Segment Tree Query 202

Question

For an integer array (index from 0 to n-1, where n is the size of this array), in the corresponding SegmentTree, each node stores an extra attribute max to denote the maximum number in the interval of the array (index from start to end).

Design a query method with three parameters root, start and end, find the maximum number in the interval [start, end] by the given root of segment tree.

Example

For array [1, 4, 2, 3], the corresponding Segment Tree is:

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

[0,0,max=1] [1,1,max=4] [2,2,max=2], [3,3,max=3]

query(root, 1, 1), return 4

query(root, 1, 2), return 4

query(root, 2, 3), return 3

query(root, 0, 2), return 4

Solution

分情况讨论，递归查询：

1. 查询区间跨越mid，则要分别查询左边区间和右边区间，再取最大值

2. 查询区间只在一边，则只要查询那一边即可

代码如下：

/**
 * Definition of SegmentTreeNode:
 * public class SegmentTreeNode {
 *     public int start, end, max;
 *     public SegmentTreeNode left, right;
 *     public SegmentTreeNode(int start, int end, int max) {
 *         this.start = start;
 *         this.end = end;
 *         this.max = max
 *         this.left = this.right = null;
 *     }
 * }
 */
public class Solution {
    /**
     *@param root, start, end: The root of segment tree and 
     *                         an segment / interval
     *@return: The maximum number in the interval [start, end]
     */
    public int query(SegmentTreeNode root, int start, int end) {
        // write your code here
        if(root == null || start > end || start > root.end || end < root.start){
            return -1;
        }

        if((start == root.start && end == root.end) || (root.start == root.end)){
            return root.max;
        }

        int mid = (root.start + root.end) / 2;
        //跨越中点
        if(start <= mid && end >= mid + 1){
            int left = query(root.left, start, mid);
            int right = query(root.right, mid + 1, end);
            return Math.max(left, right);
        }
        //左边
        if(end <= mid){
            return query(root.left, start, end);
        }
        //右边
        return query(root.right, start, end);
    }
}