leetcode Sqrt(x) Binary Search

原创于 2013-10-24 20:48:03 发布 · 970 阅读

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本文介绍了一种用于寻找整数平方根的有效算法。通过使用二分查找的方法，并注意处理乘法运算可能导致的溢出问题，该算法能够在长整型范围内准确地找到目标值的平方根。

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Pay attention to that mid * mid may be larger than int. So long long is enough.

class Solution {
 public:
  int sqrt(int x) {
    // Note: The Solution object is instantiated only once and is reused by each test case.
    int l = 0, r = x;
    while (l <= r) {
      int mid = (l + r) / 2;
      long long mid2 = (long long)mid * (long long)mid;
      long long mid12 = (long long)(mid + 1) * (long long)(mid + 1);
      
      if (mid2 <= x && mid12 > x)
        return (int)mid;
      if (mid2 > x)
        r = mid -1;
      else
        l = mid +1;
    }
  }
};