1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
|
// this function determines the larger number of two numbers and returns the larger number as max
vector <char> compare1 (const vector <char> &number1, const vector <char> &number2)
{
// assign max to the larger number and min to the smaller number
int lmax = 0;
vector<char>max(lmax);
// if the second number is longer than the first number, and hence larger
if (static_cast<int>(number2.size()) > static_cast<int>(number1.size()) )
{
lmax = static_cast<int>(number2.size());
max = number2;
}
// if the first number is longer than the second number, and hence larger
if (static_cast<int>(number1.size()) > static_cast<int>(number2.size()) )
{
lmax = static_cast<int>(number1.size());
max = number1;
}
// if the two numbers have the same length, compare integer in each position from the front of the vector until a larger integer is found, and hence the larger number can be determined
if (static_cast<int>(number1.size()) == static_cast<int>(number2.size()) )
{
lmax = static_cast <int> (number1.size());
for (i = 0; i < number1.size(); i++)
{
if (number1[i] > number2[i])
{
max = number1;
}
if (number1[i] < number2[i])
{
max = number2;
}
// quit loop once the larger number is determined
if (number1[i] != number2[i])
break;
if (number1[i] == number2[i])
{
max = number1;
}
}
}
return max;
} // end of compare1 function
// same compare function, but returns the smaller number as min
vector <char> compare2 (const vector <char> &number1, const vector <char> &number2)
{
// assign max to the larger number and min to the smaller number
int lmin = 0;
vector<char>min(lmin);
// if the second number is longer than the first number, and hence larger
if (static_cast<int>(number2.size()) > static_cast<int>(number1.size()) )
{
lmin = static_cast<int>(number1.size());
min = number1;
}
// if the first number is longer than the second number, and hence larger
if (static_cast<int>(number1.size()) > static_cast<int>(number2.size()) )
{
lmin = static_cast<int>(number2.size());
min = number2;
}
// if the two numbers have the same length, compare integer in each position from the front of the vector until a larger integer is found, and hence the larger number can be determined
if (static_cast<int>(number1.size()) == static_cast<int>(number2.size()) )
{
lmin = static_cast <int> (number1.size());
for (i = 0; i < number1.size(); i++)
{
if (number1[i] > number2[i])
{
min = number2;
}
if (number1[i] < number2[i])
{
min = number1;
}
// quit loop once the larger number is determined
if (number1[i] != number2[i])
break;
if (number1[i] == number2[i])
{
min = number2;
}
}
}
return min;
} // end of compare2 function
vector <char> multiply (const vector <char> &number1, const vector <char> &number2)
{
vector <char> result1;
vector <char> result2;
int pretimes = 0;
int carry = 0;
vector<char>max;
vector<char>min;
max = compare1(number1,number2);
min = compare2(number1,number2);
int k = min.size() - 1;
for (i = max.size() - 1; i >= 0; i--)
{
pretimes = (max[i] - 48) * (min[k] - 48) + carry;
carry = pretimes / 10;
result1.push_back (pretimes % 10 + '0');
}
if (carry != 0)
result1.push_back (carry + '0');
for (k = min.size() - 1; k >= 0; k--)
{
for (i = max.size() - 1; i >=0; i--)
{
carry = 0;
pretimes = (max[i] - 48) * (min[k-1] - 48) + carry;
carry = pretimes / 10;
result2.push_back (pretimes % 10 + '0');
}
if (carry != 0)
result2.push_back (carry + '0');
result1.push_back ('0');
result1 = addition(result1, result2);
}
if (carry != 0)
result1.push_back (carry + '0');
// reverse order of result so it's in the right order
result1 = flip(result1);
return result1;
} // end of multiply function
|
