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Binary Tree Maximum Path Sum

Certification: Advanced Level Accuracy: 0% Submissions: 0 Points: 15

Write a C program to find the maximum path sum in a binary tree. A path is defined as any route along parent-child connections from some starting node to any ending node. The path must contain at least one node and does not need to go through the root.

Example 1
    
      
  • Input: root = [1,2,3]
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  • Output: 6
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  • Explanation: 
    • Tree structure: 1 is root, 2 and 3 are its children. 
    • Possible paths: [2], [1], [3], [2,1], [1,3], [2,1,3]. 
    • Path [2,1,3] gives maximum sum: 2 + 1 + 3 = 6. 
    • Therefore, maximum path sum is 6.
    •
Example 2
    
      
  • Input: root = [-10,9,20,null,null,15,7]
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  • Output: 42
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  • Explanation: 
    • Tree has -10 as root, 9 and 20 as children of root, 15 and 7 as children of 20. 
    • The optimal path is [15,20,7] which doesn't include the root. 
    • Path sum: 15 + 20 + 7 = 42. 
    • Therefore, maximum path sum is 42.
    •
Constraints
    
      
  • The number of nodes in the tree is in the range [1, 3 * 10^4]
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  • -1000 ≤ Node.val ≤ 1000
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  • Time Complexity: O(n) where n is number of nodes
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  • Space Complexity: O(h) where h is height of tree (recursion stack)
    •
Binary TreeDeloitteSnowflake
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Hint
Solution

Solution Hints

    
      
  • Use post-order traversal to process children before parent nodes
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  • For each node, calculate maximum path sum that ends at that node
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  • Consider three cases: path through left child, path through right child, or path through both children
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  • Keep track of global maximum path sum encountered during traversal
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  • Return the maximum single-branch path sum to parent for further calculations
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  • Handle negative path sums by choosing 0 instead (don't include negative branches)
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Steps to solve by this approach:

 Step 1: Initialize a global variable to track the maximum path sum found so far.

 Step 2: Use post-order traversal to process children nodes before their parent.

 Step 3: For each node, recursively calculate maximum path sums from left and right subtrees.

 Step 4: Ignore negative path contributions by taking maximum of 0 and calculated sum.

 Step 5: Calculate the maximum path sum that passes through the current node (includes both children).

 Step 6: Update the global maximum if the current node's path sum is greater.

 Step 7: Return the maximum single-branch path sum to the parent for further calculations.

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