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