[LintCode] 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

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]

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