整数开方算法

二分法

若N大于1,则从[1, N]开始，low = 1, high = N, mid = low + (high - low) >> 1开始进行数值逼近

 

若N小于1,则从[N, 1]开始，low = 0, high = N, mid = low + (high - low) >> 1开始进行数值逼近

 

 

#include <stdio.h>
#include <stdlib.h>
#include <math.h>

#define ACCURACY 0.001

double newSqrt(double n)
{
    double low, high, mid, tmp;

    // 获取上下界
    if (n > 1)    {
        low = 1;
        high = n;
    } else {
        low = n;
        high = 1;
    }

    // 二分法求开方
    while (low <= high) {
        mid = (low + high) / 2.000;

        tmp = mid * mid;

        if (tmp - n <= ACCURACY && tmp -n >= ACCURACY * -1) {
            return mid;
        } else if (tmp > n) {
            high = mid;
        } else {
            low = mid;
        }
    }

    return -1.000;
}

int main(void) {
    double n, res;

    while (scanf("%lf", &n) != EOF) {
        res = newSqrt(n);
        printf("%lf\n", res);
    }

    return 0;
}

 

牛顿迭代法

#include <iostream>
using namespace std;
int main() {
    int N;
    cout<<"输入N的值：";
    cin>>N

    double x1 = 1;//初值
    double x2 = x1/2.0+N/2.0/x1;
    while( fabs(x2-x1)>0.001) {
        x1 = x2;
        x2 = x1/2.0+N/2.0/x1;
    }
    cout<<x1<<endl;

    return 0;
}