Question

Specify the running time of each of the following algorithms. You must fully explain your answer for each of the question!

Algorithm Ex1(ai,.., an), a): for i ← 1 to n do If ai 〉 a raj return x Algorithm Ex2((ai ,..., an), (b,..., bm)): for i ← 1 to min(n, m) do ifai 〈bi return x

Answer 1

a) O(n)
Explanation : We can see that for loop will run from 1 to n so it will run n+1 times. One time extra because when i will be n+1 so condition will fail. Statements inside for loop will run for n time. So time complexity of algorithm is O(n)


b)  O(min(n,m))
Explanation : We can see that for loop will run from 1 to min ( n, m) so it will run min(n,m)+1 times. One time extra because when i will be n+1 or m+1 so condition will fail. Statements inside for loop will run for min(n,m) time. So time complexity of algorithm is O(min(n,m))

c)  O(mnpq)
Explanation : 4 nested loop, One inside the other . Each loop will run for its range time and a,ong iwth its range because of outer loop. Hence the time complexity is O(mnpq)

d)  O(n⁴)
Explanation : 4 nested loop, One inside the other . Outer loop will run for n time, the first inner loop will run for n time itself and n times because of outer loop so its n² . Similarly 2nd inner loop will run for n³ time, and the inner most loop will run for  n⁴ time. Hence the time complexity is O(n⁴ )


(e)O(nm)
Explanation While loop will run for n time, and inner loop loop will run for m time itself and n time because of outer loop so its nm time. hence the time complexity is O(nm)


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