Some Algorithm using Math Algorithm

Algorithm-1 Sqrt(x)

Title detail

Implement int sqrt(int x)
Compute and return the square root of x, where x is guaranteed to be a non-negative integer.

Since the return type is an integer, the decimal digits are truncated and only the integer part of the result is returned.

Example 1:

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Input: 4
Output: 2

Example 2:
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Input: 8
Output: 2
Explanation: The square root of 8 is 2.82842..., and since
the decimal part is truncated, 2 is returned.

思路

牛顿迭代法

公式: $x_{k+1} = \lfloor {x_k + n / {x_k}} \rfloor / 2$

当$k \rightarrow \infty$ 时,${x_{k+1}}^2 \rightarrow n$

Algorithm

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class Solution {
public int mySqrt(int x) {
if(x<=1) return x;
long r=x;
long t = x/r;
while(r>t){
t = x/r;
r = (r + t)/2;
}
return (int)r;
}
}

题目链接