Exploring Stack-Based Problems and Solutions in Ruby

Introduction to the Lesson

Hello once again, champion of code! In this session, we will delve into the world of coding interviews by focusing on stack-based problems. We endeavor to decode interview questions that leverage the Last-In, First-Out (LIFO) magic of stacks to offer elegantly efficient solutions. After today, not only will you be able to handle stacks with ease, but you'll also be able to articulate and apply this knowledge when faced with interview questions that require depth in data structure understanding.

Problem 1: Preceding Smaller Elements

Imagine a sequence of integers representing the highs and lows of a mountain range. Each integer denotes the height of a peak, and you're moving from left to right, tracking peaks that are shorter than the current one you're standing on. For every peak, the task is to identify the height of the nearest preceding peak that is shorter — a scenario perfectly suited for stacks. Alternatively, think about monitoring daily temperatures over several months. You're interested in determining the last day when the temperature was cooler for each day you check. This is analogous to finding the previous smaller number for each entry in the array. Stacks excel at handling these types of sequence queries efficiently.

Problem 1: Naive Approach

You might be tempted to approach this problem with the vigor of a brute-force assault — looking behind each element to find a smaller one. However, this could mean reviewing multiple times and spending excessive amounts of time as you consider each element repeatedly. In a vast dataset, this would be akin to retracing your steps on each day's hike to find a shorter peak — an exhausting proposition!

Problem 1: Efficient Approach

Enter the stack — our trusty guide. As we progress through the array, we push peaks onto the stack. When we encounter a peak, we pop entries from the stack that aren't shorter than the current one. The stack's top now reveals the nearest preceding smaller peak, which we note before adding the current peak to the stack.

Problem 1: Solution Building

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Problem 2: Solution Building

Let's translate our idea into Ruby code, creating an efficient stack with minimum trace functionality:

Ruby

class MinStack
  def initialize
    @stack = []
    @min_values = []
  end

  # The push method is where most of our logic resides.
  def push(x)
    @min_values.push(x) if @min_values.empty? || x <= @min_values.last
    @stack.push(x)
  end

  # Each pop requires careful coordination between our two stacks.
  def pop
    if !@stack.empty? && @stack.last == @min_values.last
      @min_values.pop
    end
    @stack.pop unless @stack.empty?
  end

  # The top method reveals the peak of our stack cable car.
  def top
    @stack.empty? ? -1 : @stack.last
  end

  # GetMin serves as our on-demand minimum value provider.
  def get_min
    @min_values.empty? ? -1 : @min_values.last
  end
end

# Demonstration
min_stack = MinStack.new
min_stack.push(5)
min_stack.push(3)
puts min_stack.get_min # Output: 3
min_stack.pop
puts min_stack.get_min # Output: 5

class MinStack
  def initialize
    @stack = []
    @min_values = []
  end

  # The push method is where most of our logic resides.
  def push(x)
    @min_values.push(x) if @min_values.empty? || x <= @min_values.last
    @stack.push(x)
  end

  # Each pop requires careful coordination between our two stacks.
  def pop
    if !@stack.empty? && @stack.last == @min_values.last
      @min_values.pop
    end
    @stack.pop unless @stack.empty?
  end

  # The top method reveals the peak of our stack cable car.
  def top
    @stack.empty? ? -1 : @stack.last
  end

  # GetMin serves as our on-demand minimum value provider.
  def get_min
    @min_values.empty? ? -1 : @min_values.last
  end
end

# Demonstration
min_stack = MinStack.new
min_stack.push(5)
min_stack.push(3)
puts min_stack.get_min # Output: 3
min_stack.pop
puts min_stack.get_min # Output: 5

The push method introduces the key player — our @min_values stack, which retains the minimum value observed so far every time we add a new entry. Meanwhile, the pop operation is like a relay race transition, handing off the title "minimum" to the next contender when the current titleholder is knocked off the podium.

Simulating the pushing of various elements onto the stack and invoking get_min yields the correct minimum every time, thanks to our additional stack, @min_values.

Introduction to the Lesson

Problem 1: Preceding Smaller Elements

Problem 1: Naive Approach

Problem 1: Efficient Approach

Problem 1: Solution Building

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Problem 2: Stack with Minimum Trace

Problem 2: Naive Approach

Problem 2: Efficient Approach

Problem 2: Solution Building

Lesson Summary