Given a non-empty binary tree, find the maximum path sum.
For this problem, a path is defined as any sequence of nodes from some starting node to any node in the tree along the parent-child connections. The path must contain at least one node and does not need to go through the root.
Example 1:
Input: [1,2,3]
1
/ \
2 3
Output: 6
Example 2:
Input: [-10,9,20,null,null,15,7]
-10
/ \
9 20
/ \
15 7
Output: 42
Solution
There are FOUR type of sums that cross node
1: leftTree + node + rightTree
2: leftTree + node
3: node + rightTree
4: node
Just get max of those sums.
class Solution {
func maxPathSum(_ root: TreeNode?) -> Int {
var res = Int.min
maxUtil(root, &res)
return res
}
// 4 type of sum cross node
// 1: leftTree + node + rightTree
// 2: leftTree + node
// 3: node + rightTree
// 4: node
func maxUtil(_ node: TreeNode?, _ res: inout Int) -> Int{
guard let node = node else { return 0 }
let leftTree = maxUtil(node.left, &res)
let rightTree = maxUtil(node.right, &res)
let sumWithNodeAsLeaf = max(leftTree, rightTree) + node.val
let sumWithNodeAsRoot = leftTree + rightTree + node.val
let topMax = max(max(sumWithNodeAsLeaf, sumWithNodeAsRoot), node.val)
res = max(res, topMax)
return max(sumWithNodeAsLeaf, node.val)
}
}