DP on Trees Maximum Path Sum in DSA Java - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to return the maximum path sum starting from the current node.

DSA Java

int maxPathDown(TreeNode node) {
    if (node == null) return 0;
    int left = Math.max(0, maxPathDown(node.left));
    int right = Math.max(0, maxPathDown(node.right));
    maxSum = Math.max(maxSum, node.val + left + [1]);
    return node.val + Math.max(left, right);
}

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

Aright

Bleft

C0

Dnode.val

Attempts:

3 left

💡 Hint

Common Mistakes

Using only left child sum and ignoring right child.

Adding node.val twice.

We add both left and right maximum path sums to node.val to consider paths passing through the node.

2fill in blank

medium

Complete the code to update the global maximum path sum.

DSA Java

maxSum = Math.max(maxSum, [1]);

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

Anode.val

Bnode.val + left

CMath.max(left, right)

Dnode.val + left + right

Attempts:

3 left

💡 Hint

Common Mistakes

Updating maxSum with only one child's sum.

Not including node.val in the sum.

The maximum path sum at a node can include the node value plus both left and right maximum sums.

3fill in blank

hard

Fix the error in the return statement to correctly propagate the maximum path sum upwards.

DSA Java

return node.val + [1](left, right);

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

AMath.max

BMath.pow

CMath.abs

DMath.min

Attempts:

3 left

💡 Hint

Common Mistakes

Using Math.min which selects the smaller sum.

Using Math.abs which is unrelated here.

We return node.val plus the maximum of left and right sums to continue the path upwards.

4fill in blank

hard

Fill both blanks to compute the maximum path sum ignoring negative sums.

DSA Java

int left = Math.[1](0, maxPathDown(node.left));
int right = Math.[2](0, maxPathDown(node.right));

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

Amax

Bmin

Cabs

Dround

Attempts:

3 left

💡 Hint

Common Mistakes

Using Math.min which would select negative sums.

Using Math.abs which changes negative sums to positive incorrectly.

We use Math.max with 0 to ignore negative sums from children.

5fill in blank

hard

Fill in the blanks to implement the maximum path sum function correctly.

DSA Java

public int maxPathSum(TreeNode root) {
    maxSum = Integer.MIN_VALUE;
    maxPathDown([1]);
    return [2];
}

private int maxPathDown(TreeNode node) {
    if (node == null) return 0;
    int left = Math.max(0, maxPathDown(node.left));
    int right = Math.max(0, maxPathDown(node.right));
    maxSum = Math.max(maxSum, node.val + left + right);
    return node.val + Math.max(left, right);
}

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

Aroot

BmaxSum

CmaxPathDown(root)

Dnode

Attempts:

3 left

💡 Hint

Common Mistakes

Returning maxPathDown(root) instead of maxSum.

Calling maxPathDown with null or wrong node.

Call maxPathDown with root, then return maxSum which holds the maximum path sum.

Practice

1. What does the "maximum path sum" in a binary tree represent?
Maximum path sum means the largest sum of node values along any path in the tree.

easy

A. The sum of node values from root to the deepest leaf

B. The sum of all node values in the tree

C. The maximum value of a single node in the tree

D. The largest sum of node values along any path in the tree

Solution

1. Step 1: Understand the definition of maximum path sum

   The maximum path sum is the highest sum you can get by adding node values along any path in the tree. The path can start and end at any nodes.

2. Step 2: Differentiate from other sums

   It is not just the sum of all nodes, nor the max single node, nor limited to root-to-leaf paths. It considers any path.

3. Final Answer:

   The largest sum of node values along any path in the tree -> Option D

4. Quick Check:

   Maximum path sum = largest path sum [OK]

Hint: Maximum path sum is any path's largest sum, not just root paths [OK]

Common Mistakes:

• Confusing maximum path sum with sum of all nodes
• Thinking path must start at root
• Considering only single node values

2. Which of the following Java method signatures is correct for a recursive function to find maximum path sum in a binary tree node class named TreeNode?

easy

A. int maxPathSum(TreeNode root) throws Exception

B. public int maxPathSum(TreeNode root)

C. void maxPathSum(TreeNode root)

D. public static maxPathSum(TreeNode root)

Solution

1. Step 1: Check method return type and parameters

   The method should return an int (the max sum) and accept a TreeNode parameter.

2. Step 2: Validate Java syntax

   public int maxPathSum(TreeNode root) uses correct syntax. int maxPathSum(TreeNode root) throws Exception unnecessarily throws Exception, the void version returns wrong type, the version without return type is invalid.

3. Final Answer:

   public int maxPathSum(TreeNode root) -> Option B

4. Quick Check:

   Correct method signature returns int and takes TreeNode [OK]

Hint: Method must return int and accept TreeNode parameter [OK]

Common Mistakes:

• Using void return type instead of int
• Missing return type in method signature
• Adding unnecessary throws Exception

3. Given the following Java code snippet for maximum path sum in a binary tree, what is the printed output?

class TreeNode {
  int val;
  TreeNode left, right;
  TreeNode(int v) { val = v; }
}

public class Solution {
  int maxSum = Integer.MIN_VALUE;

  public int maxPathSum(TreeNode root) {
    maxGain(root);
    return maxSum;
  }

  private int maxGain(TreeNode node) {
    if (node == null) return 0;
    int leftGain = Math.max(maxGain(node.left), 0);
    int rightGain = Math.max(maxGain(node.right), 0);
    int priceNewPath = node.val + leftGain + rightGain;
    maxSum = Math.max(maxSum, priceNewPath);
    return node.val + Math.max(leftGain, rightGain);
  }

  public static void main(String[] args) {
    TreeNode root = new TreeNode(-10);
    root.left = new TreeNode(9);
    root.right = new TreeNode(20);
    root.right.left = new TreeNode(15);
    root.right.right = new TreeNode(7);
    Solution sol = new Solution();
    System.out.println(sol.maxPathSum(root));
  }
}

medium

A. 42

B. 35

C. 27

D. 20

Solution

1. Step 1: Trace maxGain for each node

   Calculate maxGain for leaves: 9 returns 9, 15 returns 15, 7 returns 7. For node 20: leftGain=15, rightGain=7, priceNewPath=20+15+7=42, maxSum=42. For root -10: leftGain=9, rightGain=20+15=35 (maxGain returns node.val + max(leftGain,rightGain), so for right child maxGain=35), priceNewPath at root = -10 + 9 + 35 = 34, maxSum remains 42.

2. Step 2: Determine maxSum after full traversal

   maxSum is updated to 42 at node 20, which is the maximum path sum.

3. Final Answer:

   42 -> Option A

4. Quick Check:

   Max path sum = 42 [OK]

Hint: Max path sum includes node plus max gains from left and right [OK]

Common Mistakes:

• Ignoring negative node values
• Not resetting maxSum correctly
• Confusing return value with maxSum

4. Identify the bug in this Java method for maximum path sum and select the fix:

private int maxGain(TreeNode node) {
  if (node == null) return 0;
  int leftGain = maxGain(node.left);
  int rightGain = maxGain(node.right);
  int priceNewPath = node.val + leftGain + rightGain;
  maxSum = Math.max(maxSum, priceNewPath);
  return node.val + Math.max(leftGain, rightGain);
}

medium

A. Change return type to void

B. Remove maxSum update line

C. Add Math.max(..., 0) to leftGain and rightGain to ignore negative sums

D. Return node.val + leftGain + rightGain instead

Solution

1. Step 1: Analyze handling of negative gains

   Without Math.max(..., 0), negative leftGain or rightGain reduce path sum incorrectly.

2. Step 2: Fix by ignoring negative gains

   Use int leftGain = Math.max(maxGain(node.left), 0) and similarly for rightGain to ignore negative paths.

3. Final Answer:

   Add Math.max(..., 0) to leftGain and rightGain to ignore negative sums -> Option C

4. Quick Check:

   Ignore negative gains with Math.max(..., 0) [OK]

Hint: Ignore negative child sums by max with zero [OK]

Common Mistakes:

• Not ignoring negative sums causing wrong maxSum
• Changing return type incorrectly
• Removing maxSum update line

5. You want to find the maximum path sum in a binary tree where nodes can have negative values. Which approach correctly applies dynamic programming on trees to solve this?

Choose the best description of the approach.

hard

A. Use post-order traversal; at each node, compute max gain from left and right ignoring negatives; update global max with node value plus both gains; return node value plus max gain of one side

B. Use pre-order traversal; sum all node values; return the sum as max path sum

C. Use in-order traversal; keep track of max node value only; return max node value

D. Use level-order traversal; sum values at each level; return max level sum

Solution

1. Step 1: Understand dynamic programming on trees

   Post-order traversal ensures children are processed before parent, allowing calculation of max gains from subtrees.

2. Step 2: Apply max gain logic ignoring negative sums

   At each node, calculate max gain from left and right children ignoring negatives, update global max path sum with node plus both gains, and return node plus max gain of one side for parent's use.

3. Final Answer:

   Use post-order traversal; at each node, compute max gain from left and right ignoring negatives; update global max with node value plus both gains; return node value plus max gain of one side -> Option A

4. Quick Check:

   Post-order + max gain ignoring negatives = correct DP approach [OK]

Hint: Use post-order and ignore negative gains for max path sum [OK]

Common Mistakes:

• Using wrong traversal order
• Summing all nodes instead of max path
• Ignoring negative values in gains