Question

(a) Give the pseudo-code for a recursive algorithm called Find_Smallest(A, n) that returns the value of the smallest element in an array of n integers called A. Assume the elements in the array are at locations A[1]..A[n].

(b) Give a recurrence T(n) for the running time of your algorithm.

(c) Solve the recurrence in part (b)

Answer 1

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Find_smallest(A,n)
if(n==1) then
return A[1]
else
return min(A[n],Find_smallest(A,n-1))
  

T(n)=T(n-1)+ 1

T(n-1)=T(n-2)+ 1

T(n-2)=T(n-3)+ 1

T(n)=T(n-2)+ 1+ 1

T(n)=T(n-3)+ 1+ 1+ 1

T(n)= T(n-i)+i

when n -i =1 then i=n-1

T(n)= T(1)+ n-1= 1+n-1= n

if we solve the recurrence we get T(n)=n