With probability 1/2 the pivot selected will be between n/2 and 3n/4 (i. e. a good pivot). Also with probability 1/2 the pivot selected will be between 1 and n/4 or between 3n/4 and n (i. e. a bad pivot). (1 points) 1. State a recurrence that expresses the worst case for bad pivots.

Required:
a. State a recurrence that expresses the worst case for bad pivots.
b. State a recurrence that expresses the worst case for good pivots.
c. State a recurrence that expresses the expected worst case by combining the first two recurrences.
d. Prove by induction that your recurrence is in O(nlog n).

The use of phrases, fragments, and punctuation can influence the mood of a passage; keeping this in mind, how would you describe the mood of the followingpassage? "fog on the essex marshes, fog on the kentish heights, fog creeping into the cabooses of collier-brigs; fog lying out on the yards, and hovering in the riggingof great ships; fog drooping on the gunwales of barges and small boats. fog in the eyes and throats of ancient greenwich pensioners, wheezing by thefiresides of their wards; fog in the stem and bowl of the afternoon pipe of the wrathful skipper; fog cruelly pinching the toes and fingers of his shivering little'prentice boy on deck." (5 points)