[Solved] Consider the following code implementing the optimal House Robber III solution. Given the tree: 3 / \ 2 3 \ \ 3 1 What is the value of rob_current when dfs is called on the root node (value 3)? | Tree: Depth-First Search

Tree: Depth-First Search - House Robber III (On Tree)

Consider the following code implementing the optimal House Robber III solution. Given the tree: 3 / \ 2 3 \ \ 3 1 What is the value of rob_current when dfs is called on the root node (value 3)?

A7

B6

C8

D9

Step-by-Step Solution

Step 1: Trace dfs on left child (value 2)
dfs(2) calls dfs(null) and dfs(3). dfs(null) returns (0,0). dfs(3) returns (3,0) because it has no children. So rob_current=3+0+0=3, not_rob_current=max(0,0)+max(0,0)=0. dfs(3) returns (3,0). For node 2: rob_current=2+0+0=2, not_rob_current=max(0,3)+max(0,0)=3. dfs(2) returns (2,3).
Step 2: Trace dfs on right child (value 3)
dfs(3) calls dfs(null) and dfs(1). dfs(1) returns (1,0). So rob_current=3+0+0=3, not_rob_current=max(0,0)+max(1,0)=1. dfs(3) returns (3,1).
Step 3: Calculate rob_current at root (value 3)
rob_current = 3 + left[1] + right[1] = 3 + 3 + 1 = 7.
Final Answer:
Option A -> Option A
Quick Check:
Sum matches known example output 7 [OK]

Quick Trick: Add node.val + not_rob of children for rob_current [OK]

Common Mistakes:

MISTAKES

Mixing rob and not_rob values for children
Off-by-one in recursion returns

Trap Explanation:

PITFALL

Confusing which child values to add for rob_current leads to wrong sums.

Interviewer Note:

CONTEXT

Tests ability to mentally execute DFS with tuple returns and aggregation.

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More Tree: Depth-First Search Quizzes

Consider the following code implementing the optimal House Robber III solution. Given the tree: 3 / \ 2 3 \ \ 3 1 What is the value of rob_current when dfs is called on the root node (value 3)?

Step 1: Trace dfs on left child (value 2)

Step 2: Trace dfs on right child (value 3)

Step 3: Calculate rob_current at root (value 3)

Final Answer:

Quick Check:

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