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。