USACO 2.1 Hamming Codes (hamming)

//Main Idea//We use the greedy algorithm and start to check the hamming distance of nummber from//the minimun num.The pity is that I can't prove the correctness of it.I will try it later./*ID: haolink1PROG: hammingLANG: C++*///#include <iostream>#include <fstream>#include <vector>using namespace std;short bit_num= 0;short min_distance = 0 ;short CountDistance(short element1,short element2);bool CheckValid(vector<short>& selected_codewords,short codeword);int main(){    ifstream fin("hamming.in");    short codewords_num = 0;    fin >> codewords_num >> bit_num >> min_distance;    short max_value = (1 << bit_num);//    for(short i = 0; i < bit_num; i++){//        max_value *= 2;//    }    vector<short> selected_codewords;    // 0 can be one of the numbers in the set, because if the minimum number in the set    // were N instead of 0, we could XOR N to each number in the set and they would     //still be the same distance apart.    selected_codewords.push_back(0);    //Note the counter start form 1;    short counter = 1;    //Start from minimun number;    for(short i = 1; i <= max_value; i++){        if(CheckValid(selected_codewords,i)){            selected_codewords.push_back(i);            counter++;        }        if(counter >= codewords_num)            break;    }    ofstream fout("hamming.out");    //Note the ouput format;    short print_num = 0;    short len = selected_codewords.size();    for(short i = 0; i < len-1; i++){        if(print_num < 9){            fout<<selected_codewords[i]<<" ";            print_num++;        }else{            fout<<selected_codewords[i]<<endl;            print_num = 0;        }    }    if(len > 0)        fout<<selected_codewords[len-1]<<endl;    return 0;}short CountDistance(short element1,short element2){    short distance = 0;    short diff = element1 ^ element2;    for(short i = 0; i < bit_num; i++){        if((1<<i)& diff)            distance++;    }    return distance;}bool CheckValid(vector<short>& selected_codewords,short codeword){    for(short i = 0; i < short(selected_codewords.size());i++){       if(CountDistance(selected_codewords[i],codeword) < min_distance)           return false;    }    return true;}