Hard

LCR 170 note: count inversions during the merge step

LeetCode 315 note: merge sort with indices, plus a BIT solution

LeetCode 827 note: label every island and record its size, then for each 0 add the sizes of the distinct neighboring islands plus 1

LeetCode 212 note: build a Trie of all words, walk it during the grid DFS, remove words once found, and prune empty nodes

LeetCode 3203 note: connect the two centers; the answer is max(d1, d2, ceil(d1/2) + ceil(d2/2) + 1)

LeetCode 305 note: each new land cell adds an island, then merges with neighboring land, subtracting 1 per successful merge; skip repeated positions

LeetCode 1220 note: state machine DP on the last vowel; turn “what may follow x” around into “what may precede x”

LeetCode 4081 note: sieve the primes, then 0/1 knapsack with dp[j] the fewest primes summing to j; adding primes from large to small, a tie gives a smaller first element, so updating on <= yields the lexicographically smallest

LeetCode 2751 note: sort by position, push right-moving robots, and let each left-moving robot collide until one side is gone

LeetCode 2584 note: coprime products ⇔ no prime factor in both parts; record each prime’s last index, extend reach left to right, and split after i when reach == i

LeetCode 2267 note: the state is (r, c, open balance); the balance can be neither negative nor more than the remaining steps; search the states with BFS / DP and succeed at the end with balance 0

LeetCode 1998 note: numbers in one component can be permuted freely; union each number with its prime factors via SPF, and the array sorts iff each position’s old and new values share a group