Longest Substring with At Least K Repeating Characters / visualized

Every sliding window rests on one property: validity must be monotone — once a window goes bad, growing it must keep it bad, so shrinking is the only sane move. “Every character appears at least k times” is the opposite: an invalid window can be repaired by adding more characters. a is invalid at k=2, and ababb is valid. So there is no shrink rule, and Act 1 shows the window eating itself alive. Act 2 restores monotonicity by fixing a parameter: pin the number of distinct characters to d, and “too many distinct” is monotone, so a normal window works — run it once for each d from 1 to 26 and take the best. The other standard fix is divide and conquer: any character whose total count in a segment is below k can never appear in the answer, so split the segment on it and recurse. Same answer, different lever — but only the fixed-d version teaches you what to do the next time a window refuses to shrink.