Max Stack

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Design a max stack that supports push, pop, top, peekMax and popMax.

1. push(x) -- Push element x onto stack.
2. pop() -- Remove the element on top of the stack and return it.
3. top() -- Get the element on the top.
4. peekMax() -- Retrieve the maximum element in the stack.
5. popMax() -- Retrieve the maximum element in the stack, and remove it. If you find more than one maximum elements, only remove the top-most one.

Example 1:

MaxStack stack = new MaxStack();
stack.push(5); 
stack.push(1);
stack.push(5);
stack.top(); -> 5
stack.popMax(); -> 5
stack.top(); -> 1
stack.peekMax(); -> 5
stack.pop(); -> 1
stack.top(); -> 5

Note:

1. -1e7 <= x <= 1e7
2. Number of operations won't exceed 10000.
3. The last four operations won't be called when stack is empty.

思路：难点在于popmax，需要把当前max stack的peek 从stack里面remove掉，同时更新当前的max，用个temp stack解决，存储当前的Integer到max的值，然后再存储回来；

class MaxStack {

    Stack<Integer> stack;
    Stack<Integer> maxStack;
    /** initialize your data structure here. */
    public MaxStack() {
        stack = new Stack<Integer>();
        maxStack = new Stack<Integer>();
    }
    
    public void push(int x) {
        stack.push(x);
        if(!maxStack.isEmpty()){
            if(x >= maxStack.peek()){
                maxStack.push(x);
            }
        } else {
            maxStack.push(x);
        }
    }
    
    public int pop() {
        int value = stack.pop();
        if(!maxStack.isEmpty() && value == maxStack.peek()){
            maxStack.pop();
        }
        return value;
    
    }
    
    public int top() {
        return stack.peek();
    }
    
    public int peekMax() {
        return maxStack.peek();
    }
    
    public int popMax() {
        int value = maxStack.pop();
        Stack<Integer> temp = new Stack<Integer>();
        while(stack.peek()!=value){
            temp.push(stack.pop());
        }
        stack.pop();
        while(!temp.isEmpty()){
            this.push(temp.pop());
        }
        return value;
    }
}

/**
 * Your MaxStack object will be instantiated and called as such:
 * MaxStack obj = new MaxStack();
 * obj.push(x);
 * int param_2 = obj.pop();
 * int param_3 = obj.top();
 * int param_4 = obj.peekMax();
 * int param_5 = obj.popMax();
 */