Cod sursa(job #3128145)

Utilizator FunnyStockyMihnea Andreescu FunnyStocky Data 8 mai 2023 19:48:08
Problema Algoritmul lui Gauss Scor 100
Compilator cpp-64 Status done
Runda Arhiva educationala Marime 2.24 kb
#include <cmath>
#include <functional>
#include <fstream>
#include <iostream>
#include <vector>
#include <algorithm>
#include <cassert>
#include <string>
#include <set>
#include <map>
#include <list>
#include <time.h>
#include <math.h>
#include <random>
#include <deque>
#include <complex>
#include <queue>
#include <unordered_map>
#include <unordered_set>
#include <iomanip>
#include <bitset>
#include <sstream>
#include <stack>
#include <chrono>
#include <cstring>
#include <numeric>
using namespace std;
typedef long double ld;
signed main() {
#ifdef ONPC
	FILE* stream;
	freopen_s(&stream, "input.txt", "r", stdin);
#else
	ios::sync_with_stdio(false);
	cin.tie(0); cout.tie(0);
	freopen("gauss.in", "r", stdin);
	freopen("gauss.out", "w", stdout);
#endif
	int n, m;
	cin >> n >> m;
	vector<vector<ld>> a(n, vector<ld>(m + 1));
	auto print = [&]() {
		for (int i = 0; i < n; i++) {
			for (int j = 0; j <= m; j++) {
				cout << fixed << setprecision(6) << a[i][j] << " ";
			}
			cout << "\n";
		}
		cout << "------------------\n";
	};
	for (int i = 0; i < n; i++) {
		for (int j = 0; j <= m; j++) {
			cin >> a[i][j];
		}
	}
	vector<int> pi(n, -1), pj(m, -1);
	while (1) {
		int r = -1, c = -1;
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++) {
				if (pi[i] == -1 && pj[j] == -1) {
					if (r == -1 || abs(a[i][j]) > abs(a[r][c])) {
						r = i;
						c = j;
					}
				}
			}
		}
		if (r == -1) {
			break;
		}
		if (abs(a[r][c]) < 1e-10) {
			break;
		}
		pi[r] = c;
		pj[c] = r;
		ld mulby = (ld)1 / (ld)a[r][c];
		for (int j = 0; j <= m; j++) {
			a[r][j] *= mulby;
		}
		for (int i = 0; i < n; i++) {
			if (i != r) {
				mulby = a[i][c];
				for (int j = 0; j <= m; j++) {
					a[i][j] -= mulby * a[r][j];
				}
			}
		}
	}
	vector<ld> sol(m);
	for (int i = 0; i < n; i++) {
		if (pi[i] != -1) {
			sol[pi[i]] = a[i][m];
		}
	}
	for (int i = 0; i < n; i++) {
		ld s = 0;
		for (int j = 0; j < m; j++) {
			s += sol[j] * a[i][j];
		}
		s -= a[i][m];
		s = abs(s);
		if (s > 1e-10) {
			cout << "Imposibil\n";
			exit(0);
		}
	}
	for (int j = 0; j < m; j++) {
		cout << fixed << setprecision(10) << sol[j] << " ";
	}
	cout << "\n";
	//print();
	return 0;
}