LeetCode 69. Sqrt(x)

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本文深入探讨了二分查找算法及其在求平方根中的应用，并介绍了 Babylonian 方法，这是一种高效的双精度类数求平方根的技术。通过实例演示了如何使用这些算法解决实际问题。

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Binary search.

#include <vector>
#include <iostream>
using namespace std;

int sqrt(int x) {
  long long left = 0;
  long long right = x;
  long long xx = x;
  while(left < right) {
    long long mid = (left + right) / 2;
    if(mid * mid <= xx && (mid + 1)* (mid + 1) > xx) {return (int) mid;}
    if(mid * mid < xx) left = mid + 1;
    else if(mid * mid > xx) right = mid - 1;
  }
}

int main(void) {
  int sq = sqrt(4);
  cout << sq << endl;
}

An algorithm named Babylonian method. Suppose we want to get 10's square root. First guess the result is 5. and then verify it.

5 != 0 ---> we get the next closer number: (5 + 10 / 5 ) /2 = 3, verify that 3 ! 5, we get the next closer number: (3 + 10 / 3 ) / 2 == 3, return 3. This method best works for double class.

double SQRT(const double fg) {
  double n = fg / 2.0;
  double lstx= 0.0;
  while(n != lstx) {
    lstx = n;
    n = (n + fg/n) / 2.0;
  }
  return n;
}