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Implement array parity and tree level views

Quick Overview

This question evaluates proficiency in array frequency analysis and binary tree traversal, testing skills in data structures, correctness reasoning, and algorithm implementation.

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Part 2: Right Side View of a Binary Tree

You are given a binary tree in level-order list form, where None represents a missing child. Return the values visible when looking at the tree from the right side, from top to bottom.

Constraints

0 <= len(tree) <= 10000
-1000 <= node values <= 1000
The input list follows standard level-order tree encoding with None for missing children

Examples

Input: ([1, 2, 3, None, 5, None, 4],)

Expected Output: [1, 3, 4]

Explanation: At each level, the rightmost visible nodes are 1, then 3, then 4.

Input: ([1, 2, None, 3],)

Expected Output: [1, 2, 3]

Explanation: The tree extends down the left side, so the visible nodes from the right are still one node per level: 1, 2, and 3.

Input: ([],)

Expected Output: []

Explanation: An empty tree has no visible nodes.

Input: ([7],)

Expected Output: [7]

Explanation: A single-node tree is visible as just that node.

Input: ([None],)

Expected Output: []

Explanation: A list starting with None represents an empty tree.

Input: ([-1, -2, -3, None, -5],)

Expected Output: [-1, -3, -5]

Explanation: The rightmost nodes by level are -1 at the root, -3 on the second level, and -5 on the third level.

Hints

Process the tree one level at a time using a queue.
At each level, the last node you visit is the one visible from the right.

Part 3: Left Side View of a Binary Tree

You are given a binary tree in level-order list form, where None represents a missing child. Return the values visible when looking at the tree from the left side, from top to bottom.

Constraints

0 <= len(tree) <= 10000
-1000 <= node values <= 1000
The input list follows standard level-order tree encoding with None for missing children

Examples

Input: ([1, 2, 3, None, 5, None, 4],)

Expected Output: [1, 2, 5]

Explanation: At each depth, the leftmost visible nodes are 1, then 2, then 5.

Input: ([1, 2, None, 3],)

Expected Output: [1, 2, 3]

Explanation: The tree goes down the left side as 1 -> 2 -> 3, so all three are visible.

Input: ([],)

Expected Output: []

Explanation: An empty tree has no visible nodes.

Input: ([7],)

Expected Output: [7]

Explanation: A tree with only a root shows just that root.

Input: ([0, -1, -1, None, -2],)

Expected Output: [0, -1, -2]

Explanation: The visible nodes from the left are the root 0, then the left child -1, then its right child -2.

Hints

Use breadth-first search to process one level at a time.
At each level, the first node you remove from the queue is the one visible from the left.

Part 4: Average Value of Each Level in a Binary Tree

You are given a binary tree in level-order list form, where None represents a missing child. Compute the average node value at each depth and return the list of averages from top to bottom.

Constraints

0 <= len(tree) <= 10000
-100000 <= node values <= 100000
The input list follows standard level-order tree encoding with None for missing children

Examples

Input: ([3, 9, 20, None, None, 15, 7],)

Expected Output: [3.0, 14.5, 11.0]

Explanation: Level 0 has [3], level 1 has [9, 20], and level 2 has [15, 7]. Their averages are 3.0, 14.5, and 11.0.

Input: ([5],)

Expected Output: [5.0]

Explanation: A single-node tree has one level, so the average is just the root value.

Input: ([],)

Expected Output: []

Explanation: An empty tree has no levels.

Input: ([1, None, 2, 3],)

Expected Output: [1.0, 2.0, 3.0]

Explanation: This compact level-order form means 2 is the right child of 1, and 3 is the left child of 2.

Input: ([-4, -2, -6, None, 0, 8],)

Expected Output: [-4.0, -4.0, 4.0]

Explanation: The levels are [-4], [-2, -6], and [0, 8], giving averages -4.0, -4.0, and 4.0.

Hints

Breadth-first search naturally groups nodes by level.
For each level, keep a running sum and divide by the number of nodes in that level.

Quick Overview