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


i came across question: implement queue in push_rear(), pop_front() , get_min() constant time operations.

i thought of using min-heap data structure has o(1) complexity get_min(). push_rear() , pop_front() o(log(n)).

does know best way implement such queue has o(1) push(), pop() , min()?

i googled this, , wanted point out algorithm geeks thread. seems none of solutions follow constant time rule 3 methods: push(), pop() , min().

thanks suggestions.

you can implement stack o(1) pop(), push() , get_min(): store current minimum each element. so, example, stack [4,2,5,1] (1 on top) becomes [(4,4), (2,2), (5,2), (1,1)].

then can use 2 stacks implement queue. push 1 stack, pop one; if second stack empty during pop, move elements first stack second one.

e.g pop request, moving elements first stack [(4,4), (2,2), (5,2), (1,1)], second stack [(1,1), (5,1), (2,1), (4,1)]. , return top element second stack.

to find minimum element of queue, @ smallest 2 elements of individual min-stacks, take minimum of 2 values. (of course, there's logic here case 1 of stacks empty, that's not hard work around).

it have o(1) get_min() , push() , amortized o(1) pop().


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