题目1095：2的幂次方 练习递归

题目描述：

    Every positive number can be presented by the exponential form.For example, 137 = 2^7 + 2^3 + 2^0。

    Let's present a^b by the form a(b).Then 137 is presented by 2(7)+2(3)+2(0). Since 7 = 2^2 + 2 + 2^0 and 3 = 2 + 2^0 , 137 is finally presented by 2(2(2)+2 +2(0))+2(2+2(0))+2(0). 
 
    Given a positive number n,your task is to present n with the exponential form which only contains the digits 0 and 2.

输入：

    For each case, the input file contains a positive integer n (n<=20000).

输出：

    For each case, you should output the exponential form of n an a single line.Note that,there should not be any additional white spaces in the line.

样例输入：

1315

样例输出：

2(2(2+2(0))+2)+2(2(2+2(0)))+2(2(2)+2(0))+2+2(0)

package 上海交大;

import java.util.Scanner;

public class 幂次方1095 {
    static int n;
    public static void main(String[] args) {
        Scanner s = new Scanner(System.in);
        while (s.hasNextInt()) {
            n = s.nextInt();
            System.out.println(f(n));
        }
    }
    static String f(int n) {
        StringBuffer sb = new StringBuffer();
        if (n < 8) {
            switch(n){
            case 0: return "0";
            case 1: return "";
            case 2: return "2";
            case 3: return "2+2(0)";
            case 4: return "2(2)";
            case 5: return "2(2)+2(0)";
            case 6: return "2(2)+2";
            case 7: return "2(2)+2+2(0)";
            }
        }else{
            String temp = Integer.toBinaryString(n);
            int len = temp.length();
            for(int i=0; i<len; i++){
                if(temp.charAt(i) == '1'){
                    if(i!=0)
                        sb.append("+");
                    sb.append("2(");
                    sb.append(f(len-i-1));
                    sb.append(")");
                }
            }
        }
        return sb.toString().replaceAll("\\(\\)", "");
    }
}