分治算法经典例题 寻找假币

一个袋子里有若干硬币，其中一枚是假币，并且和假币和真币一模一样，目前只知道假币币真币轻一点。请问如何区别:

利用分治 算法的思想:

import java.util.Scanner;public class Main {    static final int MAXNUM = 30;    private static int FalseCoin(int[] coin, int low, int high) {        int sum1 = 0, sum2 = 0, sum3 = 0;        int re = 0;        if ( low+1 == high ) {            if ( coin[low] < coin[high] ) {                re = low+1;                return re;            }            else {                re = high+1;                return re;            }        }        if ( (high-low+1)%2 == 0 ) {//如果n是偶数            //前半段            for ( int i = low; i <= low+(high-low)/2; i++ ) {                sum1 = sum1 + coin[i];            }            //后半段            for ( int i = low+(high-low)/2+1; i <= high; i++ ) {                sum2 = sum2 + coin[i];            }            if ( sum1 > sum2 ) {                re = FalseCoin(coin, low+(high-low)/2+1, high);                return re;            }            else if ( sum2 > sum1 ){//sum2 > sum1                re = FalseCoin(coin, low, low+(high-low)/2);                return re;            }            else {            }        }        else {//如果是奇数            //前半段，除去中间的一个硬币            for ( int i = low; i <= low+(high-low)/2-1; i++ ) {                sum1 = sum1 + coin[i];            }            //后半段，除去中间的一个硬币            for ( int i = low+(high-low)/2+1; i <= high;i++ ) {                sum2 = sum2 + coin[i];            }            sum3 = coin[low+(high-low)/2];            if ( sum1 > sum2 ) {                re = FalseCoin(coin, low+(high-low)/2+1, high);                return re;            }            else if ( sum2 > sum1 ){                re = FalseCoin(coin, low, low+(high-low)/2-1);                return re;            }            else {            }            if ( sum1+sum3 == sum2+sum3 ) {                re = low+(high-low)/2+1;                return re;            }        }        return re;    }    public static void main(String[] args) {        int[] coin = new int[MAXNUM];        System.out.println("分治算法求假币问题: ");        System.out.println("请输入硬币总的个数: ");        Scanner in = new Scanner(System.in);        int n = in.nextInt();        System.out.println("请输入所有硬币权值: ");        for ( int i = 0; i < n; i++ ) {            coin[i] = in.nextInt();        }        int position = FalseCoin(coin, 0, n-1);        System.out.println("假币在 " + position + "个位置 ");    }   }

//其实 本例子只是为了理解分治算法的思想，要是找出那一枚硬币，在规模小的情况下，一个个称 比一下不就好了。

分治算法的基本思想

对于一个规模为N的问题，若该规模比较难解决，
可以分解为M个小规模的子问题，相互独立的子问题。
可以采用递归算法进行解决。