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Day 29 of 30 days Leetcode challenge

Binary Tree Maximum Path Sum

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)
    }
}

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