I am trying to implement Huffman encoding in C++ using custom made priority_queue. I am storing the information in structure named Node. Here is the code
#include<bits/stdc++.h>
using namespace std;
using ll = long long;
//two same name functions are for min heap and max heap(Function overloading)
struct Node{
    char letter;
    int value;
    Node* left;
    Node* right;
    Node(char letter,int value, Node* left,Node* right){
        this->letter = letter;
        this->value = value;
        this->left = left;
        this->right = right;
    }
    bool operator < (const Node* &a){//HERE IS THE PROBLEM
        if((this->value) < (a->value))
            return true;
        else
            return false;
    }
    bool operator > (const Node* &a){//HERE IS THE PROBLEM
        if((this->value) > (a->value))
            return true;
        else
            return false;
    }
};
template <class T>
class Priority_Queue{
    public:
    int k;
    int sz;
    vector<T> v;
    Priority_Queue(int k){
        sz = 0;
        this->k = k;
    }
    void heapify(int index,int n){
        int max_index = index;
        for(int i = index*k+1;i <= min(n-1,index*k+k);++i){
            if(v[i] > v[max_index])
                max_index = i;
        }
        if(index != max_index){
            swap(v[max_index],v[index]);
            heapify(v,max_index,n);
        }
    }
    void heapify(vector<int> &v,int index,int n,bool trigger){
        //for calling min_heapify using function overloading
        int min_index = index;
        for(int i = index*k+1;i <= min(n-1,index*k+k);++i){
            if(v[i] < v[min_index])
                min_index = i;
        }
        if(index != min_index){
            swap(v[min_index],v[index]);
            heapify(v,min_index,n,trigger);
        }
    }   
    void Insert(T val){
        if(sz == (int)v.size()){
            v.push_back(val);
            ++sz;
        }
        else
            v[sz++] = val;
        int parent = (sz-1)/k;
        int node = sz-1;
        while(node >= 1){
            int parent = (node-1)/k;
            if(v[parent] < v[node]){
                swap(v[parent],v[node]);
                node = parent;
                parent = (parent-1)/k;
            }
            else
                break;
        }
    }
    void Insert(T val, bool trigger){
        if(sz == (int)v.size()){
            v.push_back(val);
            ++sz;
        }
        else
            v[sz++] = val;
        int parent = (sz-1)/k;
        int node = sz-1;
        while(node >= 1){
            int parent = (node-1)/k;
            if(v[parent] > v[node]){// IF CONDITION DOESN'T WORK
                swap(v[parent],v[node]);
                node = parent;
                parent = (parent-1)/k;
            }
            else
                break;
        }
    }
    void Pop(){
    if(sz == 0){
            cout << "Heap Underflow\n";
            return;
        }
        swap(v[0],v[sz-1]);
        --sz;
        heapify(0,sz);
    }
    void Pop(bool trigger){
        if(sz == 0){
            cout << "Heap Underflow\n";
            return;
        }
        swap(v[0],v[sz-1]);
        --sz;
        heapify(0,sz,trigger);
    }
    T Top(){
        return v[0];
    }
    void printHeap(){
        for(int i = 0; i < sz;++i){
            cout << v[i]->value << " ";
        }
        cout << "\n";
    }
};
int main()
{
    string s;
    cin >> s;
    int n = s.length();
    vector<int> freq(26,0);
    for(int i = 0; i < n;++i){
        ++freq[s[i]-'a'];
    }
    Priority_Queue<Node*> pq(2);
    for(int i = 0; i < 26;++i){
        if(freq[i] == 0)
            continue;
        pq.Insert(new Node(char(i+'a'),freq[i],NULL,NULL),true);
    }
    pq.printHeap();
}
I don't have much experience with C++ and I am having trouble overloading relational operators where I want to compare two structure pointers based on the value parameter.For example: if I enter aab , the if condition in Insert function should be executed but it never happens. I searched up a lot regarding overloading of relational operators but none of them seem to fix the issue I am facing. Can someone please help me ? What am I doing wrong while overloading the operator?
 
    