Brainteaser：Bulb Switcher求平方根的思考

前言：

这篇文章的第二种方法是自己实现求平方根，因此我们可以探讨一下，这方面的问题。记得在《数值符号与计算》这门课中，求取平方根的一个方法是牛顿法。

引用原文的章节：

if we try to find another way to compute the result (actually it is Integer Square Root of n ), we will find many methods. One of them is below credited to this stackoverflow question.

public class Solution {
public int bulbSwitch(int n) {
return isqrt(n);
}
public int isqrt(int n){
int op  = n;
int res = 0;
int one = 1 << 30;
// The second-to-top bit is set: use 1u << 14 for uint16_t type; use 1uL<<30 for uint32_t type
// "one" starts at the highest power of four <= than the argument.
while (one > op)
{
one >>= 2;
}
while (one != 0)
{
if (op >= res + one)
{
op = op - (res + one);
res = res +  2 * one;
}
res >>= 1;
one >>= 2;
}
return res;
}
}

代码的方法比课中的牛顿法稍微复杂一些。