使用C++模板的通用分段树实现

我正在尝试为更新和范围查询创建一个通用的分段树类。

我希望用户提供元素的类型T和一个函数，我将其命名为compose。

此函数接受两个类型为T的参数，并返回一个相同类型T的值。此返回值是在2个元素的范围内执行所需操作时的结果，我可以使用2个元素在任意数量的元素的范围上执行相同的操作。

类别如下：

#include <functional>
template<class T>
class SegmentTree {
    public:
        class binary_function_unitype: public std::binary_function<T,T,T> {
            public:
                virtual T operator() (T arg1, T arg2) {};
        };
    private:
        class Node {
            public:
                T value;
                int seg_start, seg_end;
                Node* left;
                Node* right;
                Node (T value, int seg_start, int seg_end, Node* left=0, Node* right=0) {
                    this->value = value;
                    this->seg_start = seg_start;
                    this->seg_end = seg_end;
                    this->left = left;
                    this->right = right;
                }
        };
        // Not expecting the compose function to be robust enough.
        T composeUtil (T arg1, T arg2) {
            if (arg1!=0 && arg2!=0)
                return compose(arg1,arg2);
            else if (arg1!=0)
                return arg1;
            else if (arg2!=0)
                return arg2;
        }
        // Creating the Segment Tree.
        Node* createTree (T leaves[], int start, int end) {
            // base case - leaf of tree.
            if (start==end)
                return new Node(leaves[start],start,start,0,0);
            // general case.
            int mid = start + (end-start)/2;
            Node* left = createTree(leaves,start,mid);
            Node* right = createTree(leaves,mid+1,end);
            T retValue = composeUtil(left->value,right->value);
            return new Node(retValue,start,end,left,right);
        }
        // Range Query helper.
        T queryUtil (Node* root, int start, int end) {
            int seg_start = root->seg_start, seg_end = root->seg_end;
            if (seg_start>end || seg_end<start)
                return 0;
            else if (seg_start>=start && seg_end<=end)
                return root->value;
            else
                return compose( queryUtil(root->left,start,end), queryUtil(root->right,start,end));
        }
        // Helper function for Updating the Segment Tree.
        void updateUtil (Node* root, int position, T updatedValue) {
            int seg_start = root->seg_start, seg_end = root->seg_end;
            if(seg_start>position || seg_end<position)
                return;
            else if(seg_start==seg_end)
                root->value = updatedValue;
            else
                root->value = composeUtil(root->left->value,root->right->value);
        }
        // Freeing the memory allocated to the Segment Tree.
        void destroyTree(Node* root) {
            if (root->left!=0)
                destroyTree(root->left);
            if (root->right!=0)
                destroyTree(root->right);
            delete root;
        }
        Node* root;
        binary_function_unitype compose;
    public:
        SegmentTree (T leaves[], binary_function_unitype compose, int start, int end) {
            this->compose = compose;
            this->root = createTree(leaves, start, end);
        }
        T query (int start, int end) {
            return queryUtil(root, start, end);
        }
        void update (int position, T updatedValue) {
            updateUtil(root, position, updatedValue);
        }
        ~SegmentTree () {
            destroyTree(root);
        }
};

当我尝试使用这个类时，发现没有使用我作为参数使用的compose函数，相反，正在使用类binary_function_unitype中的函数。

我希望用户的函数定义会覆盖类binary_function_unitype中的函数定义，我的工作就会完成。但这并没有发生。使用此类的程序如下：

#include <iostream>
#include "SegmentTree.h"
using namespace std;
class Compose: public SegmentTree<int>::binary_function_unitype {
    public:
        int operator() (int arg1, int arg2) {
            return arg1+arg2;
        }
};
int main()
{
    int num;
    cin>>num;
    int arr[num];
    for(int i=0;i<num;i++)
        cin>>arr[i];
    Compose compose;
    SegmentTree<int> segTree(arr, compose, 0, num-1);
    int s,e;
    cin>>s>>e;
    cout<<segTree.query(s-1,e-1);
    return 0;
}

有人能告诉我我的方法有什么缺陷吗？或者我是否误解了在C++中使用继承或模板的一些基本概念？

谢谢。