Homework $2$: Basic operations and application scenarios of stacks

Questions:

$1.$ What is the definition of a stack? What are its main features? Please explain the "last in$,$ first out" principle.

$2.$ Suppose we have the following Java stack operation code:

$```$

java

Stack stack $=$ new Stack;

stack.push$(1)$;

stack.push$(2)$;

stack.push$(3)$;

stack.pop$()$;

int top $=$ stack.peek$()$;

$```$

a$.$ After executing the above code, what are the remaining elements in the stack? What is the value of the top variable?

b$.$ Please explain the meaning of push, pop, and peek operations, and explain the time complexity of these operations.

$3.$ The application scenarios of stacks are very wide. Please list three typical application scenarios using stack structures and briefly explain the role of stacks in each scenario.