201.segment-tree-build.cpp

//  Tag: Segment Tree
//  Time: O(N)
//  Space: O(1)
//  Ref: -
//  Note: -

//  The structure of Segment Tree is a binary tree which each node has two attributes `start` 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.start, end=(A.start + A.end) / 2`.
//  - The right child of node A has `start=(A.start + A.end) / 2 + 1, end=A.end`.
//  - if _start_ equals to _end_, there will be no children for this node.
//  
//  Implement a `build` method with two parameters _start_ and _end_, so that we can create a corresponding segment tree with every node has the correct _start_ and _end_ value, return the root of this segment tree.
//  
//  **Example 1:**
//  ```
//  Input：[1,4]
//  Output："[1,4][1,2][3,4][1,1][2,2][3,3][4,4]"
//  Explanation：
//  	               [1,  4]
//  	             /        \
//  	      [1,  2]           [3, 4]
//  	      /     \           /     \
//  	   [1, 1]  [2, 2]     [3, 3]  [4, 4]
//  ```
//  **Example 2:**
//  ```
//  Input：[1,6]
//  Output："[1,6][1,3][4,6][1,2][3,3][4,5][6,6][1,1][2,2][4,4][5,5]"
//  Explanation：
//  	       [1,  6]
//               /        \
//        [1,  3]           [4,  6]
//        /     \           /     \
//     [1, 2]  [3,3]     [4, 5]   [6,6]
//     /    \           /     \
//  [1,1]   [2,2]     [4,4]   [5,5]
//  ```
//  
//  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](https://en.wikipedia.org/wiki/Segment_tree "Segment Tree")
//  [Interval Tree](https://en.wikipedia.org/wiki/Interval_tree "Interval Tree")

/**
 * 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;
        }

        SegmentTreeNode *node = new SegmentTreeNode(start, end);
        if (start == end) {
            return node;
        }

        int mid = (start + end) / 2;
        node->left = build(start, mid);
        node->right = build(mid + 1, end);
        return node;
    }
};