DP on Trees Diameter of Tree in DSA Rust - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to initialize the adjacency list for the tree.

DSA Rust

let mut graph: Vec<Vec<usize>> = vec![Vec::new(); [1]];

Drag options to blanks, or click blank then click option'

A0

Bedges

Cdiameter

Dn

Attempts:

3 left

💡 Hint

Common Mistakes

Using the number of edges instead of nodes for graph size.

Initializing with zero length vector.

We need to create an adjacency list with 'n' empty vectors, one for each node.

2fill in blank

medium

Complete the code to add an undirected edge between nodes u and v.

DSA Rust

graph[u].push([1]);
graph[v].push(u);

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Au

Bgraph

Cv

Ddiameter

Attempts:

3 left

💡 Hint

Common Mistakes

Pushing the same node twice.

Confusing u and v in push.

To add an edge from u to v, push v into graph[u].

3fill in blank

hard

Fix the error in the DFS function signature to accept the parent node.

DSA Rust

fn dfs(node: usize, parent: usize, graph: &Vec<Vec<usize>>, dp: &mut Vec<usize>, diameter: &mut usize) [1]

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A-> usize {

B-> bool {

C{

D-> () {

Attempts:

3 left

💡 Hint

Common Mistakes

Using void return type when a value is needed.

Returning boolean instead of length.

The DFS returns the longest path length from the current node, so it must return usize.

4fill in blank

hard

Fill both blanks to update the diameter inside DFS.

DSA Rust

if first_max + second_max > *[1] {
    *[2] = first_max + second_max;
}

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Adiameter

Bdp[node]

Cdiameter + 1

Ddp[parent]

Attempts:

3 left

💡 Hint

Common Mistakes

Updating dp[node] instead of diameter.

Using incorrect variables for comparison.

We update the global diameter variable if the sum of two longest paths is greater.

5fill in blank

hard

Fill all three blanks to return the longest path from the current node.

DSA Rust

let longest_path = first_max + 1;
dp[node] = longest_path;
return [1];

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Alongest_path

Bdp[node]

Cfirst_max

Dsecond_max

Attempts:

3 left

💡 Hint

Common Mistakes

Returning first_max without adding 1.

Returning second_max or dp[node] incorrectly.

We return the longest path length from the current node, which is longest_path.

Practice

1. What does the diameter of a tree represent in the context of DP on Trees?

easy

A. The longest path between any two nodes in the tree

B. The number of nodes in the tree

C. The height of the tree from the root

D. The sum of all edge weights in the tree

Solution

1. Step 1: Understand the definition of tree diameter

   The diameter is the longest path between any two nodes, not just from the root or sum of edges.

2. Step 2: Differentiate from other tree properties

   Height is from root to leaf, sum of edges is total weight, number of nodes is size, none equal diameter.

3. Final Answer:

   The longest path between any two nodes in the tree -> Option A

4. Quick Check:

   Diameter = Longest path [OK]

Hint: Diameter = longest path between any two nodes [OK]

Common Mistakes:

• Confusing diameter with tree height
• Thinking diameter is total nodes count
• Assuming diameter is sum of all edges

2. Which Rust syntax correctly declares a recursive function to compute the diameter of a tree represented as adjacency list Vec?

easy

A. fn diameter(node: usize, parent: usize, graph: &mut Vec) -> usize { ... }

B. fn diameter(node: usize, graph: Vec) -> usize { ... }

C. fn diameter(node: usize, parent: usize, graph: &Vec) -> usize { ... }

D. fn diameter(&self, node: usize, parent: usize) -> usize { ... }

Solution

1. Step 1: Identify correct parameter passing for graph

   Graph should be passed by reference (&Vec) to avoid copying large data.

2. Step 2: Include parent parameter to avoid revisiting parent node

   Parent node is needed to prevent cycles in undirected tree traversal.

3. Final Answer:

   fn diameter(node: usize, parent: usize, graph: &Vec) -> usize { ... } -> Option C

4. Quick Check:

   Pass graph by reference and track parent [OK]

Hint: Pass graph as &Vec and track parent node [OK]

Common Mistakes:

• Passing graph by value causing performance issues
• Missing parent parameter causing infinite recursion
• Using &mut when mutation is not needed

3. Given the following Rust code snippet to compute the diameter of a tree, what is the printed output?

fn dfs(node: usize, parent: usize, graph: &Vec, max_diameter: &mut usize) -> usize {
    let mut max1 = 0;
    let mut max2 = 0;
    for &child in &graph[node] {
        if child == parent { continue; }
        let height = dfs(child, node, graph, max_diameter);
        if height > max1 {
            max2 = max1;
            max1 = height;
        } else if height > max2 {
            max2 = height;
        }
    }
    *max_diameter = (*max_diameter).max(max1 + max2);
    max1 + 1
}

fn main() {
    let graph = vec![
        vec![1, 2],
        vec![0, 3, 4],
        vec![0],
        vec![1],
        vec![1]
    ];
    let mut max_diameter = 0;
    dfs(0, usize::MAX, &graph, &mut max_diameter);
    println!("{}", max_diameter);
}

medium

A. 3

B. 4

C. 2

D. 5

Solution

1. Step 1: Trace DFS heights from leaves

   Leaves 2, 3, 4 return height 1; node 1 gets max1=1, max2=1; node 0 gets max1=2 (from node 1), max2=1 (from node 2).

2. Step 2: Calculate max diameter updates

   At node 1, max_diameter = max(0,1+1)=2; at node 0, max_diameter = max(2,2+1)=3.

3. Final Answer:

   3 -> Option A

4. Quick Check:

   Longest path length = 3 edges [OK]

Hint: Sum two largest subtree heights at each node [OK]

Common Mistakes:

• Counting nodes instead of edges for diameter
• Not updating max_diameter correctly
• Ignoring parent to avoid revisiting

4. Identify the bug in this Rust function computing tree diameter and select the fix:

fn dfs(node: usize, graph: &Vec, max_diameter: &mut usize) -> usize {
    let mut max1 = 0;
    let mut max2 = 0;
    for &child in &graph[node] {
        let height = dfs(child, graph, max_diameter);
        if height > max1 {
            max2 = max1;
            max1 = height;
        } else if height > max2 {
            max2 = height;
        }
    }
    *max_diameter = (*max_diameter).max(max1 + max2);
    max1 + 1
}

medium

A. Initialize max1 and max2 to 1 instead of 0

B. Add a parent parameter to avoid revisiting the parent node

C. Change max_diameter to return instead of using mutable reference

D. Remove max2 variable as it is unnecessary

Solution

1. Step 1: Identify infinite recursion cause

   Without parent tracking, dfs revisits parent causing infinite recursion or stack overflow.

2. Step 2: Fix by adding parent parameter

   Pass parent node to skip revisiting it in children loop, preventing cycles.

3. Final Answer:

   Add a parent parameter to avoid revisiting the parent node -> Option B

4. Quick Check:

   Parent tracking prevents infinite recursion [OK]

Hint: Always track parent node in undirected tree DFS [OK]

Common Mistakes:

• Not passing parent causing infinite recursion
• Misusing mutable references for max_diameter
• Incorrect initialization of max heights

5. You want to find the diameter of a weighted tree where edges have weights. Which modification to the DP on Trees diameter algorithm is correct?

hard

A. Ignore weights and compute diameter as number of edges only

B. Sum all edge weights and divide by two to get diameter

C. Use BFS twice without any DP or recursion

D. Store and propagate the maximum weighted path length instead of just height counts

Solution

1. Step 1: Understand weighted tree diameter difference

   Diameter must consider edge weights, so heights become max weighted path lengths.

2. Step 2: Modify DP to accumulate weights

   Instead of counting edges, add edge weights when computing subtree heights and update max diameter accordingly.

3. Final Answer:

   Store and propagate the maximum weighted path length instead of just height counts -> Option D

4. Quick Check:

   Weighted diameter needs weighted path sums [OK]

Hint: Accumulate edge weights in DP for weighted diameter [OK]

Common Mistakes:

• Ignoring weights leads to wrong diameter
• Using BFS without weights misses weighted paths
• Incorrect formula dividing total weights