Implement a class for a stack that supports all the regular functions (push, pop) and an additional function of max() which returns the maximum element in the stack (return None if the stack is empty). Each method should run in constant time.

MaxStack.ts

class MaxStack {

    private stack: number[] = new Array<number>();
    private maxStack: number[] = new Array<number>();
    private length: number = 0;

    public push(item: number): void {
        let previousMax = this.maxStack[this.length-1] || 0;
        this.maxStack[this.length] = item > previousMax ? item : previousMax;
        this.stack[this.length++] = item;
    }

    public pop(): number {
        this.stack.length = this.maxStack.length = --this.length;
        return this.stack[this.length];
    }

    public max(): number | undefined{
         return this.maxStack[this.length - 1];
    }
}