树形分区设计 

均匀分区查询算法的失败是由于积分分布的非均匀性，那么我们自然就会想，能不能按二八定律，把score_range表设计为非均匀区间呢？比如，把低分区划密集一点，10分一个区间，然后逐渐变成100分，1000分，10000分 … 当然，这不失为一种方法，不过这种分法有一定的随意性，不容易把握好，而且整个系统的积分分布会随着使用而逐渐发生变化，最初的较好的分区方法可能会变得不适应未来的情况了。我们希望找到一种分区方法，既可以适应积分非均匀性，又可以适应系统积分分布的变化，这就是树形分区。

#include<iostream>
using namespace std;

struct TreeNode 
{
    int fromScore;
    int toScore;
    int count;
    TreeNode *left, *right;
    TreeNode(int from, int to, int c = 0): fromScore(from), toScore(to), count(c), left(NULL), right(NULL){}
};

TreeNode* createTree(TreeNode *&root, int from, int to)
{
    if(from > to) return NULL;
    root = new TreeNode(from, to);
    if(from == to) return root;
    int mid = (from & to) + ((from ^ to) >> 1);
    root->left = createTree(root->left, from, mid);
    root->right = createTree(root->right, mid+1, to);
    return root;
}

void insertNewScore(TreeNode *root, int score)
{
    if(root == NULL) return;
    if(score >= root->fromScore && score <= root->toScore)
        root->count++;
    int mid = (root->fromScore & root->toScore) + ((root->fromScore ^ root->toScore) >> 1);
    if(score <= mid) insertNewScore(root->left, score);
    else insertNewScore(root->right, score);
}

void deleteOldScore(TreeNode *root, int score)
{
    if(root == NULL) return;
    if(score >= root->fromScore && score <= root->toScore) 
        root->count--;
    int mid = (root->fromScore & root->toScore) + ((root->fromScore ^ root->toScore) >> 1); 
    if(score <= mid) deleteOldScore(root->left, score);
    else deleteOldScore(root->right, score);
}

void changeScore(TreeNode *root, int oldScore, int newScore)
{
    deleteOldScore(root, oldScore);
    insertNewScore(root, newScore);
}

void getRank(TreeNode *root, int score, int &rank)
{
    if(root == NULL) return;
    int mid = (root->fromScore & root->toScore) + ((root->fromScore ^ root->toScore) >> 1); 
    if(score > mid) getRank(root->right, score, rank);
    else if(root->right)
    {
        rank += root->right->count;
        getRank(root->left, score, rank);
    }
}

int getRank(TreeNode *root, int score)
{
    int rank = 1;
    getRank(root, score, rank);
    return rank;
}

void print(TreeNode *root)
{
    if(root != NULL)
    {
        print(root->left);
        cout<<root->fromScore <<" "<<root->toScore<<" "<<root->count<<endl;
        print(root->right);
    }
}

int main()
{
    TreeNode *root = NULL;
    createTree(root, 1, 10);
    int score[10] = {
        1, 3, 5, 6, 2, 4, 3, 1, 7, 7
    };

    for(int i = 0; i < 10; ++i)
        insertNewScore(root, score[i]);
    cout<<"Rank is as follows:"<<endl;
    print(root);
    cout<<"Rank of score=5"<<endl;
    cout<<getRank(root, 5)<<endl;
    cout<<"Alter the score"<<endl;
    changeScore(root, 2, 4);
    print(root);
    cout<<getRank(root, 3)<<endl;

    return 0;
}