LintCode 203: Segment Tree Modify (线段树经典题)

本文详细解析了段树（Segment Tree）中修改节点值的高效算法。通过递归方式更新节点值，并确保整个段树的最大值属性正确无误。文章通过实例展示了如何在O(h)时间复杂度内完成修改操作，其中h为段树的高度。

203. Segment Tree Modify

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

Example 1:

Input："[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]",2,4
Output："[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]"
Explanation：
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]

Example 2:

Input："[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]",4,0
Output："[1,4,max=4][1,2,max=4][3,4,max=0][1,1,max=2][2,2,max=4][3,3,max=0][4,4,max=0]"
Explanation：
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, 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.

Notice

We suggest you finish problem Segment Tree Build and Segment Tree Query first.

Input test data (one parameter per line)How to understand a testcase?

解法1：

/**
 * 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 root: The root of segment tree.
     * @param index: index.
     * @param value: value
     * @return: nothing
     */
    void modify(SegmentTreeNode * root, int index, int value) {
        if (index == root->start && index == root->end) {
            root->max = value;
            return;
        }
        int mid = root->start + (root->end - root->start) / 2;
        if (index <= mid) {
            modify(root->left, index, value);
        } else {
            modify(root->right, index, value);
        }
        //root->max = max(root->max, value);
        root->max = max(root->left->max, root->right->max);
        return;
    }
};