Cod sursa(job #3122209)

Utilizator HandoMihnea-Vicentiu Hando Data 17 aprilie 2023 20:55:18
Problema Algoritmul lui Gauss Scor 0
Compilator cpp-64 Status done
Runda Arhiva educationala Marime 3.67 kb
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

#define ar array
#define vt vector
#define pq priority_queue
#define pu push
#define pub push_back
#define em emplace
#define emb emplace_back
#define mt make_tuple

#define all(x) x.begin(), x.end()
#define allr(x) x.rbegin(), x.rend()
#define allp(x, l, r) x.begin() + l, x.begin() + r
#define len(x) (int)x.size()
#define uniq(x) unique(all(x)), x.end()

using namespace std;
using namespace __gnu_pbds;

using ll = long long;
using ld = long double;
using ull = unsigned long long;

template <class T, size_t N>
void re(array <T, N>& x);
template <class T> 
void re(vt <T>& x);

template <class T> 
void re(T& x) {
    cin >> x;
}

template <class T, class... M> 
void re(T& x, M&... args) {
    re(x); re(args...);
}

template <class T> 
void re(vt <T>& x) {
    for(auto& it : x)
        re(it);
}

template <class T, size_t N>
void re(array <T, N>& x) {
    for(auto& it : x)
        re(it);
}

template <class T, size_t N>
void wr(array <T, N> x);
template <class T> 
void wr(vt <T> x);

template <class T> 
void wr(T x) {
    cout << x;
}

template <class T, class ...M>  void wr(T x, M... args) {
    wr(x), wr(args...);
}

template <class T> 
void wr(vt <T> x) {
    for(auto it : x)
        wr(it, ' ');
}

template <class T, size_t N>
void wr(array <T, N> x) {
    for(auto it : x)
        wr(it, ' ');
}

template<class T, class... M>
auto mvt(size_t n, M&&... args) {
    if constexpr(sizeof...(args) == 1)
        return vector<T>(n, args...);
    else
        return vector(n, mvt<T>(args...));
}

void set_fixed(int p = 0) {
    cout << fixed << setprecision(p);
}

void set_scientific() {
    cout << scientific;
}

inline void Open(const string Name) {
    #ifndef ONLINE_JUDGE
        (void)!freopen((Name + ".in").c_str(), "r", stdin);
        (void)!freopen((Name + ".out").c_str(), "w", stdout);
    #endif
}

const double EPS = 1e-18;
const int INF = 2;

int gauss (vt <vt <double>> a, vt <double>& ans) {
    int n = len(a);
    int m = len(a[0]) - 1;

    vt <int> where(m, -1);
    for (int col = 0, row = 0; col < m and 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) {
                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) {
        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; re(n, m);
    vt <vt <double>> a(n, vt <double>(m + 1)); re(a);
    vt <double> res;

    if (gauss(a, res) == 0) {
        wr("Imposibil");
        return;
    }

    set_fixed(10);
    wr(res);
}

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);

    Open("gauss");

    int t = 1;
    for(;t;t--) {
        solve();
    }
    
    return 0;
}