[Lintcode]Segment Tree Query II

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本文介绍了一种使用段树进行区间元素计数的方法。通过构建段树，并定义每个节点额外存储区间内元素数量的属性，实现了高效查询指定区间[start,end]内数组元素的数量。通过实例展示了查询方法的具体应用。

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For an array, we can build a SegmentTree for it, each node stores an extra attribute count to denote the number of elements in the the array which value is between interval start and end. (The array may not fully filled by elements)

Design a query method with three parameters root, start and end, find the number of elements in the in array's interval [start, end] by the given root of value SegmentTree.

Example

For array [0, 2, 3], the corresponding value Segment Tree is:

                     [0, 3, count=3]
                     /             \
          [0,1,count=1]             [2,3,count=2]
          /         \               /            \
   [0,0,count=1] [1,1,count=0] [2,2,count=1], [3,3,count=1]

query(1, 1), return 0

query(1, 2), return 1

query(2, 3), return 2

query(0, 2), return 2

/**
 * Definition of SegmentTreeNode:
 * public class SegmentTreeNode {
 *     public int start, end, count;
 *     public SegmentTreeNode left, right;
 *     public SegmentTreeNode(int start, int end, int count) {
 *         this.start = start;
 *         this.end = end;
 *         this.count = count;
 *         this.left = this.right = null;
 *     }
 * }
 */
public class Solution {
    /**
     *@param root, start, end: The root of segment tree and 
     *                         an segment / interval
     *@return: The count number in the interval [start, end]
     */
    public int query(SegmentTreeNode root, int start, int end) {
        if(root == null) return 0;
        if(start > root.end || end < root.start) return 0;
        if(start <= root.start && end >= root.end) return root.count;
        
        int left = query(root.left, start, end);
        int right = query(root.right, start, end);
        return left + right;
    }

}