Segment Tree Modify 203

Question

For a Maximum Segment Tree, which each node has an extra value max to store the maximum value in this node's interval.

Implement a modify function with three parameter root, index and value to change the node's value with [start, end] = [index, index] to the new given value. Make sure after this change, every node in segment tree still has the max attribute with the correct value.

Example

For segment tree:

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

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

if call modify(root, 2, 4), we can get:

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

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

or call modify(root, 4, 0), we can get:

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

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

Challenge

Do it in O(h) time, h is the height of the segment tree.

Solution

递归解决。一开始居然想到用stack记录整条查找路径再反向更新，真是蠢哭了。

1. index比mid小，在左边区间找

2. index比mid大，在右边区间找

3. 当某一点root的左右边界和index相等时，则找到，改变value

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, index, value: The root of segment tree and 
     *@ change the node's value with [index, index] to the new given value
     *@return: void
     */
    public void modify(SegmentTreeNode root, int index, int value) {
        // write your code here
        if(root == null || index < root.start || index > root.end){
            return;
        }

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

        int mid = (root.start + root.end) / 2;
        if(index <= mid){
            modify(root.left, index, value);
        }else{
            modify(root.right, index, value);
        }

        root.max = Math.max(root.left.max, root.right.max);
    }
}