算法1

打表

C++ 代码

#include <iostream>
#include <string>

using std::cout;
using std::cin;
using std::endl;
using std::string;

void method1(int n){
    string s[30] = {
        "2(0)",            //1
        "2",               //2
        "2(2)",            //4
        "2(2+2(0))",       //8
        "2(2(2))",         //16
        "2(2(2)+2(0))",    //32
        "2(2(2)+2)",       //64
        "2(2(2)+2+2(0))",  //128
        "2(2(2+2(0)))",           //256
        "2(2(2+2(0))+2(0))",      //512
        "2(2(2+2(0))+2)",         //1024
        "2(2(2+2(0))+2+2(0))",    //2048
        "2(2(2+2(0))+2(2))",      //4096
        "2(2(2+2(0))+2(2)+2(0))", //8192
        "2(2(2+2(0))+2(2)+2)"     //16384
    };

    string ans;
    for(int i = 15; i >=0; --i){
        if((n >> i) & 1){
            if(ans.size())
                ans += "+";
            ans += s[i];
        }
    }
    cout << ans << endl;
}

int main()
{
    int num;
    while(cin >> num){
        method1(num); 
    }

    return 0;
}

算法2

递归

C++ 代码

#include <iostream>
#include <string>

using std::cout;
using std::cin;
using std::endl;
using std::string;

string dfs(int n){
    string res;
    for(int i = 14; i >= 0; i--){
        if((n>>i)&1){
            if(res.size())  res += "+";
            if(i == 0)  res += "2(0)";
            else if(i == 1) res += "2";
            else    res += "2(" + dfs(i) + ")";
        }
    }
    return res;
}

int main()
{
    int num;
    while(cin >> num){
        cout << dfs(num) << endl;
    }

    return 0;
}