-
Notifications
You must be signed in to change notification settings - Fork 0
/
karatsuba.cpp
101 lines (78 loc) · 2.97 KB
/
karatsuba.cpp
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
/*
* Name : Karatsuba Algorithm
* Description : This program takes in two numbers as input and outputs their product.
* Runs in O(n ^ (log_3(2)) time where n is the number of digits in the larger number.
* Compare that to standard multiplication algorithm taught in school, which is O(n ^ 2).
* Isn't really faster unless you are dealing with numbers with a large amount of digits seen in fields such as cryptography.
*/
#include <iostream>
#include <string>
#include <algorithm>
std::string firstxdigits(std::string s, int x) {
if (x >= s.length()) return "0";
return s.substr(0, s.length() - x);
}
std::string lastxdigits(std::string s, int x) {
if (x >= s.length()) return s;
return s.substr(s.length() - x, s.length());
}
std::string add(std::string X, std::string Y) {
std::string ans;
int XLen = X.length(), YLen = Y.length();
int carry = 0;
int MxLen = std::max(XLen, YLen);
for (int i = MxLen - 1; i >= 0; --i) {
int sum = carry;
if ((XLen - MxLen + i) >= 0) sum += (X[XLen - MxLen + i] - '0');
if ((YLen - MxLen + i) >= 0) sum += (Y[YLen - MxLen + i] - '0');
ans += ('0' + sum % 10);
carry = sum / 10;
}
if (carry) ans += (carry + '0');
reverse(ans.begin(), ans.end());
return ans;
}
std::string subtract(std::string X, std::string Y) {
std::string ans;
int XLen = X.length(), YLen = Y.length();
int carry = 0;
for (int i = XLen - 1; i >= 0; --i) {
int sum = X[i] - '0' - carry;
if ((YLen - XLen + i) >= 0) sum -= (Y[YLen - XLen + i] - '0');
ans += ('0' + (10 + sum ) % 10);
if (sum < 0) carry = 1;
else carry = 0;
}
reverse(ans.begin(), ans.end());
return ans;
}
std::string karatsuba(std::string X, std::string Y) {
int XLen = X.length();
int YLen = Y.length();
if (XLen == 1 && YLen == 1) {
return std::to_string((X[0] - '0') * (Y[0] - '0'));
}
int N = std::max(XLen, YLen) / 2;
std::string a = firstxdigits(X, N);
std::string b = lastxdigits(X, N);
std::string c = firstxdigits(Y, N);
std::string d = lastxdigits(Y, N );
std::string ac = karatsuba(a, c);
std::string bd = karatsuba(b, d);
std::string ad_plus_bc = subtract(subtract(karatsuba(add(a, b), add(c, d)), ac), bd);
for (int i = 1; i <= N * 2; ++i) ac += "0";
for (int i = 1; i <= N; ++i) ad_plus_bc += "0";
std::string ans = add(add(ac, ad_plus_bc), bd);
for (int i = 0; i < ans.size(); ++i) {
if (ans[i] != '0') {
return ans.substr(i);
}
}
return "0";
}
int main() {
std::string num1, num2;
std::cout << "Enter two numbers seperated by a space" << std::endl;
std::cin >> num1 >> num2;
std::cout << "Their product is :" << std::endl << karatsuba(num1, num2) << std::endl;
}