Hard

LeetCode 864 note: the BFS state is (position, bitmask of keys), so the same cell with different keys is a different node

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 2376 note: digit DP with state (pos, tight, started, mask); the mask records used digits, and leading zeros must not mark 0 as used

LeetCode 2163 note: try every boundary k between the two parts; the left takes the n smallest of nums[:k] (a max-heap) and the right the n largest of nums[k:] (a min-heap), one prefix and one suffix pass

LeetCode 1627 note: no pairwise GCDs; for each z > threshold, connect all multiples of z, O(n log n) unions in total

LeetCode 1944 note: a decreasing monotonic stack from right to left; everyone popped is visible, and so is the person left on top

LeetCode 420 note: three length cases; when too long, delete from runs with len % 3 == 0 first to cancel replacements

LeetCode 2193 note: greedily fix the outer pair: take the last character and swap its leftmost partner to the front, costing that index; the unpaired character ends in the middle, costing its distance there

LeetCode 4041 note: with operations in any order, BFS finds every value a number can become (up to sum) with the fewest steps, then the same grouped 0/1 knapsack as 4040

LeetCode 2328 note: strictly increasing means no cycles; dp[cell] = 1 + Σ dp[larger neighbors], processed from largest to smallest value (or by memoized DFS), summed over all cells

LeetCode 1377 note: undirected edges, seen must hold nodes, and an early arrival depends on whether the frog can still move

LeetCode 1178 note: a word only matters by its set of letters, so count 26-bit masks and enumerate each puzzle’s submasks