关于找空心球的算法和代码

看到网上有这样的面试题：

试题：有53个球和一个天平,有一个是空的,问最少要多少次才能找到空心球。最多要多少次，用程序写出来。

算法：三分法，为了保证最佳，采用近三等分方法。每次分三组。如果1、2组相等，肯定在第3组中，否则1、2组中轻的一组中。依次类推，直到找到的一组中剩下一个球时为止。

效果：

Create 53 spheres in random... Hollow sphere is [○07]

[●01][●02][●03][●04][●05][●06][○07][●08][●09][●10][●11][●12][●13][●14][●15][●16][●17][●18][●19][●20][●21][●22][●23][●24][●25][●26][●27][●28][●29][●30][●31][●32][●33][●34][●35][●36][●37][●38][●39][●40][●41][●42][●43][●44][●45][●46][●47][●48][●49][●50][●51][●52][●53]

Find round: 1 in 53 spheres.

into 3 groups:

group 1: [●01][●02][●03][●04][●05][●06][○07][●08][●09][●10][●11][●12][●13][●14][●15][●16][●17]

group 2: [●18][●19][●20][●21][●22][●23][●24][●25][●26][●27][●28][●29][●30][●31][●32][●33][●34]

group 3: [●35][●36][●37][●38][●39][●40][●41][●42][●43][●44][●45][●46][●47][●48][●49][●50][●51][●52][●53]

Find round: 2 in 17 spheres.

into 3 groups:

group 1: [●01][●02][●03][●04][●05]

group 2: [●06][○07][●08][●09][●10]

group 3: [●11][●12][●13][●14][●15][●16][●17]

Find round: 3 in 5 spheres.

into 3 groups:

group 1: [●06]

group 2: [○07]

group 3: [●08][●09][●10]

Find round: 4 in 1 spheres.

The smallest sphere is:[○07]

JAVA代码：

import java.util.Random;

public class FindSmallestSphere {

private static int findRound = 0;

public static Sphere[] initSphere(int max){

System.out.print("Create "+max+" spheres in random...");

Sphere[] s = new Sphere[max];

int idLength = String.valueOf(max).length();

for(int i=0; i<max; i++){

s[i] = new Sphere(formatId(i+1,idLength), Sphere.SOLID_SPHERE_WEIGHT);

}

Random r = new Random();

int hollowIndex =r.nextInt(max);

s[hollowIndex].setWeight(Sphere.HOLLOW_SPHERE_WEIGHT);

System.out.println(" Hollow sphere is " + s[hollowIndex]);

return s;

}

public static String show(Sphere[] spheres, String separator){

StringBuilder sb = new StringBuilder();

for(int i=0; i< spheres.length; i++){

if(i>0)sb.append(separator);

sb.append(spheres[i]);

}

return sb.toString();

}

public static int getSpheresWeight(Sphere[] spheres){

int weight = 0;

for(int i=0; i< spheres.length; i++){

weight += spheres[i].getWeight();

}

return weight;

}

public static Sphere[] subSpheres(Sphere[] spheres, int start, int end){

int max = end-start;

Sphere[] s = new Sphere[max];

for(int i=0; i<max; i++){

s[i] = spheres[start+i];

}

return s;

}

public static void find(Sphere[] spheres){

findRound++;

int total = spheres.length ;

System.out.println("Find round: " + findRound +"/t in " + total + " spheres.");

if( total == 1){

System.out.println("/tThe smallest sphere is:" + spheres[0]);

}else if( total <=3 ){

Sphere s = null;

if(spheres[0].getWeight()<spheres[1].getWeight()){

s = spheres[0];

}else if(spheres[0].getWeight()>spheres[1].getWeight()){

s = spheres[1];

}else{

s = spheres[2];

}

System.out.println("/tThe smallest sphere is:" + s);

}else{

System.out.println("/tinto 3 groups: ");

int gn = total/3;

Sphere[] g1 = subSpheres(spheres,0,gn);

Sphere[] g2 = subSpheres(spheres,gn,gn+gn);

Sphere[] g3 = subSpheres(spheres,gn+gn,total);

System.out.println("/t/tgroup 1: " + show(g1,""));

System.out.println("/t/tgroup 2: " + show(g2,""));

System.out.println("/t/tgroup 3: " + show(g3,""));

if( getSpheresWeight(g1) < getSpheresWeight(g2)){

find(g1);

}else if(getSpheresWeight(g1) == getSpheresWeight(g2)){

find(g3);

}else{

find(g2);

}

}

}

public static void main(String[] args) {

Sphere[] spheres = initSphere(53);

System.out.println(show(spheres,""));

find(spheres);

}

private static String formatId(int id, int length){

StringBuilder sb = new StringBuilder();

String idstr = String.valueOf(id);

int idlength = idstr.length();

for(int i=0; i<length-idlength;i++){

sb.append('0');

}

sb.append(idstr);

return sb.toString();

}

}

class Sphere{

public static final int SOLID_SPHERE_WEIGHT = 80;

public static final int HOLLOW_SPHERE_WEIGHT = 20;

String id;

int weight;

public Sphere(String id, int weight){

this.id = id;

this.weight = weight;

}

public String getId() {

return id;

}

public void setId(String id) {

this.id = id;

} public int getWeight() {

return weight;

}

public void setWeight(int weight) {

this.weight = weight;

}

public String getShow(){

if(this.getWeight()>=SOLID_SPHERE_WEIGHT){

return "●";

}else{

return "○";

}

}

public String toString2(){

StringBuilder sb = new StringBuilder();

sb.append("[id=").append(this.getId()).append(',').append("weight=").append(this.getWeight()).append("]");

return sb.toString();

}

public String toString(){

StringBuilder sb = new StringBuilder();

sb.append("[").append(this.getShow()).append(this.getId()).append(']');

return sb.toString();

}

}