Minimum-length substring

Define what makes a substring valid

Ask whether this is the minimum window containing every character of a target string with multiplicity, a window with all distinct characters, or another predicate. For the common minimum-window-substring version, count requirements from t, expand a right pointer over s, and track how many required character categories are currently satisfied. Once every category is satisfied, shrink the left edge while the window remains valid, updating the best length and start.

Keep counts precise

Only increment the satisfied-category counter when a character's window count reaches its required count, and only decrement it when removing a character drops below that count. Extra copies are allowed and should not invalidate the window. Characters not in the target can still sit in the window but do not affect validity. Each pointer moves forward at most n times, so time is O(|s|+|t|) and space is O(alphabet). Return the stated empty result if no covering window exists. Test repeated target letters, target longer than source, irrelevant characters, and a valid window that becomes shorter only after several left moves.