515. Find Largest Value in Each Tree Row

515. Find Largest Value in Each Tree Row

Difficulty: Medium

Topics: Tree, Depth-First Search, Breadth-First Search, Binary Tree

Given the root of a binary tree, return an array of the largest value in each row of the tree (0-indexed).

Example 1:

• Input: root = [1,3,2,5,3,null,9]
• Output: [1,3,9]

Example 2:

• Input: root = [1,2,3]
• Output: [1,3]

Constraints:

• The number of nodes in the tree will be in the range [0, 104].
• -231 <= Node.val <= 231 - 1

Solution:

The problem "Find Largest Value in Each Tree Row" requires identifying the largest value present at each level (row) of a binary tree. Given a binary tree, the goal is to traverse the tree row by row and collect the maximum value from each row. This problem involves fundamental tree traversal techniques such as Breadth-First Search (BFS) or Depth-First Search (DFS).

Key Points

1. Tree Traversal: The solution involves traversing all levels of the binary tree to identify the largest value at each level.
2. Breadth-First Search (BFS): BFS is suitable for level-by-level traversal, which simplifies finding the largest value in each row.
3. Constraints: Handle edge cases like an empty tree and nodes with large or small integer values within the constraint range.

Approach

The most straightforward approach to finding the largest value in each row is using BFS:

• Traverse the tree level by level.
• For each level, keep track of the largest value.

Alternatively, DFS can also be used:

• Recursively traverse the tree and maintain a record of the maximum value at each depth.

Plan

1. Initialize an array to store the largest values of each row.
2. Use a queue for BFS traversal:
   • Start with the root node.
   • Process all nodes at the current level before moving to the next.
3. For each level:
   • Iterate through all nodes and find the maximum value.
   • Add this value to the result array.
4. Return the result array after completing the traversal.

Solution Steps

1. Check Input: If the root is null, return an empty array.
2. Setup BFS:
   • Use a queue initialized with the root node.
   • Initialize an empty result array.
3. Traverse Levels:
   • For each level, track the maximum value.
   • Add child nodes to the queue for the next level.
4. Update Results:
   • Append the maximum value of each level to the result array.
5. Return Results: Return the result array containing the largest values for each row.

Let's implement this solution in PHP: 515. Find Largest Value in Each Tree Row

<?php
// Definition for a binary tree node.
class TreeNode {
    public $val = null;
    public $left = null;
    public $right = null;
    function __construct($val = 0, $left = null, $right = null) {
        $this->val = $val;
        $this->left = $left;
        $this->right = $right;
    }
}

/**
 * @param TreeNode $root
 * @return Integer[]
 */
function largestValues($root) {
    ...
    ...
    ...
    /**
     * go to ./solution.php
     */
}

// Example usage:
$root = new TreeNode(1);
$root->left = new TreeNode(3);
$root->right = new TreeNode(2);
$root->left->left = new TreeNode(5);
$root->left->right = new TreeNode(3);
$root->right->right = new TreeNode(9);

print_r(largestValues($root)); // Output: [1, 3, 9]
?>

Explanation:

Input: [1,3,2,5,3,null,9]

1. Level 0: Node values: [1] → Maximum: 1.
2. Level 1: Node values: [3, 2] → Maximum: 3.
3. Level 2: Node values: [5, 3, 9] → Maximum: 9. #### Output: [1, 3, 9].

Time Complexity

• BFS Traversal: Each node is processed once → O(n).
• Finding Maximum: Done during traversal → O(1) per level.
• Total: O(n).

Space Complexity

• Queue Storage: At most, the width of the tree (number of nodes at the largest level) → O(w) where w is the maximum width of the tree.

Output for Example

Input: root = [1,3,2,5,3,null,9]

Output: [1, 3, 9].

This BFS-based solution efficiently computes the largest value in each tree row with linear time complexity. It handles large trees, negative values, and edge cases like empty trees effectively.

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