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69. Sqrt(x)

  • Time: $O(\log x)$
  • Space: $O(1)$
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class Solution {
 public:
  int mySqrt(int x) {
    unsigned l = 1;
    unsigned r = x + 1u;

    while (l < r) {
      const unsigned m = (l + r) / 2;
      if (m > x / m)
        r = m;
      else
        l = m + 1;
    }

    // l := the minimum number s.t. l * l > x
    return l - 1;
  }
};

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class Solution {
  public int mySqrt(long x) {
    long l = 1;
    long r = x + 1;

    while (l < r) {
      final long m = (l + r) / 2;
      if (m > x / m)
        r = m;
      else
        l = m + 1;
    }

    // l := the minimum number s.t. l * l > x
    return (int) l - 1;
  }
}

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class Solution:
  def mySqrt(self, x: int) -> int:
    return bisect.bisect_right(range(x + 1), x,
                               key=lambda m: m * m) - 1