Given the root of a binary tree, return the sum of every tree node's tilt.
The tilt of a tree node is the absolute difference between the sum of all left subtree node values and all right subtree node values. If a node does not have a left child, then the sum of the left subtree node values is treated as 0. The rule is similar if there the node does not have a right child.
Example 1:
Input: root = [1,2,3]
Output: 1
Explanation:
Tilt of node 2 : |0-0| = 0 (no children)
Tilt of node 3 : |0-0| = 0 (no children)
Tile of node 1 : |2-3| = 1 (left subtree is just left child, so sum is 2; right subtree is just right child, so sum is 3)
Sum of every tilt : 0 + 0 + 1 = 1
Example 2:
Input: root = [4,2,9,3,5,null,7]
Output: 15
Explanation:
Tilt of node 3 : |0-0| = 0 (no children)
Tilt of node 5 : |0-0| = 0 (no children)
Tilt of node 7 : |0-0| = 0 (no children)
Tilt of node 2 : |3-5| = 2 (left subtree is just left child, so sum is 3; right subtree is just right child, so sum is 5)
Tilt of node 9 : |0-7| = 7 (no left child, so sum is 0; right subtree is just right child, so sum is 7)
Tilt of node 4 : |(3+5+2)-(9+7)| = |10-16| = 6 (left subtree values are 3, 5, and 2, which sums to 10; right subtree values are 9 and 7, which sums to 16)
Sum of every tilt : 0 + 0 + 0 + 2 + 7 + 6 = 15
Input: root = [21,7,14,1,1,2,2,3,3]
Output: 9
Constraints:
The number of nodes in the tree is in the range [0, 104].
-1000 <= Node.val <= 1000
Solutions
🧠 Cpp
/**
* Definition for a binary tree node.
* struct TreeNode {
* int val;
* TreeNode *left;
* TreeNode *right;
* TreeNode() : val(0), left(nullptr), right(nullptr) {}
* TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
* TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
* };
*/
class Solution
{
//DP solution is slower smh
//map<TreeNode*, int> sum_storage;
int sum(const TreeNode* root)
{
if(!root)
return 0;
//DP check if already computed
// auto found = sum_storage.find(root);
// if(found != sum_storage.end())
// return found->second;
//compute sum
const int tree_sum = root->val + sum(root->left) + sum(root->right);
//sum_storage.insert( make_pair(root, tree_sum) );
return tree_sum;
}
public:
int findTilt(const TreeNode* root)
{
if(!root)
return 0;
int tilt_sum = abs( sum(root->left) - sum(root->right) );
tilt_sum += findTilt(root->left) + findTilt(root->right);
return tilt_sum;
}
};
