Monotonic Decreasing Stack
Nonincreasing order means that as you move through a sequence or set, the values always get smaller or stay the same  they never get larger.
For example:
[5, 5, 3, 2, 2, 1] is in nonincreasing order. As you move through the sequence, the numbers never increase.
[10, 6, 4, 4, 2] is also nonincreasing. Each number is less than or equal to the number before it.
But [2, 4, 1, 3] is NOT nonincreasing, because 1 and 3 are larger than numbers before them.
Another way to think of it is:
 Nondecreasing means the values can increase or stay the same
 Nonincreasing means the values can decrease or stay the same
So in nonincreasing order, elements always get smaller or equal  never larger. This descending ordering is useful for algorithms like sorting stacks and queues where newest/max elements get added on top or back.
The key is that nonincreasing sequence has no increasing steps. Values always descend or stay steady.
A monotonic decreasing stack is a stack data structure where the elements are in nonincreasing order from top to bottom. Elements can be efficiently pushed and popped while maintaining order.
Java example:


C++ example:


Python example:


Monotonic stacks provide efficient push/pop from top while maintaining descending order. Useful for max tracking.
A monotonic stack is a general concept where the elements in the stack are arranged in a single, unbroken order. This order can either be nonincreasing or nondecreasing.
A Monotonic Decreasing Stack is a specific type of monotonic stack where the elements are arranged in a nonincreasing order. This means that each element in the stack is less than or equal to the element below it. It ensures that the stack’s top element is always the smallest among the current elements, and the order is maintained as elements are pushed and popped from the stack.
In summary, a Monotonic Decreasing Stack is a particular case of a monotonic stack that specifically maintains its elements in a nonincreasing order. It is useful in problems that require keeping track of minimum values or where the ordering of elements in a specific way is essential.
A monotonic decreasing stack is a data structure that maintains its elements in a decreasing order. The idea is to always ensure that the elements inside the stack are arranged in a way that the topmost element is the smallest. When a new element that is smaller than the topmost element is encountered, it is simply pushed onto the stack. If it is larger, elements are popped from the stack until a smaller element is encountered, or the stack is empty, and then the new element is pushed. This kind of structure is beneficial in scenarios like finding the nearest smaller elements, or in problems related to histograms, etc.
Solution
Java
Here’s a Java implementation of a monotonic decreasing stack:


C++
A C++ implementation of a monotonic decreasing stack:


Python
Here’s how you can implement a monotonic decreasing stack in Python:


In these implementations, the push
method ensures that the elements in the stack are in a decreasing order by removing elements from the top that are less than the new element. The top
method returns the current top element, and the pop
method can be used to remove an element from the top of the stack.