Cod sursa(job #3121679)

Utilizator FunnyStockyMihnea Andreescu FunnyStocky Data 14 aprilie 2023 18:45:58
Problema Algoritmul lui Gauss Scor 40
Compilator cpp-64 Status done
Runda Arhiva educationala Marime 2.23 kb
#include <cmath>
#include <functional>
#include <fstream>
#include <iostream>
#include <vector>
#include <algorithm>
#include <string>
#include <set>
#include <map>
#include <list>
#include <time.h>
#include <math.h>
#include <random>
#include <deque>
#include <cassert>
#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;
const ld E = (ld)1e-14;
vector<ld> G(int n, int m, vector<vector<ld>> a) {
	assert(n == (int)a.size());
	for (int i = 0; i < n; i++) {
		assert(m + 1 == (int)a[i].size());
	}
	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 || abs(a[r][c]) < E) {
			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) {
				ld coef = a[i][c];
				for (int j = 0; j <= m; j++) {
					a[i][j] -= a[r][j] * coef;
				}
			}
		}
	}
	vector<ld> sol(m, 0);
	for (int j = 0; j < m; j++) {
		int i = pj[j];
		if (i != -1) {
			sol[j] = a[i][m];
		}
	}
	for (int i = 0; i < n; i++) {
		ld estim = 0;
		for (int j = 0; j < m; j++) {
			estim += sol[j] * a[i][j];
		}
		estim -= a[i][m];
		if (abs(estim) > E) {
			return {};
		}
	}
	return sol;
}
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));
	for (int i = 0; i < n; i++) {
		for (int j = 0; j <= m; j++) {
			cin >> a[i][j];
		}
	}
	auto sol = G(n, m, a);
	if (sol.empty()) {
		cout << "Imposibil\n";
		return 0;
	}
	for (auto& x : sol) {
		cout << fixed << setprecision(6) << x << " ";
	}
	cout << "\n";
	return 0;
}