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Determine whether a given number is odious (its binary expansion has an odd number of 1s)
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/** | |
* Determines whether a given number is "odious" (its binary expansion has an odd number of ones) | |
* @param {number} num non-negative integer to test odiousness of | |
* @returns {boolean} whether `num` is odious | |
*/ | |
function isOdious(num) { | |
let numberOf1Bits = 0; | |
// Binary expansions represent numbers as sums of powers of 2 | |
// So we need to find how many powers of 2 can be subtracted from `num` | |
const exponentOfLargestPowerOf2 = Math.floor(Math.log2(num)); | |
// Iterate over powers of 2, from the largest that could fit inside `num` | |
// all the way down to 2^0 = 1 | |
for (let i = exponentOfLargestPowerOf2; i >= 0; i--) { | |
let currentPowerOf2 = Math.pow(2, i); | |
if (num - currentPowerOf2 >= 0) { | |
// The current power of 2 can be subtracted out from `num`, | |
// and is thus a "1" bit | |
num -= currentPowerOf2; | |
numberOf1Bits++; | |
} | |
} | |
return (numberOf1Bits % 2 === 1); | |
} |
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