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package algorithms;
public class strassen {
//创建一个随机数构成的nxn矩阵
public static int[][] initializationMatrix(int n){
int[][] result = new int[n][n];//创建一个nxn矩阵
for(int i = 0;i < n;i++){
for(int j = 0;j < n;j++){
result[i][j] = (int)(Math.random()*10); //随机生成1~10之间的数
}
}
return result;
}
//蛮力法求矩阵相乘
public static int[][] BruteForce(int[][] p,int[][] q,int n){
int[][] result = new int[n][n];
for(int i=0;i<n;i++){
for(int j=0;j<n;j++){
result[i][j] = 0;
for(int k=0;k<n;k++){
result[i][j] += p[i][k]*q[k][j];
}
}
}
return result;
}
//分治法求矩阵相乘
public static int[][] DivideAndConquer(int[][] p,int[][] q,int n){
int[][] result = new int[n][n];//创建一个nxn矩阵
//当n为2时，用蛮力法求矩阵相乘，返回结果结果
if(n == 2){
result = BruteForce(p,q,n);
return result;
}
//当n大于3时，采用分治法，递归求最终结果
if(n > 2){
int m = n/2;
//将矩阵p分成四块
int[][] p1 = QuarterMatrix(p,n,1);
int[][] p2 = QuarterMatrix(p,n,2);
int[][] p3 = QuarterMatrix(p,n,3);
int[][] p4 = QuarterMatrix(p,n,4);
//将矩阵q分成四块
int[][] q1 = QuarterMatrix(q,n,1);
int[][] q2 = QuarterMatrix(q,n,2);
int[][] q3 = QuarterMatrix(q,n,3);
int[][] q4 = QuarterMatrix(q,n,4);
//将结果矩阵分成同等大小的四块
int[][] result1 = QuarterMatrix(result,n,1);
int[][] result2 = QuarterMatrix(result,n,2);
int[][] result3 = QuarterMatrix(result,n,3);
int[][] result4 = QuarterMatrix(result,n,4);
//最关键的步骤，递归调用DivideAndConquer()函数，并用公式相加
result1 = AddMatrix(DivideAndConquer(p1,q1,m),DivideAndConquer(p2,q3,m),m);//y=ae+bg
result2 = AddMatrix(DivideAndConquer(p1,q2,m),DivideAndConquer(p2,q4,m),m);//s=af+bh
result3 = AddMatrix(DivideAndConquer(p3,q1,m),DivideAndConquer(p4,q3,m),m);//t=ce+dg
result4 = AddMatrix(DivideAndConquer(p3,q2,m),DivideAndConquer(p4,q4,m),m);//u=cf+dh
//合并，将四块小矩阵合成整体
result = TogetherMatrix(result1,result2,result3,result4,m);//把分成的四个小矩阵合并成一个大矩阵
}
return result;
}
//strassen法
public static int[][] StrassenMethod(int[][] p,int[][] q,int n){
int[][] result = new int[n][n];//创建一个nxn矩阵
int m = n/2;
//将矩阵p分成四块
int[][] p1 = QuarterMatrix(p,n,1);
int[][] p2 = QuarterMatrix(p,n,2);
int[][] p3 = QuarterMatrix(p,n,3);
int[][] p4 = QuarterMatrix(p,n,4);
//将矩阵q分成四块
int[][] q1 = QuarterMatrix(q,n,1);
int[][] q2 = QuarterMatrix(q,n,2);
int[][] q3 = QuarterMatrix(q,n,3);
int[][] q4 = QuarterMatrix(q,n,4);
int[][] m1 = DivideAndConquer(AddMatrix(p1,p4,m),AddMatrix(q1,q4,m),m);
int[][] m2 = DivideAndConquer(AddMatrix(p3,p4,m),q1,m);
int[][] m3 = DivideAndConquer(p1,ReduceMatrix(q2,q4,m),m);
int[][] m4 = DivideAndConquer(p4,ReduceMatrix(q3,q1,m),m);
int[][] m5 = DivideAndConquer(AddMatrix(p1,p2,m),q4,m);
int[][] m6 = DivideAndConquer(ReduceMatrix(p3,p1,m),AddMatrix(q1,q2,m),m);
int[][] m7 = DivideAndConquer(ReduceMatrix(p2,p4,m),AddMatrix(q3,q4,m),m);
//将结果矩阵分成同等大小的四块
int[][] result1 = QuarterMatrix(result,n,1);
int[][] result2 = QuarterMatrix(result,n,2);
int[][] result3 = QuarterMatrix(result,n,3);
int[][] result4 = QuarterMatrix(result,n,4);
result1 = AddMatrix(ReduceMatrix(AddMatrix(m1,m4,m),m5,m),m7,m);
result2 = AddMatrix(m3,m5,m);
result3 = AddMatrix(m2,m4,m);
result4 = AddMatrix(AddMatrix(ReduceMatrix(m1,m2,m),m3,m),m6,m);
result = TogetherMatrix(result1,result2,result3,result4,m);//把分成的四个小矩阵合并成一个大矩阵
return result;
}
//获取矩阵的四分之一，number用来确定返回哪一个四分之一
public static int[][] QuarterMatrix(int[][] p,int n,int number){
int rows = n/2; //行数减半
int cols = n/2; //列数减半
int[][] result = new int[rows][cols];
switch(number){
//左上
case 1 :
{
for(int i=0;i<rows;i++)
for(int j=0;j<cols;j++)
result[i][j] = p[i][j];
break;
}
//右上
case 2 :
{
for(int i=0;i<rows;i++)
for(int j=0;j<n-cols;j++)
result[i][j] = p[i][j+cols];
break;
}
//左下
case 3 :
{
for(int i=0;i<n-rows;i++)
for(int j=0;j<cols;j++)
result[i][j] = p[i+rows][j];
break;
}
//右下
case 4 :
{
for(int i=0;i<n-rows;i++)
for(int j=0;j<n-cols;j++)
result[i][j] = p[i+rows][j+cols];
break;
}
default:
break;
}
return result;
}
//把均分为四分之一的矩阵，合成一个矩阵
public static int[][] TogetherMatrix(int[][] a,int[][] b,int[][] c,int[][] d,int n){
int[][] result = new int[2*n][2*n];
for(int i=0;i<2*n;i++){
for(int j=0;j<2*n;j++){
if(i<n){
if(j<n)
result[i][j] = a[i][j];
else
result[i][j] = b[i][j-n];
}else{
if(j<n)
result[i][j] = c[i-n][j];
else
result[i][j] = d[i-n][j-n];
}
}
}
return result;
}
//求两个矩阵相加结果
public static int[][] AddMatrix(int[][] p,int[][] q,int n){
int[][] result = new int[n][n];
for(int i=0;i<n;i++){
for(int j=0;j<n;j++){
result[i][j] = p[i][j]+q[i][j];
}
}
return result;
}
//求两个矩阵相减结果
public static int[][] ReduceMatrix(int[][] p,int[][] q,int n){
int[][] result = new int[n][n];
for(int i=0;i<n;i++){
for(int j=0;j<n;j++){
result[i][j] = p[i][j]-q[i][j];
}
}
return result;
}
//输出矩阵的函数
public static void PrintfMatrix(int[][] matrix,int n){
for(int i=0;i<n;i++){
for(int j=0;j<n;j++)
System.out.printf("% 4d",matrix[i][j]);
System.out.println();
}
}
public static void main(String args[]){
int[][] p = initializationMatrix(8);
int[][] q = initializationMatrix(8);
//输出生成的两个矩阵
System.out.println("p：");
PrintfMatrix(p,8);
System.out.println();
System.out.println("q：");
PrintfMatrix(q,8);
//输出分治法矩阵相乘后的结果
int[][] bru_result = BruteForce(p,q,8);//新建一个矩阵存放矩阵相乘结果
System.out.println();
System.out.println("\np*q(蛮力法)：");
PrintfMatrix(bru_result,8);
//输出分治法矩阵相乘后的结果
int[][] dac_result = DivideAndConquer(p,q,8);//新建一个矩阵存放矩阵相乘结果
System.out.println();
System.out.println("p*q(分治法)：");
PrintfMatrix(dac_result,8);
//输出strassen法矩阵相乘后的结果
int[][] stra_result = StrassenMethod(p,q,8);//新建一个矩阵存放矩阵相乘结果
System.out.println("\np*q(strassen法)：");
PrintfMatrix(stra_result,8);
}
}