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 applied to a worked example.

Backtracking underlies permutations, subsets, N-queens, and constraint problems. Interviewers look for the choose/explore/un-choose template plus pruning, and knowing exactly which knob distinguishes permutations from combinations.

Turning a tree into a string and reconstructing it faithfully rests on one choice most candidates overlook. Skip it and the structure turns ambiguous. Here is the answer and the interview-grade reasoning.

LCA is the recursion staple that probes how you carry information upward from subtrees in one pass. What interviewers watch for: the post-order 'found in left, found in right' logic. Here is the answer plus the BST shortcut.

This one rewards knowing that an in-order walk of a BST produces sorted order. The signal is halting at the kth element instead of walking the entire tree.

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

The diameter is not the tree's height, and the path does not have to pass through the root. The clean solution derives 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 divides the rest into left and right subtrees. The naive version 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 distinct from the answer you track: this problem stuffs three traps into one DFS. Here is the clean O(n) solution and the reasoning that holds up under follow-ups.

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