Question

1.If a list is implemented as a singly linked stack, give the big-O worst-case time complexity of the following operations (as usual use the smallest standard big-O category that works:

a) push_front, b) push_back, c) lookup, d) read the i'th member

2.Repeat question 3 for a dynamic array (for example, as in the C++ vector class)

Answer 1

1.If a list is implemented as a singly linked stack,
give the big-O worst-case time complexity of the following operations
(as usual use the smallest standard big-O category that works:

a) push_front,
    It takes O(1), constant time. We add new node at head of list

b) push_back:
    It takes O(1). constant time. We add at last using "rear" pointer. "rear" pointer points to last node.

c) lookup:
    It takes O(n) time. We have to search from head to end of the list.

d) read the i'th member
   It takes O(i) time, we have to traverse from head to ith node.

2.Repeat question 3 for a dynamic array;

a) push_front,
    It takes O(n) time. We have to first shift elements from 2nd postion element to one by left(make room)

b) push_back:
    It takes O(1). constant time. We add at last.

c) lookup:
    It takes O(n) time. We have to search from head to end of the list.

d) read the i'th member
   It takes O(1) time, We can access array element in constant time using index