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1.1 ���Ա��ĸ��� 2
1.2 �㷨���㷨���� 6
1.2.1 �㷨�����ܷ����c���� 7
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1.3 ���Ա������惦(ch��) 9
1.4 ���Ա����?zh��n)���?ch��) 16
1.4.1 ��朱��ĸ��� 16
1.4.2 ��朱����������Č�(sh��)�F(xi��n) 18
1.4.3 ��朱푪(y��ng)���e�� 24
1.4.4 �p��朱푪(y��ng)���e�� 27
1.4.5 ����朱� 33
1.5 �����(du��)�� 33
1.5.1 �����(du��)�еĸ��� 33
1.5.2 �����(du��)�еČ�(sh��)�F(xi��n)˼· 35
1.6 ����(sh��)�` 38
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2.1 ���c�f�w 41
2.1.1 �h�Z�����}�f�w�����O(sh��)Ӌ(j��) 41
2.1.2 �f�w�����(zh��)���^�̷��� 43
2.1.3 ��Ч���f�w�㷨�O(sh��)Ӌ(j��) 45
2.2 ���η� 46
2.2.1 �o��̖(h��o)��(sh��)��Karatsuba�˷� 46
2.2.2 Karatsuba�˷��ij���?q��)��F(xi��n) 48
2.3 ���ݷ� 52
2.3.1 �˻ʺ��} 54
2.3.2 0-1�������} 58
2.4 ����(sh��)�` 62
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3.1 �����ҺͶ��ֲ����㷨 65
3.2 ���������㷨 66
3.2.1 ���� 66
3.2.2 �����x������ 67
3.2.3 ֱ�Ӳ������� 68
3.3 �w�������㷨 69
3.4 ���������㷨 71
3.5 �������������㷨 75
3.5.1 Ӌ(j��)��(sh��)���� 75
3.5.2 Ͱ���� 76
3.5.3 ����(sh��)���� 77
3.5.4 ���� 78
3.6 ����(sh��)�` 78
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4.1 ���}���� 80
4.2 ���}˼· 80
4.2.1 ���}���� 80
4.2.2 ��(sh��)��(j��)���� 80
4.2.3 ���Իؚw���� 81
4.2.4 *С���˷� 82
4.3 �(xi��ng)Ŀ��(sh��)�F(xi��n) 84
4.3.1 ��(chu��ng)���(xi��ng)Ŀ 84
4.3.2 ȫ��׃�� 86
4.3.3 �������w��� 87
4.3.4 ��(sh��)��(j��)�x�� 88
4.3.5 ��ʼ�� 89
4.3.6 ���Իؚw 89
4.3.7 �A(y��)�y���r(ji��) 90
4.4 �\(y��n)�нY(ji��)�� 90
4.5 ���¿��Y(ji��) 91
4.6 �(xi��ng)Ŀ��չ 91
��5�� �Sβ������(xi��ng)Ŀ 92
5.1 ���}���� 92
5.2 ���}˼· 93
5.2.1 ���}���� 93
5.2.2 K��Means�㷨 93
5.2.3 �㷨���� 95
5.3 �(xi��ng)Ŀ��(sh��)�F(xi��n) 95
5.3.1 ��(chu��ng)���(xi��ng)Ŀ 95
5.3.2 ȫ��׃�� 98
5.3.3 �������w��� 99
5.3.4 ��(sh��)��(j��)�x�� 99
5.3.5 ��ʼ����Ⱥ 101
5.3.6 KMeans()����(sh��) 102
5.3.7 Ӌ(j��)���c(di��n)���|(zh��)�ĵľ��x 102
5.3.8 �_����Ⱥ 103
5.3.9 Ӌ(j��)�����|(zh��)�� 104
5.3.10 �Д��Ƿ���Ҫ�^�m(x��)���� 105
5.4 �\(y��n)�нY(ji��)�� 106
5.5 ���¿��Y(ji��) 107
5.6 �(xi��ng)Ŀ��չ 108
��6�� ��ʿ�D���r(ji��)�A(y��)�y�(xi��ng)Ŀ 109
6.1 ���}���� 109
6.2 ���}˼· 109
6.2.1 ���}���� 109
6.2.2 ����BP��(j��ng)�W(w��ng)�j(lu��)ģ�� 110
6.2.3 M-P��(j��ng)Ԫģ�� 110
6.2.4 ǰ����� 112
6.2.5 ��������㷨�Ĕ�(sh��)�W(xu��)�ƌ�(d��o) 112
6.2.6 �㷨���� 114
6.3 �(xi��ng)Ŀ��(sh��)�F(xi��n) 115
6.3.1 ��(chu��ng)���(xi��ng)Ŀ 115
6.3.2 ȫ��׃�� 117
6.3.3 ���a���w���̵Ę�(g��u)�� 118
6.3.4 Ӗ(x��n)����(sh��)��(j��)�x�� 119
6.3.5 ��(j��ng)�W(w��ng)�j(lu��)�ij�ʼ�� 120
6.3.6 ��(j��ng)�W(w��ng)�j(lu��)��Ӗ(x��n)�� 121
6.3.7 ǰ���������(sh��)�Č�(sh��)�F(xi��n) 122
6.3.8 ��������ę�(qu��n)ֵ���� 123
6.3.9 �u(p��ng)����(j��ng)�W(w��ng)�j(lu��)ģ�� 124
6.4 �\(y��n)�нY(ji��)�� 125
6.5 ���¿��Y(ji��) 126
6.6 �(xi��ng)Ŀ��չ 126
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7.1 ϵ�y(t��ng)���ܽY(ji��)��(g��u) 128
7.2 ϵ�y(t��ng)�I(y��)��(w��)���� 128
7.3 ϵ�y(t��ng)���܌�(sh��)�F(xi��n) 129
7.3.1 ��(chu��ng)���(xi��ng)Ŀ 129
7.3.2 �^�ļ����a��(sh��)�F(xi��n) 130
7.3.3 �������ļ����a��(sh��)�F(xi��n) 131
7.3.4 �Α����ˆν��挍(sh��)�F(xi��n) 132
7.3.5 �������P(gu��n)�ڲˆ��x�(xi��ng)��(sh��)�F(xi��n) 133
7.3.6 ��ʼ���؈D 134
7.3.7 ����ʳ�� 135
7.3.8 ���Ƅ�(d��ng) 136
7.3.9 �����ж� 138
7.3.10 �Ƅ�(d��ng)�ٶȵ��{(di��o)�� 139
7.4 �Α��\(y��n)��Ч�� 139
7.5 ���¿��Y(ji��) 140
7.6 �(xi��ng)Ŀ��չ 140
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8.1 ϵ�y(t��ng)���ܽY(ji��)��(g��u) 141
8.2 ϵ�y(t��ng)�I(y��)��(w��)���� 141
8.3 ϵ�y(t��ng)���܌�(sh��)�F(xi��n) 142
8.3.1 ��(chu��ng)���(xi��ng)Ŀ 142
8.3.2 ���K�������� 145
8.3.3 �Α�߉���� 148
8.3.4 �Α��_ʼ�c���r(sh��)������ 157
8.3.5 �Α�����L�� 159
8.3.6 �Α���� 162
8.3.7 �Α�ͣ���^�m(x��) 162
8.4 �Α���惞(y��u)�� 164
8.4.1 ��(du��)Ԓ��(y��u)�� 164
8.4.2 ��(bi��o)�}�ڃ�(y��u)�� 167
8.4.3 ���o��(y��u)�� 172
8.5 �Α��\(y��n)��Ч�� 173
8.6 �(xi��ng)Ŀ��չ 174
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��9�� �W(xu��)���ɿ�����ϵ�y(t��ng) 176
9.1 ���}���� 176
9.2 ���}˼· 176
9.2.1 ϵ�y(t��ng)���ܷ��� 176
9.2.2 �I(y��)��(w��)���̷��� 177
9.3 ϵ�y(t��ng)���܌�(sh��)�F(xi��n) 178
9.3.1 ��(chu��ng)���(xi��ng)Ŀ 178
9.3.2 �A(y��)�O(sh��)�(xi��ng)Ŀ������Ϣ 181
9.3.3 �ļ����� 183
9.3.4 �궨�x 183
9.3.5 �Y(ji��)��(g��u)�w��Ͷ��x 185
9.3.6 system()����(sh��) 187
9.3.7 ����(sh��)�� 189
9.3.8 ������(sh��)��� 190
9.3.9 ���ˆν��� 192
9.3.10 �O(sh��)�����ֵ�ݔ��λ�� 195
9.3.11 ݔ��W(xu��)����Ϣ 197
9.3.12 Ӌ(j��)��W(xu��)���ɿ� 200
9.3.13 Ӌ(j��)���n�̳ɿ� 201
9.3.14 �W(xu��)��ӛ䛴�P 203
9.3.15 �xȡ�W(xu��)��ӛ� 204
9.3.16 ���ӌW(xu��)��ӛ� 206
9.3.17 ���W(xu��)̖(h��o)���ҌW(xu��)��ӛ� 208
9.3.18 ���������ҌW(xu��)��ӛ� 210
9.3.19 �h���W(xu��)��ӛ� 211
9.3.20 �ČW(xu��)��ӛ� 214
9.3.21 ݔ���W(xu��)��ӛ� 217
9.3.22 ��������(du��)�W(xu��)��ӛ����� 219
9.3.23 ���W(xu��)̖(h��o)��(du��)�W(xu��)��ӛ����� 221
9.3.24 ������(du��)�W(xu��)��ӛ��������� 223
9.3.25 ������(du��)�W(xu��)��ӛ䛽������� 224
9.3.26 �W(xu��)���ɿ��y(t��ng)Ӌ(j��) 227
9.3.27 �˳�ϵ�y(t��ng) 230
9.3.28 ���e(cu��)̎�� 230
9.4 ���¿��Y(ji��) 230
9.5 �(xi��ng)Ŀ��չ 231
�����īI(xi��n) 232