Ethiopian multiplication
Ethiopian multiplication
You are encouraged to solve this task according to the task description, using any language you may know.
You are encouraged to solve this task according to the task description, using any language you may know.
A method of multiplying integers using only addition, doubling, and halving.
Method:
- Take two numbers to be multiplied and write them down at the top of two columns.
- In the left-hand column repeatedly halve the last number, discarding any remainders, and write the result below the last in the same column, until you write a value of 1.
- In the right-hand column repeatedly double the last number and write the result below. stop when you add a result in the same row as where the left hand column shows 1.
- Examine the table produced and discard any row where the value in the left column is even.
- Sum the values in the right-hand column that remain to produce the result of multiplying the original two numbers together
For example: 17 x 34
17 34
Halving the first column:
17 34 8 4 2 1
Doubling the second column:
17 34 8 68 4 136 2 272 1 544
Strike-out rows whose first cell is even:
17 34 8 -- 4 --- 2 --- 1 544
Sum the remaining numbers in the right-hand column:
17 34 8 -- 4 --- 2 --- 1 544 ==== 578
So 17 multiplied by 34, by the Ethiopian method is 578.
The task is to define three functions/methods/procedures/subroutines: to half an integer; to double an integer; and one to state if an integer is even. Use these functions to create a function that does Ethiopian multiplication.
References
Python <lang python> tutor = True
def halve(x):
return int(x/2)
def double(x):
return x*2
def even(x):
return not x % 2
def ethiopian(multiplier, multiplicand):
if tutor: print( "Ethiopian multiplication of %i and %i" % (multiplier, multiplicand) ) result = 0 while multiplier >= 1: if even(multiplier): if tutor: print( "%4i %6i STRUCK" % (multiplier, multiplicand) ) else: if tutor: print( "%4i %6i KEPT" % (multiplier, multiplicand) ) result += multiplicand multiplier = halve(multiplier) multiplicand = double(multiplicand) if tutor: print() return result
</lang>
Sample output
Python 3.1 (r31:73574, Jun 26 2009, 20:21:35) [MSC v.1500 32 bit (Intel)] on win32 Type "copyright", "credits" or "license()" for more information. >>> ethiopian(17, 34) Ethiopian multiplication of 17 and 34 17 34 KEPT 8 68 STRUCK 4 136 STRUCK 2 272 STRUCK 1 544 KEPT 578 >>>