Maximum Frequency Stack

To solve the Maximum Frequency Stack, I would first clarify that when frequencies are tied, we must pop the element most recently pushed. A naive approach of scanning the stack every time would be O(N) per operation, which is inefficient. Instead, I propose an O(1) solution using three key components: a frequency map, a max-frequency tracker, and a collection of stacks indexed by frequency. We maintain a hash map called 'freq' to store the current count of each number. We also use another map called 'group', where the key is the frequency and the value is a stack of numbers having that specific frequency. When pushing a number, we increment its frequency in 'freq'. If this new frequency exceeds our current maximum, we update the max. Then, we push the number onto the stack corresponding to its new frequency in 'group'. For popping, we look at the 'group' stack associated with the current maximum frequency. The top of this stack is our answer because it represents the most frequent element added last among those with that frequency. After retrieving it, we decrement its frequency in 'freq' and remove it from the stack. If that frequency stack becomes empty, we decrement the global maximum frequency. This ensures both push and pop operations remain constant time, handling the dynamic nature of data access patterns effectively.