Binary Tree Max Path Sum: the recursive function returns node + max(left, right) to the parent, but tracks maxSum with node + left + right. two separate concerns. the path can turn at a node but can’t extend after turning. [-10,9,20,15,7] → 42, not 34.
Sort Colors trips most people on one thing: after swapping with blue, don't advance white. that element is unexamined. after swapping with red, advance both. it was already a 1. that's the Dutch National Flag algorithm. Apple, Google, Meta ask this.
Longest Palindromic Substring trips people on one thing: odd vs even palindromes. 'cbbd' → 'bb' requires the even-center check (expandAround i, i+1). only checking single chars gives you 'c', which is wrong. two expand calls per index, not one.
Combination Sum is the problem where backtracking clicks. add, recurse, pop. passing `start = i` not `i + 1` in the recursive call is what makes it combinations not permutations. without it, [2,3] and [3,2] both show up.