• Expected Output: 4
• Justification: The binary tree's deepest level has a single node with the value 4. Since it's the only node at that level, the sum is 4.

Solution

To solve this problem, the approach involves a breadth-first search (BFS) traversal of the binary tree. This method is chosen because BFS explores the tree level by level, starting from the root, making it efficient to identify the deepest leaves. By utilizing a queue to keep track of nodes and their levels, we can process each level of the tree sequentially. Once we reach the last level, we calculate the sum of all nodes at that level.

This approach is effective because it ensures that we visit all nodes in the tree while maintaining a clear distinction between different levels. By doing so, we can easily identify when we've reached the deepest level and then sum up the values of the nodes at this level. It is also efficient, as each node is visited exactly once, and no unnecessary computations are done.

Step-by-Step Algorithm

1. Check for Empty Tree:

   • If the root node is null, return 0 as the tree is empty, and there are no leaves to sum.

2. Initialize Queue and Variables:

   • Initialize a queue to hold the nodes of the tree along with their level. Start by enqueuing the root node.
   • Initialize levelSum to 0. This variable will hold the sum of the values of the nodes at the current (deepest) level.

3. Breadth-First Search (BFS) Loop:

   • While the queue is not empty, perform the following steps to process each level of the tree:
     • Note the size of the queue at the start of the loop iteration. This size represents the number of nodes at the current level, as all nodes in the queue are from the same level.
     • Reset levelSum to 0 at the start of processing a new level.
     • Loop through the nodes at the current level (using the noted size of the queue to ensure only nodes of the current level are processed):
       • Dequeue a node from the queue.
       • Add the value of the dequeued node to levelSum.
       • If the dequeued node has a left child, enqueue this child.
       • If the dequeued node has a right child, enqueue this child.

4. Return Sum of Deepest Leaves:

   • After the loop ends (i.e., the queue is empty, and all levels have been processed), levelSum contains the sum of the values of the nodes at the deepest level of the tree.
   • Return levelSum.

Algorithm Walkthrough

Let's consider the Input: root = [1,2,3,4,5,null,7]

1. Initialization:

   • The tree is not empty, so we proceed.
   • Queue = [1], levelSum = 0.

2. First Level Processing (Root Level):

   • Queue size at start = 1 (contains root node 1).
   • levelSum reset to 0.
   • Dequeue 1: Queue = [], levelSum = 1 (value of node 1).
   • Enqueue children of 1: Queue = [2, 3].

3. Second Level Processing:

   • Queue size at start = 2 (contains nodes 2 and 3).
   • levelSum reset to 0.
   • Dequeue 2: Queue = [3], levelSum = 2 (value of node 2).
   • Enqueue children of 2: Queue = [3, 4, 5].
   • Dequeue 3: Queue = [4, 5], levelSum = 5 (2 + value of node 3).
   • Enqueue right child of 3 (node 7): Queue = [4, 5, 7].

4. Third Level Processing:

   • Queue size at start = 3 (contains nodes 4, 5, and 7).
   • levelSum reset to 0.
   • Dequeue 4: Queue = [5, 7], levelSum = 4.
   • No children to enqueue.
   • Dequeue 5: Queue = [7], levelSum = 9 (4 + value of node 5).
   • No children to enqueue.
   • Dequeue 7: Queue = [], levelSum = 16 (9 + value of node 7).
   • No children to enqueue.

5. Return Sum:

   • With the queue empty and all levels processed, the loop ends.
   • levelSum is 16, which is the sum of the values of the nodes at the deepest level.
   • Return 16.

Code