Доказательство теоремы

#include<iostream>
#include<fstream>
#include<vector>

using namespace std;

int k = 0;
struct edje {
    int to = 0;
    vector<int> child;
    bool use = false;
};

void edje_sort(vector<edje>& mas, vector<int>& weight, int v) {

    for (int i = 0; i < mas[v].child.size(); ++i) {
        for (int j = 0; j < mas[v].child.size() - 1; ++j) {
            if (weight[mas[v].child[j]] >= weight[mas[v].child[j + 1]])
                swap(mas[v].child[j], mas[v].child[j + 1]);
        }
    }

    /*for (int i = 0; i < mas[v].child.size() / 2 + mas[v].child.size() % 2; ++i) {
        mas[v].use = true;
    }*/

}

void dfs(vector<edje>& mas, vector<int>& weight, int v) {

    for (int i = 0; i < mas[v].child.size(); ++i) {
        dfs(mas, weight, mas[v].child[i]);
    }

    edje_sort(mas, weight, v);

    for (int i = 0; i < mas[v].child.size() / 2 + mas[v].child.size() % 2; ++i) {
        weight[v] += weight[mas[v].child[i]];
        mas[mas[v].child[i]].use = true;
    }
    weight[v] += 1;
}

void cout_dfs(vector<edje>& mas, vector<int>& f, int v) {

    for (int i = 0; i < mas[v].child.size(); ++i) {
        if (mas[mas[v].child[i]].use) {
            cout_dfs(mas, f, mas[v].child[i]);
        }
    }

    f.push_back(v);
    ++k;
}

int main() {

    ifstream fin("input.txt");
    ofstream fout("output.txt");

    int n;
    fin >> n;
    vector<edje> mas(n);
    vector<int> weight(n);
    for (int i = 0; i < n; ++i) {
        int j = 0;
        do {
            fin >> j;
            if (j != 0) {
                mas[i].child.push_back(j - 1);
                mas[j - 1].to = i;
            }
        } while (j != 0);
    }

    dfs(mas, weight, 0);

    vector<int> f;

    cout_dfs(mas, f, 0);
    fout << k << endl;

    for (int i = 0; i < f.size(); ++i) {
        fout << f[i] + 1 << endl;
    }

    return 0;
}