#439 Segment Tree Build II

最新推荐文章于 2024-10-21 09:04:45 发布

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最新推荐文章于 2024-10-21 09:04:45 发布

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分类专栏： lintcode 文章标签： lintcode segment tree

本文链接：https://blog.youkuaiyun.com/haifischxia/article/details/52219679

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本文详细介绍了一种高级数据结构——区间树（又称段树）的构建方法。通过递归方式创建区间树，每个节点对应数组中特定区间的最大值。文章提供了具体实现案例，帮助读者理解区间树的工作原理。

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题目描述：

The structure of Segment Tree is a binary tree which each node has two attributesstart and end denote an segment / interval.

start and end are both integers, they should be assigned in following rules:

The root's start and end is given by build method.
The left child of node A has start=A.left, end=(A.left + A.right) / 2.
The right child of node A has start=(A.left + A.right) / 2 + 1, end=A.right.
if start equals to end, there will be no children for this node.

Implement a build method with a given array, so that we can create a corresponding segment tree with every node value represent the corresponding interval max value in the array, return the root of this segment tree.

Have you met this question in a real interview?

Yes

Clarification

Segment Tree (a.k.a Interval Tree) is an advanced data structure which can support queries like:

which of these intervals contain a given point
which of these points are in a given interval

See wiki:
Segment Tree
Interval Tree

Example

Given [3,2,1,4]. The segment tree will be:

                 [0,  3] (max = 4)
                  /            \
        [0,  1] (max = 3)     [2, 3]  (max = 4)
        /        \               /             \
[0, 0](max = 3)  [1, 1](max = 2)[2, 2](max = 1) [3, 3] (max = 4)

题目思路：

这题先从最下面的子树找起，start==end的时候，max就是A[start]。找完子树的max就可以得到root的max了。还是用recursion就行。

Mycode（AC = 86ms）：

/**
 * 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 A: a list of integer
     *@return: The root of Segment Tree
     */
    SegmentTreeNode * build(vector<int>& A) {
        // write your code here
        return buildTree(A, 0, A.size() - 1);
    }
    
    SegmentTreeNode* buildTree(vector<int>& A, int start, int end) {
        if (start > end) {
            return NULL;
        }
        else if (start == end) {
            return new SegmentTreeNode(start, end, A[start]);
        }
        else {
            SegmentTreeNode *root = new SegmentTreeNode(start, end, A[start]);
            root->left = buildTree(A, start, (start + end) / 2);
            root->right = buildTree(A, (start + end) / 2 + 1, end);
            
            int max_val = INT_MIN;
            if (root->left) max_val = max(max_val, root->left->max);
            if (root->right) max_val = max(max_val, root->right->max);
            root->max = max_val;
            
            return root;
        }
    }
};