Question

For each of the following two program fragments:

a. Give an analysis of the running time (Big-Oh will do).

(1) std::vector<int> my_vect;

for( i = 0; i < n; i++ ) my_vect.insert(0, i);





(2) std::vector<int> my_vect;

for( i = 0; i < n; i++ ) my_vect.push_back(i);






(3) std::list<int> my_list; for( i = 1; i < n; i++ ) my_list.insert(i, 0);





(4) std::list<int> my_list; for( i = 1; i < n; i++ ) my_list.push_front(i);

Answer 1

Note:
   the complexities of push_back and push_front is O(1)
   and for insert() is O(n+m)//where n is number of elements inserted and number of elements moved
now
(1) std::vector<int> my_vect;

for( i = 0; i < n; i++ ) //runs n times
my_vect.insert(0, i);//inserts i at position 0//its worst case here is O(n)
total complexity : O(n*n)

2) std::vector<int> my_vect;

for( i = 0; i < n; i++ ) //runs n times
my_vect.push_back(i);//O(1)
total complexity : O(n)

(3) std::list<int> my_list;
for( i = 1; i < n; i++ ) //runs n-1 times
my_list.insert(i, 0);//inserts at position i//O(1)
total complexity :O(n)

(4) std::list<int> my_list;
for( i = 1; i < n; i++ ) //runs n-1 times
my_list.push_front(i);//O(n)//for moving in worst case
total complexity O(n*n)