(onsite) Implement multiplication without using the multiplication operator

Question

Anonymous · Accepted Answer

At first I struggled to jump into an optimized solution but seeing that I was stumbling the interviewer suggested that I start with a basic implementation (using a for loop and addition).  From here I was asked about the performance of this approach.  The interviewer then lead me to work on a faster approach which in the 45 minutes I was unable to code a working example.

Matt · Answer

Divide by the inverse? Or use some bitwise operators.

5*5 ~= 5/(1/5). (obvious inverse...)


or some JS, binary representation -> shift by powers of 2, add the rest (or you could compute out the powers of 2 again and keep adding or something):


const mult = (a,b) => {
    let _a = a.toString(2),
    	_b = b.toString(2)
    
    console.log(a,b)
    
    const npow2 = Math.floor(Math.log2(b))
    const delta = b - Math.pow(2,npow2)
    
    _a = parseInt(_a+Array(npow2).fill(1).map($ => 0).join(''), 2)
    
    Array(delta).fill(1).map($ => _a+=a)
    console.log({_a, _b, npow2, delta})
}

mult(5,17)

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