Cod sursa(job #3124531)

Utilizator FunnyStockyMihnea Andreescu FunnyStocky Data 29 aprilie 2023 11:35:33
Problema Algoritmul lui Gauss Scor 100
Compilator cpp-64 Status done
Runda Arhiva educationala Marime 2.08 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 <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 int N = 300 + 7;
int n, m, pairi[N], pairj[N];
ld a[N][N], sol[N];
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
	cin >> n >> m;
	for (int i = 1; i <= n; i++) {
		for (int j = 1; j <= m + 1; j++) {
			cin >> a[i][j];
		}
	}
	for (int i = 1; i <= n; i++) {
		pairi[i] = -1;
	}
	for (int j = 1; j <= m; j++) {
		pairj[j] = -1;
	}
	while (1) {
		int r = -1, c = -1;
		for (int i = 1; i <= n; i++) {
			for (int j = 1; j <= m; j++) {
				if (pairi[i] == -1 && pairj[j] == -1) {
					if (abs(a[i][j]) > 1e-14) {
						if (r == -1 || abs(a[i][j]) > abs(a[r][c])) {
							r = i;
							c = j;
						}
					}
				}
			}
		}
		if (r == -1) {
			break;
		}
		pairi[r] = c;
		pairj[c] = r;
		ld mulby = (ld)1 / a[r][c];
		for (int j = 1; j <= m + 1; j++) {
			a[r][j] *= mulby;
		}
		for (int i = 1; i <= n; i++) {
			if (i != r) {
				mulby = a[i][c];
				for (int j = 1; j <= m + 1; j++) {
					a[i][j] -= a[r][j] * mulby;
				}
			}
		}
	}
	for (int j = 1; j <= m; j++) {
		if (pairj[j] != -1) {
			sol[j] = a[pairj[j]][m + 1];
		}
	}
	for (int i = 1; i <= n; i++) {
		ld e = 0;
		for (int j = 1; j <= m; j++) {
			e += sol[j] * a[i][j];
		}
		e -= a[i][m + 1];
		if (abs(e) > 1e-10) {
			cout << "Imposibil\n";
			return 0;
		}
	}
	for (int i = 1; i <= m; i++) {
		cout << fixed << setprecision(10) << sol[i] << " ";
	}
	cout << "\n";
	return 0;
}