Add divide and conquer multiplication algorithm

Author: 31ahe

divide&conquer.py

@@ -0,0 +1,87 @@
+def classic_multiplication(num1, num2):
+ n, m = len(num1), len(num2)
+ result = [0] * (n + m + 1) 
+
+ for i in range(n):
+ for j in range(m):
+ result[i + j] += num1[n - 1 - i] * num2[m - 1 - j]
+ result[i + j + 1] += result[i + j] // 10
+ result[i + j] %= 10
+
+ while len(result) > 1 and result[-1] == 0:
+ result.pop()
+
+ return result[::-1]
+
+def operator_add(num1, num2):
+ result_size = max(len(num1), len(num2))
+ result = [0] * (result_size + 1)
+ carry = 0
+
+ for i in range(result_size):
+ num1_digit = num1[-(i + 1)] if i < len(num1) else 0
+ num2_digit = num2[-(i + 1)] if i < len(num2) else 0
+
+ _sum = carry + num1_digit + num2_digit
+ result[-(i + 1)] = _sum % 10
+ carry = _sum // 10
+
+ result[0] = carry
+
+ # Remove leading zeros
+ while len(result) > 1 and result[0] == 0:
+ result.pop(0)
+
+ return result
+
+
+
+def dq_prod(u, v, threshold):
+ n = max(len(u), len(v))
+
+ if n <= threshold:
+ return classic_multiplication(u, v)
+ 
+ else:
+ m = n // 2
+
+ x = u[:m]
+ y = u[m:]
+ w = v[:m]
+ z = v[m:]
+
+ p1 = dq_prod(x, w, threshold)
+ p2 = dq_prod(y, z, threshold)
+ p3 = dq_prod(x, z, threshold)
+ p4 = dq_prod(w, y ,threshold)
+ p5 = operator_add(p3, p4)
+
+ p1 = p1 + [0] * (2 * m)
+ p5 = p5 + [0] * m 
+
+ result = operator_add(operator_add(p1, p5), p2)
+ return result
+
+
+
+def main():
+
+ num1 = [1,2,3,4]
+ print("num 1:", num1)
+
+ num2 = [3,2,1,3]
+ print("num 2:", num2)
+
+ classic_result = classic_multiplication(num1, num2)
+ dq_result = dq_prod(num1, num2, 1)
+
+ print("Classic Result: ")
+ print(classic_result)
+
+ print("Divide and Conquer Result: ")
+ print(dq_result)
+
+
+if __name__ == "__main__":
+ main()
+