# Cormen Edition 3 Exercise 8.3 Question 1 (Page No. 199)

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RADIX-SORT(A, d)
1     for i = 1 to d
2     use a stable sort to sort array A on digit i

illustrate the operation of RADIX-SORT on the following list of English words: COW, DOG, SEA, RUG, ROW, MOB, BOX, TAB, BAR, EAR, TAR, DIG, BIG, TEA, NOW, FOX.

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Show how to sort $n$ integers in the range $0$ to $n^3-1$ in $O(n)$ time.
BUCKET-SORT(A) 1 let B[0...n-1] be a new array 2 n = A.length 3 for i – 0 to n – 1 4 make B[i] an empty list 5 for i = 1 to n 6 insert A[i] into list B[nA[i]] 7 for i = 0 to n – 1 8 sort list B[i] with insertion sort 9 concatenate the lists B[0] , B[1] , ….,B[n-1] together in order illustrate the operation of BUCKET-SORT on the array $A=\langle .79,.13,.16,.64,.39,.20,.89,.53,.71,.42\rangle$
COUNTING-SORT(A, B, k) 1 let C[0, ,k] be a new array 2 for i = 0 to k 3 C[i] = 0 4 for j = 1 to A.length 5 C[A[j]] = C[A[j]] + 1 6 // C[i] now contains the number of elements equal to i . 7 for i =1 to k 8 C[i] = C[i] + C[i-1] 9 // C[i] now contains the ... [C[A[j]]] = A[j] 12 C[A[j]] = C[A[j]] - 1 illustrate the operation of COUNTING-SORT on the array $A=\langle 6,0,2,0,1,3,4,6,1,3,2 \rangle$