线段树(SegmentTree)基础模板

Posted 2022-05-29 qbits

线段树模板题来源：https://www.lintcode.com/problem/segment-tree-build/description

201.?线段树的构造

/**
 * Definition of SegmentTreeNode:
 * class SegmentTreeNode 
 * public:
 *     int start, end;
 *     SegmentTreeNode *left, *right;
 *     SegmentTreeNode(int start, int end) 
 *         this->start = start, this->end = end;
 *         this->left = this->right = NULL;
 *     
 * 
 */


class Solution 
public:
    /*
     * @param start: start value.
     * @param end: end value.
     * @return: The root of Segment Tree.
     */
    SegmentTreeNode * build(int start, int end) 
        // write your code here
        if(start > end) return nullptr;
        auto root = new SegmentTreeNode(start, end);
        if(start < end)
            auto mid = (start + end) / 2;
            root->left = build(start, mid);
            root->right = build(mid+1, end);
        
        
        return root;
    
;

202.?线段树的查询

/**
 * Definition of SegmentTreeNode:
 * class SegmentTreeNode 
 * public:
 *     int start, end, max;
 *     SegmentTreeNode *left, *right;
 *     SegmentTreeNode(int start, int end, int max) 
 *         this->start = start;
 *         this->end = end;
 *         this->max = max;
 *         this->left = this->right = NULL;
 *     
 * 
 */

class Solution 
public:
    /**
     * @param root: The root of segment tree.
     * @param start: start value.
     * @param end: end value.
     * @return: The maximum number in the interval [start, end]
     */
    int query(SegmentTreeNode * root, int start, int end) 
        // write your code here
        auto mid = root->start + (root->end - root->start) / 2;
        if(start <= root->start && root->end <= end) return root->max;
        else if(start > mid) return query(root->right, start, end);
        else if(end <= mid) return query(root->left, start, end);
        else return max(query(root->left, start, mid), query(root->right, mid+1, end));
    
;

203. 线段树的修改

/**
 * Definition of SegmentTreeNode:
 * class SegmentTreeNode 
 * public:
 *     int start, end, max;
 *     SegmentTreeNode *left, *right;
 *     SegmentTreeNode(int start, int end, int max) 
 *         this->start = start;
 *         this->end = end;
 *         this->max = max;
 *         this->left = this->right = NULL;
 *     
 * 
 */

class Solution 
public:
    /**
     * @param root: The root of segment tree.
     * @param index: index.
     * @param value: value
     * @return: nothing
     */
    void modify(SegmentTreeNode * root, int index, int value) 
        // write your code here
        if(root == nullptr || index > root->end || index < root->start) return;
        if(root->start == root->end) 
            root->max = value;
            return ;
        
        auto mid = root->start + (root->end - root->start) / 2;

        if(index > mid)
            modify(root->right, index, value);
         else 
            modify(root->left, index, value);
        
        root->max = max(root->right->max, root->left->max);
        
    
;

247. 线段树查询 II

/**
 * Definition of SegmentTreeNode:
 * class SegmentTreeNode 
 * public:
 *     int start, end, count;
 *     SegmentTreeNode *left, *right;
 *     SegmentTreeNode(int start, int end, int count) 
 *         this->start = start;
 *         this->end = end;
 *         this->count = count;
 *         this->left = this->right = NULL;
 *     
 * 
 */


class Solution 
public:
    /*
     * @param root: The root of segment tree.
     * @param start: start value.
     * @param end: end value.
     * @return: The count number in the interval [start, end]
     */
    int query(SegmentTreeNode * root, int start, int end) 
        // write your code here
        if(root == NULL) return 0;
        if(start <= root->start && root->end <= end) return root->count;
        auto mid = root->start + (root->end - root->start) / 2;
        if(end <= mid) return query(root->left, start, end);
        else if(start > mid) return query(root->right, start, end);
        else return query(root->left, start, mid) + query(root->right, mid + 1, end); 
    
;

248.?统计比给定整数小的数的个数

class Solution 
public:
    /**
     * @param A: An integer array
     * @param queries: The query list
     * @return: The number of element in the array that are smaller that the given integer
     */
    struct SegmentTreeNode 
        int start, end, count;
        SegmentTreeNode* left, *right;
        SegmentTreeNode(int start_, int end_) : 
        start(start_), end(end_), count(0), left(nullptr), right(nullptr)  
    ;
    
    SegmentTreeNode* build(int start, int end)
        if(start > end) return nullptr;
        auto root = new SegmentTreeNode(start, end);
        if(start != end)
            auto mid = (start + end) / 2;
            root->left = build(start, mid);
            root->right = build(mid+1, end);
        
        
        return root;
    
    
    void add(SegmentTreeNode* root, int index, int val)
        auto mid = (root->start + root->end) / 2;
        if(root->start == root->end) 
            root->count += val;
            return;
        
        
        if(index > mid)
            add(root->right, index, val);
         else 
            add(root->left, index, val);
        
        
        root->count += val;
        
    
    
    int query(SegmentTreeNode* root, int start, int end)
        if(start <= root->start && root->end <= end) return root->count;
        auto mid = (root->start + root->end) / 2;
        if(start > mid) return query(root->right, start, end);
        else if(end <= mid) return query(root->left, start, end);
        else return query(root->right, mid+1, end) + query(root->left, start, mid);
    
    vector<int> countOfSmallerNumber(vector<int> &A, vector<int> &queries) 
        // write your code here
        auto root = build(0, 10000);
        for(int i = 0; i < A.size(); i++)
            add(root, A[i], 1);
        
        
        vector<int> ret;
        for(int i = 0;  i < queries.size(); i++)
            ret.push_back(query(root, 0, queries[i]-1));
        
        
        return ret;
    
;

249.?统计前面比自己小的数的个数

class Solution 
public:
    /**
     * @param A: an integer array
     * @return: A list of integers includes the index of the first number and the index of the last number
     */
     struct SegmentTreeNode 
        int start, end, count;
        SegmentTreeNode* left, *right;
        SegmentTreeNode(int start_, int end_) : 
        start(start_), end(end_), count(0), left(nullptr), right(nullptr)  
    ;
    
    SegmentTreeNode* build(int start, int end)
        if(start > end) return nullptr;
        auto root = new SegmentTreeNode(start, end);
        if(start != end)
            auto mid = (start + end) / 2;
            root->left = build(start, mid);
            root->right = build(mid+1, end);
        
        
        return root;
    
    
    void add(SegmentTreeNode* root, int index, int val)
        auto mid = (root->start + root->end) / 2;
        if(root->start == root->end) 
            root->count += val;
            return;
        
        
        if(index > mid)
            add(root->right, index, val);
         else 
            add(root->left, index, val);
        
        
        root->count += val;
        
    
    
    int query(SegmentTreeNode* root, int start, int end)
        if(start > end) return 0;
        if(start <= root->start && root->end <= end) return root->count;
        auto mid = (root->start + root->end) / 2;
        if(start > mid) return query(root->right, start, end);
        else if(end <= mid) return query(root->left, start, end);
        else return query(root->right, mid+1, end) + query(root->left, start, mid);
    
    vector<int> countOfSmallerNumberII(vector<int> &A) 
        // write your code here
        auto root = build(0, 10000);
        vector<int> ret;
        for(int i = 0; i < A.size(); i++)
            auto c = query(root, 0, A[i]-1);
           
            ret.push_back(c);
          
            add(root, A[i], 1);
        

        return ret;
    
;