(C++)ポインタに関するエラー

Segmentation fault (core dumped)

#include<bits/stdc++.h>
using namespace std;

template <typename T>
struct per_array{
    int depth;
    struct node;
    vector<node*> v;

    struct node{
        bool isleaf;
        node* child[20] = {};
        T val;

        void grow(int depth){
            if (depth == 0){
                isleaf = 1;
                return;
            }

            isleaf = 0;
            for (int i = 0; i < 20; i++){
                node* ptr = (node*)malloc(sizeof(node));
                child[i] = ptr;
            }

            for (int i = 0; i < 20; i++){
                child[i]->grow(depth - 1);
            }
            return;
        }

        node* set(int index, T a){
            if (isleaf) {
                val = a;
                return this;
            }

            return child[index % 20]->set(index / 20, a);
        }

        T get(int index){
            if (index == 0 && isleaf) {
                return val;
            }

            return child[index % 20]->get(index / 20);
        }

        node* copy(node* original, int index, T a){
            if (index == 0 || original->isleaf){
                val = a;
                isleaf = 1;
                return this;
            }

            isleaf = 0;
            for (int i = 0; i < 20; i++){
                if (index % 20 == i) {
                    child[i] = copy(original->child[i], index / 20, a);//おそらくエラー元
                }
                else child[i] = original->child[i];
            }
            return this;
        }
    };

    per_array(vector<T> const a){
        //aで初期化
        depth = 0;
        int t = 1;
        while (t < (int)a.size()){
            t *= 20;
            depth++;
        }

        node n;
        v.emplace_back(&n);
        n.grow(depth);
        for (int i = 0; i < (int)a.size(); i++){
            v[0]->set(i, a[i]);
        }
    }

    void correct(int n, T m){
        //最新verのm番目を破壊的に変更
        (*v.rbegin())->set(n, m);
        return;
    }

    int update(int n, T m){
        //最新verのn番目を保存的に変更（返り値は永続配列中の番号）
        node* ptr;
        ptr = ptr->copy(*v.rbegin(), n, m);
        v.emplace_back(ptr);
        return (int)(v.size() - 1);
    }

    void correct(int index, int n, T m){
        //index番目のverのn番目を破壊的に変更
        v[index]->set(n, m);
        return;
    }

    int back(int index){
        //verをindexに巻き戻す
        v.emplace_back(v[index]);
        return (int)(v.size() - 1);
    }

    T at(int n, int m){
        //n番目のverのm番目を返す
        return v[n]->get(m);
    }
};

int main(){
    vector<int> a = {3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5};
    per_array<int> pa(a);
    cout << pa.depth << endl << endl;

    cout << pa.at(0, 0) << endl; //3
    cout << pa.at(0, 2) << endl; //4
    cout << pa.at(0, 4) << endl; //5
    cout << pa.at(0, 6) << endl; //2
    cout << pa.at(0, 8) << endl; //3
    cout << endl;

    pa.update(8, 10);//エラー発生
    cout << pa.at(0, 8) << endl; //3
    cout << pa.at(1, 8) << endl; //10
}