recursion

DP feels like pattern-matching magic until you have a method. The signal is a repeatable drill: spot overlapping subproblems and optimal substructure, define the state and recurrence, then memoize or tabulate. Here is that method on a worked example.

Backtracking is the pattern behind permutations, subsets, N-queens, and constraint problems. The signal is the choose/explore/un-choose template plus pruning, and knowing exactly which knob separates permutations from combinations.

Encoding a tree into a string and rebuilding it exactly hinges on one decision most candidates skip. Miss it and the structure becomes ambiguous. Here is the answer and the interview-grade reasoning.

LCA is the recursion classic that tests how you propagate information up from subtrees in a single pass. The signal is the post-order 'found in left, found in right' logic. Here is the answer plus the BST shortcut.

This problem rewards knowing that an in-order traversal of a BST yields sorted order. The signal is stopping early at the kth element rather than traversing the whole tree.

Validating a BST catches people who only check parent-child pairs and miss violations buried deep in a subtree. The signal is propagating min/max bounds or using in-order monotonicity. Here is the answer.

The diameter is not the tree's height, and the path need not pass through the root. The clean solution computes height and best path in one DFS, updating a global max at every node. Here is the answer and the subtlety candidates miss.

Preorder names the root; inorder splits the rest into left and right subtrees. Doing it naively is O(n squared); the strong answer uses a value-to-index map and a moving preorder pointer for O(n). Here is the answer and why both orders are required.

Negative subtrees, a path that bends through any node, and a return value that differs from the answer you track: this problem packs three traps into one DFS. Here is the clean O(n) solution and the reasoning that survives follow-ups.

Generating then filtering is O(2^(2n)) and wasteful. Backtracking with two counters builds only valid strings by enforcing the balance rule at every step. Here is the template and why the pruning conditions are exactly right.