    cin >> n >> m;
    vector<vector<long double>> a(n, vector<long double>(m+1));
    vector<long double> ans(n);
    for(int i = 0; i < n; i++){
        for(int j = 0; j <= m; j++)
            cin >> a[i][j];
    }
    if(!gauss(a, ans)){
        cout << "Imposibil\n";
        return;
    }
    cout << fixed << setprecision(10);
    for(auto i : ans)
        cout << i << ' ';
    cout << '\n';
}
 
int main(){
    freopen("gauss.in", "r", stdin);
    freopen("gauss.out", "w", stdout);
    ios::sync_with_stdio(0); cin.tie(0);
    int t = 1;
    //cin >> t;
    while(t--){
        solve();
    }
}