\u4e00\u3001\u4e24\u4e2a\u77e9\u9635\u76f8\u4e58\u7684\u7ecf\u5178\u7b97\u6cd5:
\n\u82e5\u8bbeQ=M*N\u5176\u4e2d\uff0cM\u662fm1*n1\u77e9\u9635\uff0cN\u662fm2*n2\u77e9\u9635\u3002\u5f53n1=m2\u65f6\u6709\uff1a<\/p>\n
\r\n for (i=1;i<m1; ++i )\r\n for ( j=1; j<=n2; ++j){\r\n Q[i][j]=0;\r\n for(k=1; k<=n1; ++k) Q[i][j]+=M[i][k]*N[k][j];\r\n\r\n }\r\n<\/pre>\n\u6b64\u7b97\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u662fO(m1*n1*n2)\u3002<\/p>\n
\u4e8c\u3001\u65af\u7279\u62c9\u68ee\u7b97\u6cd5<\/p>\n
\u65af\u7279\u62c9\u68ee\u65b9\u6cd5\uff0c\u662f\u7531v.\u65af\u7279\u62c9\u68ee\u57281969\u5e74\u63d0\u51fa\u7684\u4e00\u4e2a\u65b9\u6cd5\u3002<\/p>\n
\u6211\u4eec\u5148\u8ba8\u8bba\u4e8c\u9636\u77e9\u9635\u7684\u8ba1\u7b97\u65b9\u6cd5\u3002
\n\u5bf9\u4e8e\u4e8c\u9636\u77e9\u9635
\na11 a12 b11 b12
\nA = a21 a22 B = b21 b22
\n\u5148\u8ba1\u7b97\u4e0b\u97627\u4e2a\u91cf(1)
\nx1 = (a11 + a22) * (b11 + b22);
\nx2 = (a21 + a22) * b11;
\nx3 = a11 * (b12 – b22);
\nx4 = a22 * (b21 – b11);
\nx5 = (a11 + a12) * b22;
\nx6 = (a21 – a11) * (b11 + b12);
\nx7 = (a12 – a22) * (b21 + b22);
\n\u518d\u8bbeC = AB\u3002\u6839\u636e\u77e9\u9635\u76f8\u4e58\u7684\u89c4\u5219\uff0cC\u7684\u5404\u5143\u7d20\u4e3a(2)
\nc11 = a11 * b11 + a12 * b21
\nc12 = a11 * b12 + a12 * b22
\nc21 = a21 * b11 + a22 * b21
\nc22 = a21 * b12 + a22 * b22
\n\u6bd4\u8f83(1)(2)\uff0cC\u7684\u5404\u5143\u7d20\u53ef\u4ee5\u8868\u793a\u4e3a(3)
\nc11 = x1 + x4 – x5 + x7
\nc12 = x3 + x5
\nc21 = x2 + x4
\nc22 = x1 + x3 – x2 + x6
\n\u6839\u636e\u4ee5\u4e0a\u7684\u65b9\u6cd5\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u8ba1\u7b974\u9636\u77e9\u9635\u4e86\uff0c\u5148\u5c064\u9636\u77e9\u9635A\u548cB\u5212\u5206\u6210\u56db\u57572\u9636\u77e9\u9635\uff0c\u5206\u522b\u5229\u7528\u516c\u5f0f\u8ba1\u7b97\u5b83\u4eec\u7684\u4e58\u79ef\uff0c\u518d\u4f7f\u7528(1)(3)\u6765\u8ba1\u7b97\u51fa\u6700\u540e\u7ed3\u679c\u3002
\nma11 ma12 mb11 mb12
\nA4 = ma21 ma22 B4 = mb21 mb22<\/p>\n
\u5176\u4e2d<\/p>\n
a11 a12 a13 a14 b11 b12 b13 b14
\nma11 = a21 a22 ma12 = a23 a24 mb11 = b21 b22 mb12 = b23 b24<\/p>\n
a31 a32 a33 a34 b31 b32 b33 b34
\nma21 = a41 a42 ma22 = a43 a44 mb21 = b41 b42 mb22 = b43 b44<\/p>\n
\u5b9e\u73b0<\/p>\n
\r\n\/\/ \u8ba1\u7b972X2\u77e9\u9635\r\nvoid Multiply2X2(float& fOut_11, float& fOut_12, float& fOut_21, float& fOut_22,\r\nfloat f1_11, float f1_12, float f1_21, float f1_22,\r\nfloat f2_11, float f2_12, float f2_21, float f2_22)\r\n{\r\nconst float x1((f1_11 + f1_22) * (f2_11 + f2_22));\r\nconst float x2((f1_21 + f1_22) * f2_11);\r\nconst float x3(f1_11 * (f2_12 - f2_22));\r\nconst float x4(f1_22 * (f2_21 - f2_11));\r\nconst float x5((f1_11 + f1_12) * f2_22);\r\nconst float x6((f1_21 - f1_11) * (f2_11 + f2_12));\r\nconst float x7((f1_12 - f1_22) * (f2_21 + f2_22));\r\nfOut_11 = x1 + x4 - x5 + x7;\r\nfOut_12 = x3 + x5;\r\nfOut_21 = x2 + x4;\r\nfOut_22 = x1 - x2 + x3 + x6;\r\n}\r\n\/\/ \u8ba1\u7b974X4\u77e9\u9635\r\nvoid Multiply(CLAYMATRIX& mOut, const CLAYMATRIX& m1, const CLAYMATRIX& m2)\r\n{\r\nfloat fTmp[7][4];\r\n\/\/ (ma11 + ma22) * (mb11 + mb22)\r\nMultiply2X2(fTmp[0][0], fTmp[0][1], fTmp[0][2], fTmp[0][3],\r\nm1._11 + m1._33, m1._12 + m1._34, m1._21 + m1._43, m1._22 + m1._44,\r\nm2._11 + m2._33, m2._12 + m2._34, m2._21 + m2._43, m2._22 + m2._44);\r\n\/\/ (ma21 + ma22) * mb11\r\nMultiply2X2(fTmp[1][0], fTmp[1][1], fTmp[1][2], fTmp[1][3],\r\nm1._31 + m1._33, m1._32 + m1._34, m1._41 + m1._43, m1._42 + m1._44,\r\nm2._11, m2._12, m2._21, m2._22);\r\n\/\/ ma11 * (mb12 - mb22)\r\nMultiply2X2(fTmp[2][0], fTmp[2][1], fTmp[2][2], fTmp[2][3],\r\nm1._11, m1._12, m1._21, m1._22,\r\nm2._13 - m2._33, m2._14 - m2._34, m2._23 - m2._43, m2._24 - m2._44);\r\n\/\/ ma22 * (mb21 - mb11)\r\nMultiply2X2(fTmp[3][0], fTmp[3][1], fTmp[3][2], fTmp[3][3],\r\nm1._33, m1._34, m1._43, m1._44,\r\nm2._31 - m2._11, m2._32 - m2._12, m2._41 - m2._21, m2._42 - m2._22);\r\n\/\/ (ma11 + ma12) * mb22\r\nMultiply2X2(fTmp[4][0], fTmp[4][1], fTmp[4][2], fTmp[4][3],\r\nm1._11 + m1._13, m1._12 + m1._14, m1._21 + m1._23, m1._22 + m1._24,\r\nm2._33, m2._34, m2._43, m2._44);\r\n\/\/ (ma21 - ma11) * (mb11 + mb12)\r\nMultiply2X2(fTmp[5][0], fTmp[5][1], fTmp[5][2], fTmp[5][3],\r\nm1._31 - m1._11, m1._32 - m1._12, m1._41 - m1._21, m1._42 - m1._22,\r\nm2._11 + m2._13, m2._12 + m2._14, m2._21 + m2._23, m2._22 + m2._24);\r\n\/\/ (ma12 - ma22) * (mb21 + mb22)\r\nMultiply2X2(fTmp[6][0], fTmp[6][1], fTmp[6][2], fTmp[6][3],\r\nm1._13 - m1._33, m1._14 - m1._34, m1._23 - m1._43, m1._24 - m1._44,\r\nm2._31 + m2._33, m2._32 + m2._34, m2._41 + m2._43, m2._42 + m2._44);\r\n\/\/ \u7b2c\u4e00\u5757\r\nmOut._11 = fTmp[0][0] + fTmp[3][0] - fTmp[4][0] + fTmp[6][0];\r\nmOut._12 = fTmp[0][1] + fTmp[3][1] - fTmp[4][1] + fTmp[6][1];\r\nmOut._21 = fTmp[0][2] + fTmp[3][2] - fTmp[4][2] + fTmp[6][2];\r\nmOut._22 = fTmp[0][3] + fTmp[3][3] - fTmp[4][3] + fTmp[6][3];\r\n\/\/ \u7b2c\u4e8c\u5757\r\nmOut._13 = fTmp[2][0] + fTmp[4][0];\r\nmOut._14 = fTmp[2][1] + fTmp[4][1];\r\nmOut._23 = fTmp[2][2] + fTmp[4][2];\r\nmOut._24 = fTmp[2][3] + fTmp[4][3];\r\n\/\/ \u7b2c\u4e09\u5757\r\nmOut._31 = fTmp[1][0] + fTmp[3][0];\r\nmOut._32 = fTmp[1][1] + fTmp[3][1];\r\nmOut._41 = fTmp[1][2] + fTmp[3][2];\r\nmOut._42 = fTmp[1][3] + fTmp[3][3];\r\n\/\/ \u7b2c\u56db\u5757\r\nmOut._33 = fTmp[0][0] - fTmp[1][0] + fTmp[2][0] + fTmp[5][0];\r\nmOut._34 = fTmp[0][1] - fTmp[1][1] + fTmp[2][1] + fTmp[5][1];\r\nmOut._43 = fTmp[0][2] - fTmp[1][2] + fTmp[2][2] + fTmp[5][2];\r\nmOut._44 = fTmp[0][3] - fTmp[1][3] + fTmp[2][3] + fTmp[5][3];\r\n}\r\n<\/pre>\n\u6bd4\u8f83<\/p>\n
\u5728\u6807\u51c6\u7684\u5b9a\u4e49\u7b97\u6cd5\u4e2d\u6211\u4eec\u9700\u8981\u8fdb\u884cn * n * n\u6b21\u4e58\u6cd5\u8fd0\u7b97\uff0c\u65b0\u7b97\u6cd5\u4e2d\u6211\u4eec\u9700\u8981\u8fdb\u884c7log2n\u6b21\u4e58\u6cd5\uff0c\u5bf9\u4e8e\u6700\u5e38\u7528\u76844\u9636\u77e9\u9635\uff1a \u3000 \u539f\u7b97\u6cd5 \u65b0\u7b97\u6cd5
\n\u52a0\u6cd5\u6b21\u6570 48 72(48\u6b21\u52a0\u6cd5\uff0c24\u6b21\u51cf\u6cd5)
\n\u4e58\u6cd5\u6b21\u6570 64 49
\n\u9700\u8981\u989d\u5916\u7a7a\u95f4 16 * sizeof(float) 28 * sizeof(float)
\n\u65b0\u7b97\u6cd5\u8981\u6bd4\u539f\u7b97\u6cd5\u591a\u4e8624\u6b21\u51cf\u6cd5\u8fd0\u7b97\uff0c\u5c11\u4e8615\u6b21\u4e58\u6cd5\u3002\u4f46\u56e0\u4e3a\u6d6e\u70b9\u4e58\u6cd5\u7684\u8fd0\u7b97\u901f\u5ea6\u8981\u8fdc\u8fdc\u6162\u4e8e\u52a0\/\u51cf\u6cd5\u8fd0\u7b97\uff0c\u6240\u4ee5\u65b0\u7b97\u6cd5\u7684\u6574\u4f53\u901f\u5ea6\u6709\u6240\u63d0\u9ad8\u3002<\/p>\n
\u4e09\u3001Strassen\u77e9\u9635\u4e58\u6cd5<\/p>\n
\u77e9\u9635\u4e58\u6cd5\u662f\u7ebf\u6027\u4ee3\u6570\u4e2d\u6700\u5e38\u89c1\u7684\u8fd0\u7b97\u4e4b\u4e00\uff0c\u5b83\u5728\u6570\u503c\u8ba1\u7b97\u4e2d\u6709\u5e7f\u6cdb\u7684\u5e94\u7528\u3002\u82e5A\u548cB\u662f2\u4e2an\u00d7n\u7684\u77e9\u9635\uff0c\u5219\u5b83\u4eec\u7684\u4e58\u79efC=AB\u540c\u6837\u662f\u4e00\u4e2an\u00d7n\u7684\u77e9\u9635\u3002A\u548cB\u7684\u4e58\u79ef\u77e9\u9635C\u4e2d\u7684\u5143\u7d20C[i,j]\u5b9a\u4e49\u4e3a:<\/p>\n
\u82e5\u4f9d\u6b64\u5b9a\u4e49\u6765\u8ba1\u7b97A\u548cB\u7684\u4e58\u79ef\u77e9\u9635C\uff0c\u5219\u6bcf\u8ba1\u7b97C\u7684\u4e00\u4e2a\u5143\u7d20C[i,j]\uff0c\u9700\u8981\u505an\u4e2a\u4e58\u6cd5\u548cn-1\u6b21\u52a0\u6cd5\u3002\u56e0\u6b64\uff0c\u6c42\u51fa\u77e9\u9635C\u7684n2\u4e2a\u5143\u7d20\u6240\u9700\u7684\u8ba1\u7b97\u65f6\u95f4\u4e3a0(n3)\u3002<\/p>\n
60\u5e74\u4ee3\u672b\uff0cStrassen\u91c7\u7528\u4e86\u7c7b\u4f3c\u4e8e\u5728\u5927\u6574\u6570\u4e58\u6cd5\u4e2d\u7528\u8fc7\u7684\u5206\u6cbb\u6280\u672f\uff0c\u5c06\u8ba1\u7b972\u4e2an\u9636\u77e9\u9635\u4e58\u79ef\u6240\u9700\u7684\u8ba1\u7b97\u65f6\u95f4\u6539\u8fdb\u5230O(nlog7)=O(n2.18)\u3002<\/p>\n
\u9996\u5148\uff0c\u6211\u4eec\u8fd8\u662f\u9700\u8981\u5047\u8bben\u662f2\u7684\u5e42\u3002\u5c06\u77e9\u9635A\uff0cB\u548cC\u4e2d\u6bcf\u4e00\u77e9\u9635\u90fd\u5206\u5757\u6210\u4e3a4\u4e2a\u5927\u5c0f\u76f8\u7b49\u7684\u5b50\u77e9\u9635\uff0c\u6bcf\u4e2a\u5b50\u77e9\u9635\u90fd\u662fn\/2\u00d7n\/2\u7684\u65b9\u9635\u3002\u7531\u6b64\u53ef\u5c06\u65b9\u7a0bC=AB\u91cd\u5199\u4e3a:<\/p>\n
(1)<\/p>\n
\u7531\u6b64\u53ef\u5f97:<\/p>\n
C11=A11B11+A12B21 (2)<\/p>\n
C12=A11B12+A12B22 (3)<\/p>\n
C21=A21B11+A22B21 (4)<\/p>\n
C22=A21B12+A22B22 (5)<\/p>\n
\u5982\u679cn=2\uff0c\u52192\u4e2a2\u9636\u65b9\u9635\u7684\u4e58\u79ef\u53ef\u4ee5\u76f4\u63a5\u7528(2)-(3)\u5f0f\u8ba1\u7b97\u51fa\u6765\uff0c\u5171\u97008\u6b21\u4e58\u6cd5\u548c4\u6b21\u52a0\u6cd5\u3002\u5f53\u5b50\u77e9\u9635\u7684\u9636\u5927\u4e8e2\u65f6\uff0c\u4e3a\u6c422\u4e2a\u5b50\u77e9\u9635\u7684\u79ef\uff0c\u53ef\u4ee5\u7ee7\u7eed\u5c06\u5b50\u77e9\u9635\u5206\u5757\uff0c\u76f4\u5230\u5b50\u77e9\u9635\u7684\u9636\u964d\u4e3a2\u3002\u8fd9\u6837\uff0c\u5c31\u4ea7\u751f\u4e86\u4e00\u4e2a\u5206\u6cbb\u964d\u9636\u7684\u9012\u5f52\u7b97\u6cd5\u3002\u4f9d\u6b64\u7b97\u6cd5\uff0c\u8ba1\u7b972\u4e2an\u9636\u65b9\u9635\u7684\u4e58\u79ef\u8f6c\u5316\u4e3a\u8ba1\u7b978\u4e2an\/2\u9636\u65b9\u9635\u7684\u4e58\u79ef\u548c4\u4e2an\/2\u9636\u65b9\u9635\u7684\u52a0\u6cd5\u30022\u4e2an\/2\u00d7n\/2\u77e9\u9635\u7684\u52a0\u6cd5\u663e\u7136\u53ef\u4ee5\u5728c*n2\/4\u65f6\u95f4\u5185\u5b8c\u6210\uff0c\u8fd9\u91ccc\u662f\u4e00\u4e2a\u5e38\u6570\u3002\u56e0\u6b64\uff0c\u4e0a\u8ff0\u5206\u6cbb\u6cd5\u7684\u8ba1\u7b97\u65f6\u95f4\u8017\u8d39T(n)\u5e94\u8be5\u6ee1\u8db3\uff1a<\/p>\n
\u8fd9\u4e2a\u9012\u5f52\u65b9\u7a0b\u7684\u89e3\u4ecd\u7136\u662fT(n)=O(n3)\u3002\u56e0\u6b64\uff0c\u8be5\u65b9\u6cd5\u5e76\u4e0d\u6bd4\u7528\u539f\u59cb\u5b9a\u4e49\u76f4\u63a5\u8ba1\u7b97\u66f4\u6709\u6548\u3002\u7a76\u5176\u539f\u56e0\uff0c\u4e43\u662f\u7531\u4e8e\u5f0f(2)-(5)\u5e76\u6ca1\u6709\u51cf\u5c11\u77e9\u9635\u7684\u4e58\u6cd5\u6b21\u6570\u3002\u800c\u77e9\u9635\u4e58\u6cd5\u8017\u8d39\u7684\u65f6\u95f4\u8981\u6bd4\u77e9\u9635\u52a0\u51cf\u6cd5\u8017\u8d39\u7684\u65f6\u95f4\u591a\u5f97\u591a\u3002\u8981\u60f3\u6539\u8fdb\u77e9\u9635\u4e58\u6cd5\u7684\u8ba1\u7b97\u65f6\u95f4\u590d\u6742\u6027\uff0c\u5fc5\u987b\u51cf\u5c11\u5b50\u77e9\u9635\u4e58\u6cd5\u8fd0\u7b97\u7684\u6b21\u6570\u3002\u6309\u7167\u4e0a\u8ff0\u5206\u6cbb\u6cd5\u7684\u601d\u60f3\u53ef\u4ee5\u770b\u51fa\uff0c\u8981\u60f3\u51cf\u5c11\u4e58\u6cd5\u8fd0\u7b97\u6b21\u6570\uff0c\u5173\u952e\u5728\u4e8e\u8ba1\u7b972\u4e2a2\u9636\u65b9\u9635\u7684\u4e58\u79ef\u65f6\uff0c\u80fd\u5426\u7528\u5c11\u4e8e8\u6b21\u7684\u4e58\u6cd5\u8fd0\u7b97\u3002Strassen\u63d0\u51fa\u4e86\u4e00\u79cd\u65b0\u7684\u7b97\u6cd5\u6765\u8ba1\u7b972\u4e2a2\u9636\u65b9\u9635\u7684\u4e58\u79ef\u3002\u4ed6\u7684\u7b97\u6cd5\u53ea\u7528\u4e867\u6b21\u4e58\u6cd5\u8fd0\u7b97\uff0c\u4f46\u589e\u52a0\u4e86\u52a0\u3001\u51cf\u6cd5\u7684\u8fd0\u7b97\u6b21\u6570\u3002\u8fd97\u6b21\u4e58\u6cd5\u662f:<\/p>\n
M1=A11(B12-B22)<\/p>\n
M2=(A11+A12)B22<\/p>\n
M3=(A21+A22)B11<\/p>\n
M4=A22(B21-B11)<\/p>\n
M5=(A11+A22)(B11+B22)<\/p>\n
M6=(A12-A22)(B21+B22)<\/p>\n
M7=(A11-A21)(B11+B12)<\/p>\n
\u505a\u4e86\u8fd97\u6b21\u4e58\u6cd5\u540e\uff0c\u518d\u505a\u82e5\u5e72\u6b21\u52a0\u3001\u51cf\u6cd5\u5c31\u53ef\u4ee5\u5f97\u5230:<\/p>\n
C11=M5+M4-M2+M6<\/p>\n
C12=M1+M2<\/p>\n
C21=M3+M4<\/p>\n
C22=M5+M1-M3-M7<\/p>\n
\u4ee5\u4e0a\u8ba1\u7b97\u7684\u6b63\u786e\u6027\u5f88\u5bb9\u6613\u9a8c\u8bc1\u3002\u4f8b\u5982:<\/p>\n
C22=M5+M1-M3-M7<\/p>\n
=(A11+A22)(B11+B22)+A11(B12-B22)-(A21+A22)B11-(A11-A21)(B11+B12)<\/p>\n
=A11B11+A11B22+A22B11+A22B22+A11B12<\/p>\n
-A11B22-A21B11-A22B11-A11B11-A11B12+A21B11+A21B12<\/p>\n
=A21B12+A22B22<\/p>\n
\u7531(2)\u5f0f\u4fbf\u77e5\u5176\u6b63\u786e\u6027\u3002<\/p>\n
\u81f3\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u5b8c\u6574\u7684Strassen\u7b97\u6cd5\u5982\u4e0b\uff1a<\/p>\n
\r\nprocedure STRASSEN(n,A,B,C);\r\nbegin\r\n if n=2 then MATRIX-MULTIPLY(A\uff0cB\uff0cC)\r\n else begin\r\n \u5c06\u77e9\u9635A\u548cB\u4f9d(1)\u5f0f\u5206\u5757;\r\n STRASSEN(n\/2,A11,B12-B22,M1);\r\n STRASSEN(n\/2,A11+A12,B22,M2);\r\n STRASSEN(n\/2,A21+A22,B11,M3);\r\n STRASSEN(n\/2,A22,B21-B11,M4);\r\n STRASSEN(n\/2,A11+A22,B11+B22,M5);\r\n STRASSEN(n\/2,A12-A22,B21+B22,M6);\r\n STRASSEN(n\/2,A11-A21,B11+B12,M7);\r\n ;\r\n end;\r\nend;\r\n<\/pre>\n\u5176\u4e2dMATRIX-MULTIPLY(A\uff0cB\uff0cC)\u662f\u6309\u901a\u5e38\u7684\u77e9\u9635\u4e58\u6cd5\u8ba1\u7b97C=AB\u7684\u5b50\u7b97\u6cd5\u3002<\/p>\n
Strassen\u77e9\u9635\u4e58\u79ef\u5206\u6cbb\u7b97\u6cd5\u4e2d\uff0c\u7528\u4e867\u6b21\u5bf9\u4e8en\/2\u9636\u77e9\u9635\u4e58\u79ef\u7684\u9012\u5f52\u8c03\u7528\u548c18\u6b21n\/2\u9636\u77e9\u9635\u7684\u52a0\u51cf\u8fd0\u7b97\u3002\u7531\u6b64\u53ef\u77e5\uff0c\u8be5\u7b97\u6cd5\u7684\u6240\u9700\u7684\u8ba1\u7b97\u65f6\u95f4T(n)\u6ee1\u8db3\u5982\u4e0b\u7684\u9012\u5f52\u65b9\u7a0b:<\/p>\n
\u6309\u7167\u89e3\u9012\u5f52\u65b9\u7a0b\u7684\u5957\u7528\u516c\u5f0f\u6cd5\uff0c\u5176\u89e3\u4e3aT(n)=O(nlog7)\u2248O(n2.81)\u3002\u7531\u6b64\u53ef\u89c1\uff0cStrassen\u77e9\u9635\u4e58\u6cd5\u7684\u8ba1\u7b97\u65f6\u95f4\u590d\u6742\u6027\u6bd4\u666e\u901a\u77e9\u9635\u4e58\u6cd5\u6709\u9636\u7684\u6539\u8fdb\u3002<\/p>\n
\u6709\u4eba\u66fe\u5217\u4e3e\u4e86\u8ba1\u7b972\u4e2a2\u9636\u77e9\u9635\u4e58\u6cd5\u768436\u79cd\u4e0d\u540c\u65b9\u6cd5\u3002\u4f46\u6240\u6709\u7684\u65b9\u6cd5\u90fd\u8981\u505a7\u6b21\u4e58\u6cd5\u3002\u9664\u975e\u80fd\u627e\u5230\u4e00\u79cd\u8ba1\u7b972\u9636\u65b9\u9635\u4e58\u79ef\u7684\u7b97\u6cd5\uff0c\u4f7f\u4e58\u6cd5\u7684\u8ba1\u7b97\u6b21\u6570\u5c11\u4e8e7\u6b21\uff0c\u6309\u4e0a\u8ff0\u601d\u8def\u624d\u6709\u53ef\u80fd\u8fdb\u4e00\u6b65\u6539\u8fdb\u77e9\u9635\u4e58\u79ef\u7684\u8ba1\u7b97\u65f6\u95f4\u7684\u4e0a\u754c\u3002\u4f46\u662fHopcroft\u548cKerr(197l)\u5df2\u7ecf\u8bc1\u660e\uff0c\u8ba1\u7b972\u4e2a2\u00d72\u77e9\u9635\u7684\u4e58\u79ef\uff0c7\u6b21\u4e58\u6cd5\u662f\u5fc5\u8981\u7684\u3002\u56e0\u6b64\uff0c\u8981\u60f3\u8fdb\u4e00\u6b65\u6539\u8fdb\u77e9\u9635\u4e58\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u6027\uff0c\u5c31\u4e0d\u80fd\u518d\u5bc4\u5e0c\u671b\u4e8e\u8ba1\u7b972\u00d72\u77e9\u9635\u7684\u4e58\u6cd5\u6b21\u6570\u7684\u51cf\u5c11\u3002\u6216\u8bb8\u5e94\u5f53\u7814\u7a763\u00d73\u62165\u00d75\u77e9\u9635\u7684\u66f4\u597d\u7b97\u6cd5\u3002\u5728Strassen\u4e4b\u540e\u53c8\u6709\u8bb8\u591a\u7b97\u6cd5\u6539\u8fdb\u4e86\u77e9\u9635\u4e58\u6cd5\u7684\u8ba1\u7b97\u65f6\u95f4\u590d\u6742\u6027\u3002\u76ee\u524d\u6700\u597d\u7684\u8ba1\u7b97\u65f6\u95f4\u4e0a\u754c\u662fO(n2.367)\u3002\u800c\u76ee\u524d\u6240\u77e5\u9053\u7684\u77e9\u9635\u4e58\u6cd5\u7684\u6700\u597d\u4e0b\u754c\u4ecd\u662f\u5b83\u7684\u5e73\u51e1\u4e0b\u754c\u03a9(n2)\u3002\u56e0\u6b64\u5230\u76ee\u524d\u4e3a\u6b62\u8fd8\u65e0\u6cd5\u786e\u5207\u77e5\u9053\u77e9\u9635\u4e58\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u6027\u3002\u5173\u4e8e\u8fd9\u4e00\u7814\u7a76\u8bfe\u9898\u8fd8\u6709\u8bb8\u591a\u5de5\u4f5c\u53ef\u505a\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"
\u4e00\u3001\u4e24\u4e2a\u77e9\u9635\u76f8\u4e58\u7684\u7ecf\u5178\u7b97\u6cd5: \u82e5\u8bbeQ=M*N\u5176\u4e2d\uff0cM\u662fm1*n1\u77e9\u9635\uff0cN\u662fm2*n2\u77e9\u9635\u3002\u5f53n1=m2\u65f6\u6709\uff1a […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6],"tags":[],"class_list":["post-448","post","type-post","status-publish","format-standard","hentry","category-code_related"],"_links":{"self":[{"href":"https:\/\/kyle.ai\/blog\/wp-json\/wp\/v2\/posts\/448","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/kyle.ai\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kyle.ai\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kyle.ai\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/kyle.ai\/blog\/wp-json\/wp\/v2\/comments?post=448"}],"version-history":[{"count":1,"href":"https:\/\/kyle.ai\/blog\/wp-json\/wp\/v2\/posts\/448\/revisions"}],"predecessor-version":[{"id":5191,"href":"https:\/\/kyle.ai\/blog\/wp-json\/wp\/v2\/posts\/448\/revisions\/5191"}],"wp:attachment":[{"href":"https:\/\/kyle.ai\/blog\/wp-json\/wp\/v2\/media?parent=448"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kyle.ai\/blog\/wp-json\/wp\/v2\/categories?post=448"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kyle.ai\/blog\/wp-json\/wp\/v2\/tags?post=448"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}