To pop the actual value just return e/DUMMY_VALUE and set the new minimum as (minFoundSoFar % DUMMY_VALUE). The idea is to store min element found till current insertion) along with all the elements as a reminder of a DUMMY_VALUE, and the actual element as a multiple of the DUMMY_VALUE.įor example, while pushing an element ‘e’ into the stack, store it as (e * DUMMY_VALUE + minFoundSoFar), this way we know what was the minimum value present in the stack at the time ‘e’ was being inserted. The above approach can be optimized further and the solution can be made to work in O(1) time complexity and O(1) space complexity.

The complexity in the worst case is the same as above but in other cases, it will take slightly less space than the above approach as repetition is neglected.įurther optimized O(1) time complexity and O(1) space complexity solution : For ‘Get Min’ operation: O(1) (As we have used an auxiliary which has it’s top as the minimum element).For Delete operation: O(1) (As deletion ‘pop’ in a stack takes constant time).Nodes can flow vertically (in columns) or horizontally (in rows). For Insert operation: O(1) (As insertion ‘push’ in a stack takes constant time) The StackPane layout pane places all of the nodes within a single stack with each new.In the below implementation, SpecialStack inherits from Stack and has one Stack object min which works as an auxiliary stack. The following is the implementation for SpecialStack class. When 16 is inserted, both stacks change to following. When 15 is inserted, both stacks change to following. When 29 is inserted, both stacks change to following. When 19 is inserted, both stacks change to following. When we insert 18, both stacks change to following. Let us assume that both stacks are initially empty and 18, 19, 29, 15, and 16 are inserted to the SpecialStack. We can see that all the above operations are O(1). Return the top element of the auxiliary stack.Int getMin() // returns the minimum element from Special Stack Step 1 is necessary to make sure that the auxiliary stack is also updated for future operations. pop the top element from the actual stack and return it.pop the top element from the auxiliary stack.

Int Pop() // removes an element from Special Stack and return the removed element If x is greater than y then push y to the auxiliary stack.If x is smaller than y then push x to the auxiliary stack.2) compare x with the top element of the second stack (the auxiliary stack).If we click the contact menu then contact detail will be shown on the remaining pages. The vertical menu contains the heading of content. But the default vertical menu is placed on the left side. The vertical menu can place on the left or right side of the web pages. 1) push x to the first stack (the stack with actual elements) The vertical menu in bootstrap works fixed and is responsive as per requirement.ISRO CS Syllabus for Scientist/Engineer Exam.ISRO CS Original Papers and Official Keys.GATE CS Original Papers and Official Keys.Finally, initialize the plugin in jQuery document ready function. After that, create markup for menu and add your main & sub navigation links in it. So, lets start by loading jQuery and Stack Menu‘s CSS & JavaScript files into your HTML document. You need to get started with Stack Menu plugin in order to make vertical menu with submenu.

Vartically stack menu