Reconstruct the missing numbers

Define the range before reconstructing

Ask whether values should cover 1..n, 0..n, an arbitrary interval, and whether one or many values may be missing. A hash-set baseline is clear: insert observed values, then scan the expected range and emit absent values. It uses O(n + r) time and O(n) space for range size r. If values are guaranteed in 1..n and mutation is allowed, mark abs(value)-1 negative or cyclically place each value; the unmarked or misplaced indexes are missing, with O(n) time and O(1) auxiliary space. Explain that duplicates and out-of-range values need an explicit policy. Test missing endpoints, no missing values, repeated values, one element, and inputs where marking would overflow or violate immutability.