高斯消元-原创手记-慕课网

整数

#include<cstdio>

#include<iostream>

#include<algorithm>

#include<string>

#include<cmath>

#include<cstring>

using namespace std;

const int N=105;

int a[N][N];

int x[N];

bool free_x[N];

inline int gcd(int a,int b){return b?gcd(b,a%b):a;}

inline int lcm(int a,int b){return a/gcd(a,b)*b;}

int gauss(int m,int n)

{

int k,max_r,col=0,ta,tb;

int LCM,temp,num,free_index;

for(int i=0;i<n;i++)x[i]=0,free_x[i]=true;

for(k=0;k<m&&col<n;k++,col++)

{

max_r=k;

for(int i=k+1;i<m;i++)if(abs(a[i][col])>abs(a[max_r][col]))max_r=i;

if(max_r!=k)for(int j=k;j<=n;j++)swap(a[k][j],a[max_r][j]);

if(a[k][col]==0){k--;continue;}

for(int i=k+1;i<m;i++)

{

if(a[i][col]!=0)

{

LCM=lcm(abs(a[i][col]),abs(a[k][col]));

ta=LCM/abs(a[i][col]);

tb=LCM/abs(a[k][col]);

if(a[i][col]*a[k][col]<0)tb=-tb;

for(int j=col;j<=n;j++)a[i][j]=a[i][j]*ta-a[k][j]*tb;

}

for(int i=k;i<m;i++)if(a[i][col]!=0)return -1;

if(k<n)

{

for(int i=k-1;i>=0;i--)

{

num=0;

for(int j=0;j<n;j++)

{

if(a[i][j]!=0&&free_x[j])num++,free_index=j;

}

if(num>1)continue;

temp=a[i][n];

for(int j=0;j<n;j++)

{

if(a[i][j]!=0&&j!=free_index)temp-=a[i][j]*x[j];

}

x[free_index]=temp/a[i][free_index];

free_x[free_index]=false;

}

return n-k;

}

for(int i=n-1;i>=0;i--)

{

temp=a[i][n];

for(int j=i+1;j<n;j++)

{

if(a[i][j]!=0)temp-=a[i][j]*x[j];

}

if(temp%a[i][i]!=0)return -2;

x[i]=temp/a[i][i];

}return 0;

}

浮点数

#include <iostream>

#include <algorithm>

#include <cstdio>

#include <cstring>

#include <cmath>

using namespace std;

const int N = 1010;

const double EPS=1e-7;

int m,n;

double a[N][N],x[N];

int Gauss(int m,int n){

int col=0, k=0;///col为列号,k为行号

for (;k<m&&col<n;++k,++col){

int r = k;

for (int i=k+1;i<m;++i)

if(fabs(a[i][col])>fabs(a[r][col]))r=i;

if (fabs(a[r][col])<EPS){k--;continue;}///列全为0

if (r!=k)for(int i=col;i<=n;++i)

swap(a[k][i],a[r][i]);

for (int i=k+1;i<m;++i)///消元

if(fabs(a[i][col])>EPS){

double t = a[i][col]/a[k][col];

for (int j=col;j<=n;j++)a[i][j]-=a[k][j]*t;

a[i][col] = 0;

}

for(int i=k ;i<m ;++i)///无解

if (fabs(a[i][n])>EPS) return -1;

if (k < n) return n - k; ///自由元个数

for (int i =n-1; i>=0; i--){///回带求解

double temp = a[i][n];

for (int j=i+1; j<n; ++j)

temp -= x[j] * a[i][j];

x[i] = (temp / a[i][i]);

}

return 0;

}

异或方程组

#include<cstdio>

#include<iostream>

#include<algorithm>

#include<cstring>

#include<cmath>

#include<string>

using namespace std;

const int N = 205;

int a[N][N];

int x[N];

int gauss(int m, int n)

{

int max_r, col=0, k;

for (int i = 0; i < n; i++)x[i] = 0;

for (k = 0; k < m&&col < n; k++, col++)

{

max_r = k;

for (int i = k + 1; i < m; i++)if (abs(a[i][col]) > abs(a[max_r][col]))max_r = i;

if (max_r != k)for (int j = k; j <= n; j++)swap(a[k][j], a[max_r][j]);

if (a[k][col] == 0) { k--; continue; }

for (int i = k + 1; i < m; i++)

{

if (a[i][col] != 0)

{

for (int j = col; j <= n; j++)a[i][j] ^= a[k][j];

}

for (int i = k;i<m; i++)

{

if (a[i][col] != 0)return -1;

}

if (k < n)return n - k;

for (int i = n - 1; i >= 0; i--)

{

x[i] = a[i][n];

for (int j = i + 1; j < n; j++)

{

x[i]^= (a[i][j] & x[j]);

}

}return 0;

}

线性基

void gauss(int n)

{

for(int i=0;i!=n;i++)

{

for(int j=63;j>=0;j--)

{

if(a[i]>>j&1)

{

if(b[j])a[i]^=b[j];

else

{

b[j]=a[i];

for(int k=j-1;k>=0;k--)if(b[k] and (b[j]>>k&1))b[j]^=b[k];

for(int k=j+1;k<=63;k++)if(b[k]>>j&1)b[k]^=b[j];break;

}

gauss51cto数学