【云栖社区002-二分估值法】要求不用数学库，求 sqrt (2)精确到小数点后10位(Java版)

如题

• 初步审题的时候，想到的是暴力搜索：初步设置一个合法的种子，依次按照1e-2，1e-3，1e-4，1e-5，1e-6 , 1e-7...暴力搜索，额，就是太麻烦了。

打比赛搜索写多了，一看见题目就想到搜索。。。

• 细想了一下，进行优化，二分估值法，貌似很合适.
• 试了试，又调了数学库求值开根号2 ，没问题。

代码

package com.szs;
/**
 * @description 要求不用数学库，求 sqrt (2)精确到小数点后 10位
 * @author Administrator
 */
public class Main {
	public static void main(String[] args) {	
		//手写二分估值
		System.out.println(myCalculate(1.4,1.4,1.5));
		//调用函数输出
		System.out.println("----------sqrt= "+Math.sqrt(2.0));
	}
	//根号2约等于 1.414
	private static double myCalculate(double ans,double low,double high) {
		double mid = 0;
		// 二分法,结束条件：差值小于等于1e-10即可
		while(high-low>1e-10){
			
			 mid = (high+low)/2.0;
			System.out.println("-----------mid= "+mid+"  mid*mid= "+mid*mid);
			//二分，逐步向中间值收拢
			if(mid*mid <= 2.0){
				low=mid;
			}
			else{
				high=mid;
			}
			
		}
		
		return mid;
	}
	
}

测试输出结果

-----------mid= 1.45  mid*mid= 2.1025
-----------mid= 1.4249999999999998  mid*mid= 2.0306249999999997
-----------mid= 1.4124999999999999  mid*mid= 1.9951562499999995
-----------mid= 1.4187499999999997  mid*mid= 2.0128515624999994
-----------mid= 1.415625  mid*mid= 2.0039941406249997
-----------mid= 1.4140625  mid*mid= 1.99957275390625
-----------mid= 1.41484375  mid*mid= 2.0017828369140624
-----------mid= 1.414453125  mid*mid= 2.0006776428222657
-----------mid= 1.4142578125  mid*mid= 2.0001251602172854
-----------mid= 1.41416015625  mid*mid= 1.999848947525024
-----------mid= 1.414208984375  mid*mid= 1.9999870514869693
-----------mid= 1.4142333984375002  mid*mid= 2.000056105256081
-----------mid= 1.4142211914062501  mid*mid= 2.0000215782225137
-----------mid= 1.414215087890625  mid*mid= 2.000004314817488
-----------mid= 1.4142120361328125  mid*mid= 1.9999956831429155
-----------mid= 1.4142135620117187  mid*mid= 1.9999999989778732
-----------mid= 1.4142143249511718  mid*mid= 2.0000021568970987
-----------mid= 1.4142139434814451  mid*mid= 2.0000010779373403
-----------mid= 1.414213752746582  mid*mid= 2.00000053845757
-----------mid= 1.4142136573791504  mid*mid= 2.000000268717713
-----------mid= 1.4142136096954345  mid*mid= 2.0000001338477906
-----------mid= 1.4142135858535765  mid*mid= 2.0000000664128312
-----------mid= 1.4142135739326476  mid*mid= 2.000000032695352
-----------mid= 1.4142135679721832  mid*mid= 2.000000015836613
-----------mid= 1.414213564991951  mid*mid= 2.0000000074072433
-----------mid= 1.4142135635018347  mid*mid= 2.0000000031925578
-----------mid= 1.4142135627567767  mid*mid= 2.0000000010852155
-----------mid= 1.4142135623842478  mid*mid= 2.0000000000315445
-----------mid= 1.4142135621979832  mid*mid= 1.9999999995047089
-----------mid= 1.4142135622911156  mid*mid= 1.999999999768127
1.4142135622911156
----调用数学库计算-----sqrt2= 1.4142135623730951