algorithm - Implement a queue in which push_rear(), pop_front() and get_min() are all constant time operations - Stack Overflow

You can implement a stack with O(1) pop(), push() and get_min(): just store the current minimum together with each element. So, for example, the stack [4,2,5,1] (1 on top) becomes [(4,4), (2,2), (5,2), (1,1)]. Then you can use two stacks to implement the queue. Push to one stack, pop from another one; if the second stack is empty during the pop, move all elements from the first stack to the second one. E.g for a pop request, moving all the elements from first stack [(4,4), (2,2), (5,2), (1,1)], the second stack would be [(1,1), (5,1), (2,1), (4,1)].

Read full article from algorithm - Implement a queue in which push_rear(), pop_front() and get_min() are all constant time operations - Stack Overflow