# Design and Analysis of Algorithm

Consider the algorithm for the sorting problem that sorts an array by counting, for each of its elements, the number of smaller elements and then uses this information to put the element in its appropriate position in the sorted array:

Algorithm ComparisonCountingSort(A[0..n 1], S[0..n 1])

//Sorts an array by comparison counting

//Input: Array A[0..n 1] of orderable values

//Output: Array S[0..n 1] of As elements sorted in nondecreasing order

for i 0 to n 1 do

Count[i] 0

for i 0 to n 2 do

for j i + 1 to n 1 do

if A[i]

Count[j] Count[j]+1

else Count[i] Count[i]+1

for i 0 to n 1 do

S[Count[i]] A[i]

a. Apply this algorithm to sorting the list 60, 35, 81, 98, 14, 47.

b. Is this algorithm stable?

c. Is it in place?

Consider the algorithm for the sorting problem that sorts an array by counting, for each of its elements, the number of smaller elements and then uses this information to put the element in its appropriate position in the sorted array: Algorithm ComparisonCounting Sort (A[0..n1],S[0.n1]) //Sorts an array by comparison counting //Input: Array A[0..n - 1] of orderable values //Output: Array S[0..n - 1] of A's elements sorted in nondecreasing order for i0 to n1 do Count [i]0 for i0 to n2 do for ji+1 to n1 do if A[i]