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873天前/** |
*矩阵计算类 |
*/ |
class Matrix{ |
|
/* |
* 根据字符串解析密钥矩阵 |
* param key 密钥 |
* param rank 密钥矩阵的阶 |
* return 返回密钥矩阵 |
*/ |
public static int[][] getKeyMatrix(String key,int rank){ |
key=key.trim(); |
String[] akey=key.split(" "); |
int key_len=akey.length; |
int[][] pk=new int[rank][rank]; //密钥矩阵 |
|
for(int i=0;i<key_len;i++){ |
String num=akey[i]; |
int row=i/rank,col=i%rank; |
pk[row][col]=num.charAt(0)-'0'; //初始化第一位 |
for(int j=1;j<num.length();j++){ |
pk[row][col]=pk[row][col]*10+num.charAt(j)-'0'; |
} |
} |
return pk; |
} |
|
/* 矩阵a、b相乘，返回矩阵c */ |
public static int[][] Multi(int[][] a,int[][] b){ |
int row=a.length, |
col=b[0].length, |
rank=b.length; |
int[][] c=new int[row][col]; |
|
for(int i=0;i<row;i++){ |
for(int j=0;j<col;j++){ |
c[i][j]=0; |
for(int k=0;k<rank;k++){ |
c[i][j]+=a[i][k]*b[k][j]; |
} |
c[i][j]%=modular; |
} |
} |
return c; |
} |
|
/* |
* 计算行列式的值 |
* param n 矩阵的阶 |
* param N 矩阵 |
*/ |
public static int Det(int n,int[][] matrix) { |
if (n == 1) { |
return matrix[0][0]; |
} |
int[][] matrix2 = new int[n - 1][n - 1]; |
int result = 0; |
for (int i = 0; i < n; i++) { // 去除第0行第i列 |
for (int j = 0; j < n-1; j++) { |
for (int p = 0; p < i; p++) { // 上移一行 |
matrix2[j][p] = matrix[j + 1][p]; |
} |
for (int q = i + 1; q < n; q++) { //右下往左上移 |
matrix2[j][q - 1] = matrix[j + 1][q]; |
} |
} |
result = result + (int) Math.pow(-1, i + 1) * matrix[0][i] |
* Det(n - 1, matrix2); |
} |
return result; |
} |
|
/*转置矩阵*/ |
public static int[][] tranMatrix(int n,int[][] matrix){ |
for(int i=0;i<n;i++) |
for(int j=i+1;j<n;j++){ |
int tmp=matrix[i][j]; |
matrix[i][j]=matrix[j][i]; |
matrix[j][i]=tmp; |
} |
return matrix; |
} |
|
/*代数余子式*/ |
public static int getAdjunct(int n,int[][] matrix,int r,int c){ |
int[][] matrix2 = new int[n - 1][n - 1]; |
int result=0; |
for(int i=0;i<r;i++){ //上半部分 |
for(int j=0;j<c;j++) { |
matrix2[i][j]=matrix[i][j]; |
} |
for(int j=c;j<n-1;j++){ |
matrix2[i][j]=matrix[i][j+1]; |
} |
} |
for (int i = r; i < n-1; i++) { //下半部分 |
for (int p = 0; p < c; p++) { |
matrix2[i][p] = matrix[i + 1][p]; |
} |
for (int q = c + 1; q < n; q++) { |
matrix2[i][q - 1] = matrix[i + 1][q]; |
} |
} |
result=Det(n-1, matrix2); //对matrix2求n-1阶行列式 |
if((r+c)%2==1) result=-result; |
return result; |
} |
|
/* |
* 矩阵的逆 |
* |
*/ |
public static int[][] ReverseMatrix(int n,int[][] matrix){ |
int[][] matrix2=new int[n][n]; |
for(int i=0;i<n;i++) |
for(int j=0;j<n;j++) |
matrix2[i][j]=matrix[i][j]; |
|
int det=Det(n, matrix); |
NumberTheory.extended_gcd(det, modular); |
int inverse=NumberTheory.x; //乘法逆元 |
while(inverse<0) |
inverse+=26; |
for (int i = 0; i < n; i++) { |
for (int j = 0; j < n; j++) { |
matrix2[i][j]=(inverse*getAdjunct(n, matrix, j, i))%modular; |
while(matrix2[i][j]<0){ |
matrix2[i][j]+=modular; |
} |
} |
} |
return matrix2; |
} |
private static int modular=26; |
} |
|
class NumberTheory { |
public static int extended_gcd(int a, int b) { |
int ret, tmp; |
if (b == 0) { |
x = 1; |
y = 0; |
return a; |
} |
ret = extended_gcd(b, a % b); |
tmp = x; |
x = y; |
y = tmp - a / b * y; |
return ret; |
} |
public static int x,y; |
public final static int modular=26; |
} |
