Combinatorics

Combinatorial counting (pairs, ways to split), building the k-th permutation digit by digit, geometry (nearest point, law of cosines, triangle inequality), problems that become formulas after sorting or an observation, plus carry arithmetic, base conversion and fast exponentiation

LeetCode 2963 note: all occurrences of a value must share a part, so last occurrences cut the array into b indivisible blocks; each boundary may be cut or not, giving 2^(b-1)

LeetCode 2912 note: many cells, but only four classes relative to the destination (itself, same row, same column, neither); each class’s total moves together in O(k)

LeetCode 60 note: make k 0-indexed; once the first digit is fixed there are (n-1)! arrangements, so k // (n-1)! picks the first digit among those remaining, then repeat for the next position

Generating all valid parentheses combinations using backtracking approach

LeetCode 3518 note: a palindrome is determined by its left half, so this is the k-th permutation of a multiset; try characters position by position and use permutation counts, updated in O(1), to find k’s branch