Princeton Algorithms: Part 2 [week 7: Final Exam Part II]

Question Explanation

The correct answer is: 0 2 3 2 1 1 1 3 4

 0: Original input
 2: MSD radix sort after the first call to key-indexed counting
 3: 3-way radix quicksort after the first partitioning step
 2: MSD radix sort after the second call to key-indexed counting
 1: LSD radix sort after 3 passes
 1: LSD radix sort after 1 pass
 1: LSD radix sort after 2 passes
 3: 3-way radix quicksort after the second partitioning step
 4: Sorted

Question Explanation

The correct answer is: A B B C D C D D


Below are the sorted cyclic suffixes and the next[] array:

  i  suffixes[i]   t   next[i]
 -----------------------------
* 0  A ? ? ? ? ? ? D     1
  1  B ? ? ? ? ? ? A     2
  2  B ? ? ? ? ? ? B     3
  3  C ? ? ? ? ? ? B     6
  4  C ? ? ? ? ? ? D     7
  5  D ? ? ? ? ? ? D     0
  6  D ? ? ? ? ? ? C     4
  7  D ? ? ? ? ? ? C     5

Since first = 0, the first character is A (the first character in row 0).

Since next[0] = 1, the second character is B (the first character in row 1).

Since next[next[0]] = 2, the third character is B (the first character in row 2).

Since next[next[next[0]]] = 3, the fourth character is C (the first character in row 3).