# 895. Maximum Frequency Stack

#### Hard

***

Design a stack-like data structure to push elements to the stack and pop the most frequent element from the stack.

Implement the `FreqStack` class:

* `FreqStack()` constructs an empty frequency stack.
* `void push(int val)` pushes an integer `val` onto the top of the stack.
* `int pop()` removes and returns the most frequent element in the stack.
  * If there is a tie for the most frequent element, the element closest to the stack's top is removed and returned.

 

**Example 1:**

```
Input
["FreqStack", "push", "push", "push", "push", "push", "push", "pop", "pop", "pop", "pop"]
[[], [5], [7], [5], [7], [4], [5], [], [], [], []]
Output
[null, null, null, null, null, null, null, 5, 7, 5, 4]

Explanation
FreqStack freqStack = new FreqStack();
freqStack.push(5); // The stack is [5]
freqStack.push(7); // The stack is [5,7]
freqStack.push(5); // The stack is [5,7,5]
freqStack.push(7); // The stack is [5,7,5,7]
freqStack.push(4); // The stack is [5,7,5,7,4]
freqStack.push(5); // The stack is [5,7,5,7,4,5]
freqStack.pop();   // return 5, as 5 is the most frequent. The stack becomes [5,7,5,7,4].
freqStack.pop();   // return 7, as 5 and 7 is the most frequent, but 7 is closest to the top. The stack becomes [5,7,5,4].
freqStack.pop();   // return 5, as 5 is the most frequent. The stack becomes [5,7,4].
freqStack.pop();   // return 4, as 4, 5 and 7 is the most frequent, but 4 is closest to the top. The stack becomes [5,7].
```

 

**Constraints:**

* `0 <= val <= 109`
* At most `2 * 104` calls will be made to `push` and `pop`.
* It is guaranteed that there will be at least one element in the stack before calling `pop`.

```python
class FreqStack:

    def __init__(self):
        self.counter = Counter()
        self.stack = defaultdict(list) # {count : [ele1, ele2]}
        self.max_freq = 0

    def push(self, val: int) -> None:
        self.counter[val] += 1
        self.max_freq = max(self.max_freq, self.counter[val])
        self.stack[self.counter[val]].append(val)
        

    def pop(self) -> int:
        max_element = self.stack[self.max_freq].pop()
        self.counter[max_element] -= 1
        # If max_freq list goes empty decrease by 1
        if not self.stack[self.max_freq]:
            self.max_freq -= 1
        return max_element
        


# Your FreqStack object will be instantiated and called as such:
# obj = FreqStack()
# obj.push(val)
# param_2 = obj.pop()
```