Why Bottom View of Binary Tree in DSA Rust?

The Big Idea

Discover how to see a tree's hidden bottom secrets without confusion or guesswork!

The Scenario

Imagine you have a tall tree in your backyard. You want to see which branches are visible if you look at the tree from the bottom, but you only have a list of branches and their heights. Trying to figure out which branches you can see from below by just looking at the list is confusing and hard.

The Problem

Manually checking each branch's position and height to decide which one is visible from the bottom is slow and error-prone. You might miss some branches or get confused about which one hides another. This makes it hard to get a clear picture of the tree's bottom view.

The Solution

The bottom view of a binary tree helps by automatically showing which nodes (branches) are visible when looking from the bottom. It uses a smart way to track positions and heights, so you get a clear, simple list of visible nodes without guessing or mistakes.

Before vs After

✗ Before

let branches = vec![("A", 1), ("B", 2), ("C", 1)];
// Manually check which branch is visible from bottom
// Confusing and error-prone

✓ After

fn bottom_view(root: &Option<Box<Node>>) -> Vec<i32> {
    // Automatically find visible nodes from bottom
    // Easy and clear result
    Vec::new()
}

What It Enables

This concept lets you quickly and correctly find which parts of a tree are visible from the bottom, making complex tree views simple and clear.

Real Life Example

In city planning, when designing buildings, you might want to know which parts of a skyline are visible from the ground. Bottom view logic helps computers figure this out easily.

Key Takeaways

Manual checking of tree views is confusing and slow.

Bottom view uses position tracking to find visible nodes automatically.

This makes understanding tree structures from below easy and error-free.

Practice

1. What does the bottom view of a binary tree represent?

easy

A. Nodes visible when the tree is viewed from the left side

B. Nodes visible when the tree is viewed from the top

C. Nodes visible when the tree is viewed from the bottom

D. Nodes visible when the tree is viewed from the right side

Solution

1. Step 1: Understand the bottom view concept

   The bottom view shows nodes visible when looking at the tree from below, meaning the lowest nodes at each horizontal distance.

2. Step 2: Compare with other views

   Top view shows nodes from above, left and right views show nodes from sides, so bottom view is unique for bottom perspective.

3. Final Answer:

   Nodes visible when the tree is viewed from the bottom -> Option C

4. Quick Check:

   Bottom view = nodes visible from below [OK]

Hint: Bottom view shows lowest nodes at each horizontal distance [OK]

Common Mistakes:

• Confusing bottom view with top view
• Thinking bottom view is left or right side view
• Assuming all nodes are visible in bottom view

2. Which Rust data structure is best suited to store nodes by their horizontal distance when computing bottom view?

easy

A. Vec<Node>

B. HashMap

C. LinkedList<Node>

D. BinaryHeap<Node>

Solution

1. Step 1: Identify the need for horizontal distance mapping

   We need to map horizontal distances (integers) to nodes, so a key-value structure is required.

2. Step 2: Choose appropriate Rust data structure

   HashMap allows storing nodes with horizontal distance keys efficiently.

3. Final Answer:

   HashMap<i32, Node> -> Option B

4. Quick Check:

   Use HashMap for horizontal distance mapping [OK]

Hint: Use HashMap to map horizontal distance to nodes [OK]

Common Mistakes:

• Using Vec which doesn't map keys to values
• Using LinkedList which is sequential, not key-based
• Using BinaryHeap which is for priority, not mapping

3. Given the following Rust code snippet for bottom view, what is the printed output?

struct Node {
    val: i32,
    left: Option,
    right: Option,
}

// Tree:
//       1
//      / \
//     2   3
//      \   \
//       4   5

// Bottom view expected: 2 -> 4 -> 3 -> 5

fn main() {
    // Assume bottom_view function returns Vec<i32> of bottom view nodes
    let bottom = vec![2, 4, 3, 5];
    for val in bottom {
        print!("{} -> ", val);
    }
    print!("null\n");
}

medium

A. 2 -> 3 -> 4 -> 5 -> null

B. 1 -> 2 -> 3 -> 4 -> 5 -> null

C. 4 -> 2 -> 5 -> 3 -> null

D. 2 -> 4 -> 3 -> 5 -> null

Solution

1. Step 1: Understand the tree structure and bottom view

   The tree has nodes 2,4,3,5 visible from bottom at horizontal distances -1,0,1,2 respectively.

2. Step 2: Trace the printed output from the vector

   The vector contains [2,4,3,5], printed with arrows and ending with null.

3. Final Answer:

   2 -> 4 -> 3 -> 5 -> null -> Option D

4. Quick Check:

   Bottom view print matches vector [OK]

Hint: Match printed output with bottom view vector [OK]

Common Mistakes:

• Confusing node order in bottom view
• Printing all nodes instead of bottom view nodes
• Missing the final 'null' in output

4. Identify the bug in this Rust snippet for bottom view calculation:

fn bottom_view(root: Option) -> Vec<i32> {
    let mut map = std::collections::HashMap::new();
    let mut queue = std::collections::VecDeque::new();
    queue.push_back((root.unwrap(), 0));

    while let Some((node, hd)) = queue.pop_front() {
        map.insert(hd, node.val);
        if let Some(left) = node.left {
            queue.push_back((left, hd - 1));
        }
        if let Some(right) = node.right {
            queue.push_back((right, hd + 1));
        }
    }

    let mut keys: Vec<_> = map.keys().cloned().collect();
    keys.sort();
    keys.iter().map(|k| map[k]).collect()
}

medium

A. Using unwrap() on root without checking if it's None

B. Not updating map with bottom-most node at each horizontal distance

C. Incorrect horizontal distance calculation for left child

D. Not sorting keys before collecting bottom view nodes

Solution

1. Step 1: Check root unwrap usage

   Calling unwrap() on root without checking if root is None can cause panic if tree is empty.

2. Step 2: Verify other logic correctness

   Horizontal distances and map updates are correct; keys are sorted before collecting nodes.

3. Final Answer:

   Using unwrap() on root without checking if it's None -> Option A

4. Quick Check:

   unwrap() on None causes panic [OK]

Hint: Check unwrap() usage on Option before unwrapping [OK]

Common Mistakes:

• Ignoring possibility of empty tree causing panic
• Assuming map updates only once per horizontal distance
• Forgetting to sort keys before output

5. You have a binary tree where multiple nodes share the same horizontal distance and depth. How should you modify the bottom view algorithm in Rust to ensure the node with the greatest depth is shown in the bottom view?

hard

A. Store (node value, depth) in the map and update only if new depth >= stored depth

B. Store only node values and overwrite map entry whenever a node is visited

C. Use a stack instead of queue to traverse nodes

D. Sort nodes by value before inserting into the map

Solution

1. Step 1: Understand the need to track depth

   Bottom view requires the lowest node at each horizontal distance, so depth must be tracked.

2. Step 2: Modify map to store node value and depth

   Store tuple (value, depth) and update map only if new node's depth is greater or equal to existing depth.

3. Step 3: Ignore other options

   Overwriting blindly loses depth info; stack changes traversal order; sorting by value doesn't solve depth issue.

4. Final Answer:

   Store (node value, depth) in the map and update only if new depth >= stored depth -> Option A

5. Quick Check:

   Track depth to keep bottom-most node [OK]

Hint: Track depth and update map only if deeper node found [OK]

Common Mistakes:

• Ignoring node depth leading to wrong bottom view
• Overwriting map entries without depth check
• Changing traversal method without addressing depth