2.9 KiB
2.9 KiB
id | title | challengeType | forumTopicId | dashedName |
---|---|---|---|---|
599d1566a02b571412643b84 | Ethiopian multiplication | 5 | 302257 | ethiopian-multiplication |
--description--
Ethiopian multiplication is 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 × 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 868413622721 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
.
--instructions--
The task is to define three named functions/methods/procedures/subroutines:
- one to halve an integer,
- one to double an integer, and
- one to state if an integer is even
Use these functions to create a function that does Ethiopian multiplication.
--hints--
eth_mult
should be a function.
assert(typeof eth_mult === 'function');
eth_mult(17,34)
should return 578
.
assert.equal(eth_mult(17, 34), 578);
eth_mult(23,46)
should return 1058
.
assert.equal(eth_mult(23, 46), 1058);
eth_mult(12,27)
should return 324
.
assert.equal(eth_mult(12, 27), 324);
eth_mult(56,98)
should return 5488
.
assert.equal(eth_mult(56, 98), 5488);
eth_mult(63,74)
should return 4662
.
assert.equal(eth_mult(63, 74), 4662);
--seed--
--seed-contents--
function eth_mult(a, b) {
}
--solutions--
function eth_mult(a, b) {
let sum = 0; a = [a]; b = [b];
let half = a => a / 2,
double = a => a * 2,
is_even = a => a % 2 == 0;
while (a[0] !== 1) {
a.unshift(Math.floor(half(a[0])));
b.unshift(double(b[0]));
}
for (let i = a.length - 1; i > 0; i -= 1) {
if (!is_even(a[i])) {
sum += b[i];
}
}
return sum + b[0];
}