When to Use Aliens Trick

Look for these signs that Aliens Trick applies:

$1.$ "Exactly $K$" constraint in the problem statement (not "at most $K$").

$2.$ Standard DP would require $dp[i][k]$ with large $k$ dimension, making it too slow.

$3.$ It's a partition, grouping, or selection problem where you're choosing how to divide things.

$4.$ Convex cost structure: adding one more item/segment gives diminishing returns. If you see all four patterns, try the Aliens Trick. It's rare but transforms problems from $O(n \cdot K)$ to $O(n \log C)$, making otherwise impossible problems solvable.