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Problem-Solving Approach

Problem-Solving Approach

How to Identify Tree Problems

Look for these keywords in problem statements:

“Binary tree”, “BST”, “root”, “leaves”, “path”
“Ancestor”, “descendant”, “subtree”
“Level”, “depth”, “height”, “width”
“Maximum/minimum path”, “diameter”

When to Use DFS vs BFS

Use DFS When…	Use BFS When…
Computing height/depth	Level-by-level processing
Path sum / root-to-leaf paths	Finding shortest path
Subtree problems (is mirror, same tree, etc.)	Right/left view of tree
LCA, diameter, balanced checks	Zigzag traversal, level averages
Tree serialization/deserialization	Connect next pointers level-by-level

Recursive Thinking Patterns

There are 3 types of recursive approaches for trees:

Pattern 1: Return a value (bottom-up)

→ Compute something at each node using children's results
→ Example: height, diameter, path sums

Pattern 2: Pass a value down (top-down)

→ Carry information from parent to children
→ Example: path sum (carry remaining target down)

Pattern 3: Use external state (global variable)

→ Maintain a result variable outside recursion, update inside
→ Example: diameter, max path sum

Edge Cases to Always Consider

Edge Case	What to check
`root === null`	Handle empty tree; return appropriate default (0, [], null)
Single node tree	Leaf node is both root, left, and right boundary
Skewed tree (all left or right)	Don’t assume O(log N) depth; stack may overflow
Negative values in nodes	Path sum with all negatives; don’t discard negative paths
Duplicate values in BST	Clarify how duplicates are handled (left or right subtree)
Integer overflow	Sum of path may exceed `Number.MAX_SAFE_INTEGER` in JS

Common Technique Combinations

Hard problems often combine multiple basic techniques:

"Max Path Sum"       = DFS returning gain + global max tracking
"Serialize/Deserialize" = Preorder + Queue reconstruction
"Cameras on Tree"    = Greedy postorder with state propagation
"Vertical Order"     = BFS + sort by (col, row, val)

Important Patterns — Key tree patterns
Tree Traversals — DFS & BFS
Tips & Common Mistakes — Avoid common pitfalls