高斯消元模板

入门去看：英雄哪里出来和诚叙(两位大佬)。

理解后的部分修改的两个板子：整型和浮点型。

//整型版
#include <string.h>
#include <cstdio>
#define ll long long
using namespace std;
struct GAUSS {
    const static int mod = 1e9+7;
    const static int maxn = 1005;
    int r, c, free_x, cnt;  //cnt表示x取值的值域
    ll matrix[maxn][maxn];
    ll x[maxn];
    ll ans;
    void init(int _r, int _c, int _cnt)
    {
        r = _r, c = _c, cnt = _cnt;
        memset(matrix, 0, sizeof matrix);
    }
    //构造增广矩阵(系数, b)
    void Link(int r, int c, ll val)
    {
        matrix[r][c] = val;
    }
    ll _abs(ll x)
    {
        return x < 0? -x: x;
    }
    ll qpow(int base, int n)
    {
        ll ans = 1;
        for(int i = 1; i <= n; ++i) ans *= base;
        return ans;
    }
    void ex_gcd(ll a, ll b, ll &d, ll &x, ll &y)
    {
        if(b == 0)
        {
            x = 1, y = 0, d = a;
            return;
        }
        ex_gcd(b, a%b, d, y, x);
        y -= a/b*x;
    }
    void swap_row(int a, int b)
    {
        for(int i = 0; i <= c; ++i)
        {
            ll tmp = matrix[a][i];
            matrix[a][i] = matrix[b][i];
            matrix[b][i] = tmp;
        }
    }
    void swap_col(int a, int b)
    {
        for(int i = 0; i < r; ++i)
        {
            ll tmp = matrix[i][a];
            matrix[i][a] = matrix[i][b];
            matrix[i][b] = tmp;
        }
    }
    bool gauss()
    {
        int row, col, maxrow, i, j;
        for(row = 0, col = 0; row < r && col < c; ++row)
        {
            maxrow = row;
            for(i = row+1; i < r; ++i)
            {
                if(_abs(matrix[i][col]) > _abs(matrix[maxrow][col])) maxrow = i;
            }
            if(matrix[maxrow][col] == 0)
            {
                ++col;
                --row;
                continue;
            }
            if(maxrow != row) swap_row(row, maxrow);
            for(i = row+1; i < r; ++i)
            {
                if(matrix[i][col])
                {
                    ll tmp = matrix[i][col];    //matrix[i][col]必须暂时保存，在首次计算时就会被改变
                    for(j = col; j <= c; ++j)
                    {
                        matrix[i][j] = (matrix[i][j]*matrix[row][col]-matrix[row][j]*tmp)%mod;
                        if(matrix[i][j] < 0) matrix[i][j] += mod;
                    }
                }
            }
            ++col;
        }
        for(i = row; i < r; ++i)
            if(matrix[i][c]) return false;  //无解
        free_x = c-row;
        //转化为上三角 
        for(i = 0; i < r && i < c; ++i)
        {
            if(matrix[i][i] == 0)
            {
                for(j = i+1; j < c; ++j)//虽然此处条件是判断是否<c，但实际上要么一定能找到系数矩阵中一列，要么连带b向量中全找不到
                if(matrix[i][j]) 
                {
                    swap_col(i, j);
                    break;
                }
            }
        }
        ans = qpow(cnt, free_x);
        return true;
    }
    //如果存在唯一解，下面计算每个未知数的值 
    void calc_x()
    {
        for(int i = c-1; i >= 0; --i)
        {
            ll tmp = matrix[i][c];
            for(int j = i+1; j < c; ++j)
                tmp = (tmp-matrix[i][j]*x[j]+mod)%mod;
            ll D, X, Y;
            ex_gcd(matrix[i][i], mod, D, X, Y);
            X = (X%mod+mod)%mod;
            x[i] = X*tmp%mod;
        }
    }
} AC;
void solve()
{
	int r, c, cnt;
	scanf("%d %d %d", &r, &c, &cnt);
    AC.init(r, c, cnt); 
    
    for(int i = 0; i < r; ++i)
    for(int j = 0; j <= c; ++j) //输入增广矩阵(系数, b)
    {
    	int x;
    	scanf("%lld", &x);
		AC.Link(i, j, x);	
	}      

    if(!AC.gauss()) printf("No Answer.\n");
    {
    	printf("%lld\n", AC.ans);
    	if(AC.ans == 1)
    	{
		    AC.calc_x();
		    for(int i = 0; i < c; ++i)
		        printf("%lld ", AC.x[i]);
	    	printf("\n");
	    }
	}
}
int main()
{
    solve();
    return 0;
}

//浮点数版
#include <string.h>
#include <cstdio>
#include <cmath>
#define LL long long
using namespace std;
struct GAUSS {
	const static int maxn = 105;
	const static double eps = 1e-12;
	int r, c, free_x;
	double matrix[maxn][maxn];
	double x[maxn];
	void init(int _r, int _c)
	{
		r = _r, c = _c;
		//浮点数也可以这么清零 
		memset(matrix, 0, sizeof matrix);
	}
	//构造增广矩阵(系数, b)
    void Link(int r, int c, double val)
    {
        matrix[r][c] = val;
    }
	inline bool sgn(double x)	//判断绝对值是否小于极小数, = 0代表为极小数 
	{
	    return (x > eps) - (x < -eps);
	}
	void swap_row(int a, int b)
	{
		for(int i = 0; i <= c; ++i)
		{
			double tmp = matrix[a][i];
			matrix[a][i] = matrix[b][i];
			matrix[b][i] = tmp;
		}
	}
	void swap_col(int a, int b)
	{
		for(int i = 0; i < r; ++i)
		{
			double tmp = matrix[i][a];
			matrix[i][a] = matrix[i][b];
			matrix[i][b] = tmp;
		}
	}
	bool gauss()
	{
		int row, col, maxrow, i, j;
		for(row = 0, col = 0; row < r && col < c; ++row)
		{
			maxrow = row;
			for(i = row+1; i < r; ++i)	//先进行此处判断，因为绝对值小于极小数的数都被认为是0
			{
				if(fabs(matrix[i][col]) > fabs(matrix[maxrow][col])) maxrow = i;
			}
			if(sgn(matrix[maxrow][col]) == 0)
			{
				++col;
				--row;
				continue;
			}
			if(maxrow != row) swap_row(row, maxrow);
			for(i = row+1; i < r; ++i)
			{
				if(sgn(matrix[i][col]) != 0)
				{
					double tmp = matrix[i][col];
					for(j = col; j <= c; ++j)
					{
						matrix[i][j] -= tmp/matrix[row][col]*matrix[row][j];
					}
				}
			}
			++col;
		}
		for(i = row; i < r; ++i)
			if(sgn(matrix[row][c]) != 0) return false;	//无解
		free_x = c-row; 
		for(i = 0; i < r && i < c; ++i)
		{
			if(sgn(matrix[i][i]) == 0)
			{
				for(j = i+1; j < c; ++j)
				if(sgn(matrix[i][j]) != 0) 
				{
					swap_col(i, j);
					break;
				}
			}
		}
		return true;
	}
	void calc_x()
	{
		for(int i = c-1; i >= 0; --i)
		{
			double tmp = matrix[i][c];
			for(int j = i+1; j < c; ++j)
				tmp = tmp-matrix[i][j]*x[j];
			x[i] = tmp/matrix[i][i];
		}
	}
} AC; 
void solve()
{
	int r, c;
	scanf("%d %d", &r, &c);
	AC.init(r, c);
	for(int i = 0; i < r; ++i)
	for(int j = 0; j < c; ++j)
	{
		double x;
		scanf("%lf", &x);
		AC.Link(i, j, x);	
	}
	AC.gauss();
	AC.calc_x();
	for(int i = 0; i < c-1; ++i)
		printf("%.2f ", AC.x[i]+AC.eps);	//避免-0.0的输出
	printf("%.2f\n", AC.x[c-1]+AC.eps);
}
int main()
{
	solve();
	return 0;
}

附：-0.0的产生是因为被用来表示一个可以四舍五入为零的负数，或者是一个从负方向上趋近于零的数。所以浮点数运算时最终结果需要加一个eps避免-0.0。

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