This solution is generated by ChatGPT, correctness is not guaranteed. You might also be able to find a solution fromcommunity posts.

# AI solution for JavaScript Coding Question on BFE.dev 103. implement Math.sqrt()

One possible solution for `mySqrt()` is to use binary search to find the integer square root.

``function mySqrt(x) {  // Special case  if (x === 0) return 0;  // Binary search for integer square root  let left = 1, right = x;  while (left <= right) {    let mid = Math.floor((left + right) / 2);    if (mid * mid === x) return mid;    if (mid * mid < x) {      left = mid + 1;    } else {      right = mid - 1;    }  }  // Return the floor of the last mid  return right;}``

The time complexity of this solution is O(log x) and the space complexity is O(1), as we only use a few constant variables.

This solution is already optimal in terms of time complexity, but there is a way to improve the space complexity. Instead of using the `left` and `right` variables to track the range of possible square roots, we can simply define two pointers and update them until they meet:

``function mySqrt(x) {  // Special case  if (x === 0) return 0;  // Binary search for integer square root with two pointers  let lo = 1, hi = x;  while (lo < hi) {    let mid = Math.floor((lo + hi) / 2);    if (mid * mid === x) return mid;    if (mid * mid < x) {      lo = mid + 1;    } else {      hi = mid - 1;    }  }  // Return the floor of the last mid  return lo * lo > x ? lo - 1 : lo;}``

This solution still has a time complexity of O(log x), but the space complexity is now O(1).