數(shù)據(jù)結(jié)構(gòu)和算法代碼分治strassen說明

StrassenStrassen矩陣乘法是通過遞歸實現(xiàn)的，它將一般情況下二階矩陣乘法（可擴展到nStrassenn2的冪）87次，將計算時O(n3)O(n281)。矩陣CABC11=A11B11+A12B21C12=A11B12+A12B22C21=A21B11+A22B21C22=A21B12+A、B、C842，O(n3)。Strassen72M1=A11(B12-B12)M2=(A11+A12)B22M3=(A21+A22)B11M4=A22(B21-B11)M5=(A11+A22)(B11+B22)M6=(A12-A22)(B21+B22)M7=(A11-A21)(B11+B12)C11=M5+M4-M2+M6C12=M1+M2C21=M3+C22=M5+M1-M3-Strassenn2nn=m*2k,#include<iostreamh>#include<mathh>#defineM20#defineN100intkk,mm;typedefstruct{intmatrixintvoidMakeMAndK(int{{}}voidDivideMM(matrixA,matrix{inti,j,ii,jj,dis;{S[ii][jj]m[i][j]=Am[i+(ii-1)*dis][j+(jj-T[ii][jj]m[i][j]=Bm[i+(ii-1)*dis][j+(jj-1)*dis];cc[ii][jj]m[i][j]=0;}}voidDivide(matrix&d,matrix&d11,matrix&d12,matrix&d21,matrix&d22,int{inti,j;{d11m[i][j]=dd12d21d22}}matrixMerge(matrixa11,matrixa12,matrixa21,matrixa22,int{inti,j;matrixa;{}return}

am[i][j]=a11am[i][j+n]=a12am[i+n][j]=a21amatrixAdhocMatrixMultiply(matrixx,matrix/*2的矩陣乘法函數(shù){intm1,m2,m3,m4,m5,m6,m7;matrixz;m1=(xm[1][1]+xm2=xm[1][2]*(ym[2][1]-ym3=(xm[2][1]+xm4=xm[2][1]*(ym[1][2]-ym5=(xm[1][2]+xm[2][1])*(y.m[1][1]+ym6=(xm[2][1]-xm[1][1])*(y.m[1][1]+ym7=(xm[1][2]-xm[2][2])*(y.m[2][2]+ym[2][1]);zm[1][1]=m1+m2;zm[1][2]=m5-m1+m4-zm[2][1]=m5-m3+m2-zreturn}matrixMatrixPlus(matrixf,matrixg,intn)*矩陣加法函數(shù){inti,j;matrixh;hm[i][j]=fm[i][j]+greturn}matrixMatrixMinus(matrixf,matrixg,intn)*矩陣減法函數(shù){inti,j;matrixh;hm[i][j]=fm[i][j]-greturn}matrixMatrixMultiply(matrixa,matrixb,intn)/strassen{intmatrixa11,a12,a21,a22;matrixb11,b12,b21,b22;matrixmatrixm1,m2,m3,m4,m5,m6,m7;{}{

returnc;Divide(a,a11,a12,a21,a22,k);拆分A、B、C矩陣c=Merge(c11,c12,c21,c22,k);合并Creturn}}void{inti,j,k,dis;}void{inti,j,ii,jj,dis;last[i+(ii-1)*dis][j+(jj-1)*dis]=cc[ii][jj]}void{inti,j,n;matrixA,B;{cout<<"A:"<<endl