Multiplication Algorithms - Karatsuba Multiplication Added in Python and CPP (#36)

* Create README.md

* Create karatsuba.py

* Create karatsuba.cpp

multiplication/README.md

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+# Multiplication algorithms
+
+### C or C++
+
+1. [Karatsuba Multiplication](c-or-cpp/karatsuba.cpp)
+
+### Python
+
+1. [Karatsuba Multiplication](python/karatsuba.py)

multiplication/c-or-cpp/karatsuba.cpp

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+#include <iostream>
+#include <string>
+#include <math.h>
+using namespace std;
+
+int equalize_strings(string &x, string &y) {
+  int n = x.length();
+  int m = y.length();
+  string zeros(abs(n - m), '0');
+  if (n > m) {
+    y = zeros + y;
+  } else if (m > n) {
+    x = zeros + x;
+  }
+  return x.length();
+}
+
+string sum(string x, string y) {
+  int len = equalize_strings(x, y);
+  int carry = 0;
+  string result;
+  for (int i = 1; i <= len; i++) {
+    int dgt1 = x[len - i] - '0';
+    int dgt2 = y[len - i] - '0';
+    int dgt3 = (dgt1 + dgt2 + carry) % 10;
+    result = to_string(dgt3) + result;
+    carry = (dgt1 + dgt2 + carry) / 10;
+  }
+  if (carry) {
+    result = '1' + result;
+  }
+  return result;
+}
+
+string subtract(string x, string y) {
+  int len = equalize_strings(x, y);
+  int carry = 0;
+  string result;
+  for (int i = 0; i < len; i++) {
+    if (y[i] < x[i]) {
+      break;
+    } else if (x[i] < y[i]) {
+      string temp = x;
+      x = y;
+      y = temp;
+      break;
+    }
+  }
+  for (int i = 1; i <= len; i++) {
+    int dgt1 = x[len - i] - '0';
+    int dgt2 = y[len - i] - '0';
+    int dgt3 = dgt1 - dgt2 - carry;
+    if (dgt3 < 0) {
+      dgt3 += 10;
+      carry = 1;
+    } else {
+      carry = 0;
+    }
+    result = to_string(dgt3) + result;
+  }
+  return result;
+}
+
+string kmul(string x, string y) {
+  int len = equalize_strings(x, y);
+  if(len == 1){
+    return to_string((x[0]-'0') * (y[0]-'0'));
+  }
+  int mid = len / 2;
+  string a = x.substr(0, mid);
+  string b = x.substr(mid, len - mid);
+  string c = y.substr(0, mid);
+  string d = y.substr(mid, len - mid);
+  string ac = kmul(a, c);
+  string bd = kmul(b, d);
+  string ab_cd = kmul(sum(a, b), sum(c, d));
+  string ad_bc = subtract(ab_cd, sum(ac,bd));
+  string zeros(len - mid, '0');
+
+  string result = sum(ac + zeros + zeros, ad_bc + zeros);
+  result = sum(result, bd);
+  result.erase(0, min(result.find_first_not_of('0'), result.size()-1));
+  return result;
+}
+
+int main() {
+  string x, y;
+  cin >> x >> y;
+  cout << kmul(x, y) << endl;
+  return 0;
+}

multiplication/python/karatsuba.py

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+def equalize_strings(x, y):
+  n = len(x)
+  m = len(y)
+  zeros = abs(n - m) * '0'
+  if n > m:
+    y = zeros + y
+  elif m > n:
+    x = zeros + x
+  return x, y, len(x)
+
+def sum(x, y):
+  x, y, size = equalize_strings(x, y)
+  carry = 0
+  result = ''
+  for i in range(1, size+1):
+    # print(i)
+    dgt1 = int(x[size - i])
+    dgt2 = int(y[size - i])
+    dgt3 = (dgt1 + dgt2 + carry) % 10
+    result = str(dgt3) + result
+    carry = int((dgt1 + dgt2 + carry) / 10)
+    # print(dgt1, dgt2, dgt3, result, carry)
+
+  if carry:
+    result = '1' + result
+  return result
+
+def subtract(x, y):
+  x, y, size = equalize_strings(x, y)
+  carry = 0
+  result = ""
+  for i in range(size):
+    if y[i] < x[i]:
+      break
+    elif x[i] < y[i]:
+      tmp = x
+      x = y
+      y = tmp
+      break
+
+  for i in range(1, size+1):
+    dgt1 = int(x[size - i])
+    dgt2 = int(y[size - i])
+    dgt3 = dgt1 - dgt2 - carry
+    if dgt3 < 0:
+      dgt3 += 10
+      carry = 1
+    else:
+      carry = 0
+    result = str(dgt3) + result
+  return result
+
+def kmul(x ,y):
+  x, y, size = equalize_strings(x, y)
+  if size == 1:
+    return str(int(x) * int(y))
+  mid = int(size / 2)
+  a = x[:mid]
+  b = x[mid:]
+  c = y[:mid]
+  d = y[mid:]
+  ac = kmul(a, c)
+  bd = kmul(b, d)
+  ab_cd = kmul(sum(a, b), sum(c, d))
+  ad_bc = subtract(ab_cd, sum(ac, bd))
+  zeros = "0" * (size - mid)
+
+  result = sum(ac + 2 * zeros, ad_bc + zeros)
+  result = sum(result, bd)
+  result = result.lstrip('0')
+  return result
+
+x = "134231412"
+y = "141324"
+print(kmul(x, y))