Stack & Queue

http://www.zhitongguigu.com

Stack & Queue

Two Different Data Structure
Stack: LIFO (Last in first out)
Queue: FIFO (First in first out)

http://www.zhitongguigu.com

Stack: LIFO

LIFO: Last In First Out

http://www.zhitongguigu.com

Tower of Hanoi

Queue: FIFO

FIFO: First In First Out

http://www.zhitongguigu.com

Queue: FIFO

FIFO: First In First Out

http://www.zhitongguigu.com

Stack

Stack<String> stack = new Stack<String>();
Stack<String> stack = new Stack<>();

Java

C++

stack <string> cards;

http://www.zhitongguigu.com

Stack<String> stack = new Stack<String>();
Stack<String> stack = new Stack<>();

List<Map<Integer,Set<String>>> p = new ArrayList<Map<Integer,Set<String>>>();
List<Map<Integer,Set<String>>> p = new ArrayList<>();

// polymorphism
List<Map<Integer,Set<String>>> p = new ArrayList<>();
ArrayList<Map<Integer,Set<String>>> p = new ArrayList<>();

Java Diamond Operator

http://www.zhitongguigu.com

Basic Operation

size
pop
push
peek

size
pop
push
top

Java

C++

http://www.zhitongguigu.com

Stack

How to use Array to implement a stack?

http://www.zhitongguigu.com

🤔

What might be the problems

Array -> Stack

class Stack<T> {
  private int top;
  int capacity;
  T[] stack;
  public Stack(int inCapacity) {
    capacity = inCapacity;
    stack = (T[]) new Object[capacity];
    top = -1;
  }
  public int size() {
    return top + 1;
  }
  public void push(T value) {
    if(top + 1 == capacity) {
      throw new IllegalStateException("Stack is full");
    } else {
      stack[++ top] = value;
    }
  }
  public T peek() {
    if(top == -1) {
      throw new IllegalStateException("Stack is empty");
    }
    else return stack[top];
  }
  public T pop() {
    if(top == -1) {
      throw new IllegalStateException("Stack is empty");
    } 
    else return stack[top--];
  }
}

http://www.zhitongguigu.com

🤔

Memory Leak

public T pop() {
  if(top == -1) {
    throw new IllegalStateException("Stack is empty");
  } 
  else return stack[top--];
}

http://www.zhitongguigu.com

class Stack<T> {
  private int top;
  int capacity;
  T[] stack;
  public Stack(int inCapacity) {
    capacity = inCapacity;
    stack = (T[]) new Object[capacity];
    top = -1;
  }
  public int size() {
    return top + 1;
  }
  public void push(T value) {
    if(top + 1 == capacity) {
      throw new IllegalStateException("Stack is full");
    } else {
      stack[++ top] = value;
    }
  }
  public T peek() {
    if(top == -1) {
      throw new IllegalStateException("Stack is empty");
    }
    else return stack[top];
  }
  public T pop() {
    if(top == -1) {
      throw new IllegalStateException("Stack is empty");
    } 
    else {
        T result = stack[top--];
        stack[top + 1] = null;
        return result;
    }
  }
}

http://www.zhitongguigu.com

When to use Stack?

Invoke a function
Recursion (This is a special case of the first)
DFS (Depth-first Search) (This is a special case of the second)

http://www.zhitongguigu.com

Stack in Operating System

Stack and Heap
Stack is Faster
Heap can dynamically allocate space
Objects are all in heap
Functions are in stacks

http://www.zhitongguigu.com

static void method(int value) {
    int a = value;
    int[] arr = new int[3];
    method(a + 2);
}

public static void main(String[] args) {
    method(3);
}

🤔

http://www.zhitongguigu.com

static void method(int value) {
    if (value > 5) {
        return;
    }
    int a = value;
    int[] arr = new int[3];
    method(a + 2);
}

public static void main(String[] args) {
    method(3);
}

Stack in Operating System

Stack and Heap
Stack is Faster
Heap can dynamically allocate space
Objects are all in heap
Functions are in stacks

http://www.zhitongguigu.com

Stack in Operating System

http://www.zhitongguigu.com

Queue

LinkedList<String> names = new LinkedList<>();

Java

C++

queue <string> names;

http://www.zhitongguigu.com

Queue in Java is an Interface. Usually we use linkedlist to implement features for queues

Basic Operations

size
remove (poll)
add (offer)
element (peek)

size
pop_front
push_back

Java

C++

http://www.zhitongguigu.com

Queue

How to use Array to implement a queue?

http://www.zhitongguigu.com

What might be the problems

🤔

Array => Queue

class Queue<T> {
    private int front;
    private int rear;
    int capacity;
    int size;
    T[] queue;
    public Queue(int inCapacity) {
        capacity = inCapacity;
        queue = (T[]) new Object[capacity];
        front = 0;
        rear = 0;
        size = 0;
    }
    public int size() {
        return size;
    }
}

http://www.zhitongguigu.com

Array => Queue (Cont.d)

class Queue<T> {
    public void add(T value) {
        if (size == capacity) {
            throw new IllegalStateException("Queue is full");

        } else {
            queue[rear] = value;
            rear = (rear + 1) % capacity;
            size++;
        }
    }
    public T remove() {
        T value = null;
        if (size == 0) {
            throw new IllegalStateException("Cannot remove empty queue");
        } else {
            value = queue[front];
            front = (front + 1) % capacity;
            size--;
        }
        return value;
    }
}

http://www.zhitongguigu.com

When to use Queue?

BFS (Breadth-first Search)
Priority Queue (Heap)
Multi Task Queue (Design)

http://www.zhitongguigu.com

LinkedList Rule Them All

http://www.zhitongguigu.com

Head

Tail

pop

(poll)

pollFirst

remove

removeFirst

push

addFirst

offerFirst

peek

(element)

getFirst

peekFirst

pollLast

removeLast

add

(offer)

addAll

addLast

offerLast

peekLast

getLast

java.util.LinkedList

http://www.zhitongguigu.com

Practice 1

Implement Queue using Stacks

Use two Stacks to implement a queue

http://www.zhitongguigu.com

Implement Queue using Stacks

Use two Stacks to implement a queue

Consider the basic operations of these two data structures

How to minimize the time complexity?

http://www.zhitongguigu.com

Implement Queue using Stacks

http://www.zhitongguigu.com

Implement Queue using Stacks

class MyQueue {
    LinkedList<Integer> stack = new LinkedList<>();
    // Push element x to the back of queue.
    public void push(int x) {
        LinkedList<Integer> temp = new LinkedList<>();
        while (!stack.isEmpty()) {
            temp.push(stack.pop());
        }
        stack.push(x);
        while (!temp.isEmpty()) {
            stack.push(temp.pop());
        }
    }
    // Removes the element from in front of queue.
    public void pop() {
        stack.pop();
    }
    // Get the front element.
    public int peek() {
        return stack.peek();
    }
    // Return whether the queue is empty.
    public boolean empty() {
        return stack.isEmpty();
    }
}

Big O

O(n)

http://www.zhitongguigu.com

Implement Queue using Stacks

class MyQueue {
    Stack<Integer> temp = new Stack<Integer>();
    Stack<Integer> value = new Stack<Integer>();
    // Push element x to the back of queue.
    public void push(int x) {
        value.push(x);
    }
    // Removes the element from in front of queue.
    public void pop() {
        if(temp.isEmpty()) {
            while(!value.isEmpty()) {
                temp.push(value.pop());
            }
        }
        temp.pop();        
    }
    // Get the front element.
    public int peek() {
        if(temp.isEmpty()) {
            while(!value.isEmpty()) {
                temp.push(value.pop());
            }
        }
        return temp.peek();        
    }
    // Return whether the queue is empty.
    public boolean empty() {
        return temp.isEmpty() && value.isEmpty();       
    }
}

Big O

O(1)

Any Problem?

🤔

http://www.zhitongguigu.com

Implement Queue using Stacks

class MyQueue {
    Stack<Integer> temp = new Stack<Integer>();
    Stack<Integer> value = new Stack<Integer>();
    // Push element x to the back of queue.
    public void push(int x) {
        value.push(x);
    }
    // Removes the element from in front of queue.
    public void pop() {
        reorder();
        temp.pop();        
    }
    // Get the front element.
    public int peek() {
        reorder();
        return temp.peek();        
    }
    // Return whether the queue is empty.
    public boolean empty() {
        return temp.isEmpty() && value.isEmpty();       
    }
    private void reorder() {
        if(temp.isEmpty()) {
            while(!value.isEmpty()) {
                temp.push(value.pop());
            }
        }
    }
}

Practice 2

a stack with max()

Instead normal stack operation, this stack will have a max() function that could return the current max value of the stack

http://www.zhitongguigu.com

a stack with max()

http://www.zhitongguigu.com

One stack cannot tell the max in O(1)

Need another stack to store the max

time <=> space

class MaxStack {
  Stack element;
  Stack maxValue;
  public MaxStack(int inCapacity) {
    element = new Stack(inCapacity);
    maxValue = new Stack(inCapacity);
  }
  public int size() {
    return element.size();
  }
  public void push(int value) {
    int currentMax;
    if(element.size() == 0) {
      currentMax = Integer.MIN_VALUE;
    } else {
      currentMax = maxValue.peek();
    }
    element.push(value);
    if(currentMax > value) {
      maxValue.push(currentMax);
    }
    else maxValue.push(value);
  }
  public int pop() {
    maxValue.pop();
    return element.pop();
  }
  public int getMax() {
    return maxValue.peek();
  }
}

http://www.zhitongguigu.com

EmptyStackException

store < n extra

🤔

class MaxStack {
  Stack element;
  Stack maxValue;
  public MaxStack(int inCapacity) {
    element = new Stack(inCapacity);
    maxValue = new Stack(inCapacity);
  }
  public int size() {
    return element.size();
  }
  public void push(int value) {
    element.push(value);
    if(maxValue.isEmpty() || maxValue.peek() <= value) {
        maxValue.push(value);
    }
  }
  public int pop() {
    if (!maxValue.isEmpty() && maxValue.peek() == element.peek()) {
        maxValue.pop();
    }
    return element.pop();
  }
  public int getMax() {
    return maxValue.peek();
  }
}

http://www.zhitongguigu.com

🤔

only use one stack

~~store < n extra~~

!maxValue.isEmpty()

class MaxStack {
    private class Element {
        int val;
        int max;
        public Element(int val, int max) {
            this.val = val;
            this.max = max;
        }
    }
    Stack<Element> stack = new Stack<>();
    public int size() {
        return stack.size();
    }
    public void push(int x) {
        int max = (stack.isEmpty()) ? x : Math.max(x, stack.peek().max);
        stack.push(new Element(x, max));
    }
    public int pop() {
        return stack.pop().val;
    }
    public int getMax() {
        return stack.peek().max;
    }
}

http://www.zhitongguigu.com

Practice 3

Valid Parentheses

http://www.zhitongguigu.com

Valid Parentheses

http://www.zhitongguigu.com

We need to use the stack to store the information: Which left parentheses has not been matched yet.

Stack can help store every unused parentheses, no matter when the parentheses appears

public boolean isValid(String s) {
	Stack<Character> pair = new Stack<Character>();
	int n = s.length();
	if(n == 0) return true;
	for(int i = 0; i < n; i ++) {
		if(s.charAt(i) == '(' || s.charAt(i) == '[' || s.charAt(i) == '{')  {
			pair.push(s.charAt(i));
		}
		else if(s.charAt(i) == ')') {
			if(pair.isEmpty()) return false;
			if(pair.pop() != '(') return false;
		}
		else if(s.charAt(i) == ']') {
			if(pair.isEmpty()) return false;
			if(pair.pop() != '[') return false;
		}
		else if(s.charAt(i) == '}') {
			if(pair.isEmpty()) return false;
			if(pair.pop() != '{') return false;
		}
	}
	if(pair.isEmpty()) return true;
	return false;
}

http://www.zhitongguigu.com

🤔

public boolean isValid(String s) {
	Stack<Character> pair = new Stack<Character>();
	int n = s.length();
	if(n == 0) return true;
	for(int i = 0; i < n; i ++) {
		if(s.charAt(i) == '(' || s.charAt(i) == '[' || s.charAt(i) == '{')  {
			pair.push(s.charAt(i));
		}
		else if(s.charAt(i) == ')') {
			if(pair.isEmpty() || pair.pop() != '(') return false;
		}
		else if(s.charAt(i) == ']') {
			if(pair.isEmpty() || pair.pop() != '[') return false;
		}
		else if(s.charAt(i) == '}') {
			if(pair.isEmpty() || pair.pop() != '{') return false;
		}
	}
	return pair.isEmpty();
}

http://www.zhitongguigu.com

🤔

messy?

public boolean isValid(String s) {
    LinkedList<Character> stack = new LinkedList<>();
    Map<Character, Character> hm = new HashMap<>();
    hm.put(')', '(');
    hm.put(']', '[');
    hm.put('}', '{');
    for (int i = 0; i < s.length(); i++) {
        char c = s.charAt(i);
        if (hm.containsKey(c)) {
            if (stack.isEmpty() || !hm.get(c).equals(stack.pop())) {
                return false;
            }
        } else {
            stack.push(c);
        }
    }
    return stack.isEmpty();
}

http://www.zhitongguigu.com

Practice 4

Bad Hair Day

http://www.zhitongguigu.com

       
=       
=       =        Cows facing right -->
=     = =
=   = = =
= = = = = =
1 2 3 4 5 6

http://www.zhitongguigu.com

All the cows are facing right, and they can only see other cows in front of it and shorter than itself. It can be blocked by other taller cows.

Example: 6 2 3 1 7 4 Output: 5

http://www.zhitongguigu.com

SUM(each cow can see how many other cows?) = SUM(each cow can be seen by how many other cows)

http://www.zhitongguigu.com

SUM(each cow can see how many other cows?) = SUM(each cow can be seen by how many other cows)

How to use Stack?

How could Stack help record this?

Only allow cows whose height is lower than you into the stack

http://www.zhitongguigu.com

How to use Stack?

Example: 6 2 3 1 7 4 Result: 5

Stack: 6

Stack: 6 2

Stack: 6 3

Stack: 6 3 1

Stack: 7

Stack: 7 4

Stack: 7

Stack: empty

Add 6

Add 2

Pop 2 Add 3

Add 1

Pop 6 3 1 Add 7

Add 4

Pop 4

Pop 7

  public static int seeCows(int[] cow) {
    int length = cow.length;
    int totalNum = 0;
    Stack<Integer> cowStack = new Stack<Integer>();
    for(int i = 0; i < length; i ++){
      if(cowStack.size() == 0 || cowStack.peek() > cow[i]) {
        cowStack.push(cow[i]);
      }
      else {
        while(cowStack.size() > 0 && cowStack.peek() <= cow[i]) {
          cowStack.pop();
          totalNum += cowStack.size();
        }
        cowStack.push(cow[i]);
      }
    }
    while(cowStack.size() > 0) {
      cowStack.pop();
      totalNum += cowStack.size();
    }
    return totalNum;
  }

http://www.zhitongguigu.com

Big O?

O(n)

Monotonic Stack

单调栈

http://www.zhitongguigu.com

Find an element's left/right larger/smaller element in O(n) time.

Practice 5

Largest Rectangle in Histogram

http://www.zhitongguigu.com

Largest Rectangle in Histogram

Similar thought: How to use stack to find the right border?

Example: 2 1 5 6 2 3

Only put rectangle higher than peek into stack

The element before it is the left border

The element pushes it out is the right border

Monotonically increasing or decreasing?

http://www.zhitongguigu.com

Largest Rectangle in Histogram

Example: 2 1 5 6 2 3

Stack: 2

Stack: 1

Stack: 1 5

Stack: 1 5 6

Stack: 1 2

Stack: 1 2 3

Stack: 1 2

Stack: 1

Stack: Empty

Add 2

Pop 2 Add 1

Add 5

Add 6

Pop 6 5 Add 2

Add 3

Pop 3

Pop 2

Pop 1

2*1

6*1, 5*2

3*1

2*4

1*6

http://www.zhitongguigu.com

Largest Rectangle in Histogram

Example: 2 1 5 6 2 3

How do we know the width?

Instead of directly putting height into stack, we put the index. Anyway height can be accessed by the index easily. And using index, we can know the width

http://www.zhitongguigu.com

Largest Rectangle in Histogram

0 1 2 3 4 5

2 1 5 6 2 3

Stack: 0

Stack: 1

Stack: 1 2

Stack: 1 2 3

Stack: 1 4

Stack: 1 4 5

Stack: 1 4

Stack: 1

Stack: empty

Add 0

Pop 0 Add 1

Add 2

Add 3

Pop 2 3 Add 4

Add 5

Pop 5

Pop 4

Pop 1

2*1

6*1, 5*2

3*1

2*4

1*6

http://www.zhitongguigu.com

public int largestRectangleArea(int[] height) {
    int area = 0;
    jStack<Integer> stack = new Stack<Integer>();
    for (int i = 0; i < height.length; i++) {
        if (stack.empty() || height[stack.peek()] < height[i]) {
            stack.push(i);
        } else {
            int start = stack.pop();
            int width = stack.empty() ? i : i - stack.peek() - 1;
            area = Math.max(area, height[start] * width);
            i--;
        }
    }
    while (!stack.empty()) {
        int start = stack.pop();
        int width = stack.empty() ? height.length : height.length - stack.peek() - 1;
        area = Math.max(area, height[start] * width);
    }
    return area;
}

🤔

http://www.zhitongguigu.com

public int largestRectangleArea(int[] height) {
    int n = height.length;
    int result = 0;
    Stack<Integer> stack = new Stack<>();
    for (int i = 0; i <= n; i++) {
        int cur = (i == n) ? 0 : height[i];
        while (!stack.isEmpty() && cur < height[stack.peek()]) {
            int area = height[stack.pop()] * (stack.isEmpty() ? i : i - 1 - stack.peek());
            result = Math.max(area, result);
        }
        stack.push(i);
    }
    return result;
}

cur <= height[stack.peek()]

Exist Balance Number

http://www.zhitongguigu.com

Given an array of integers.

Is there a number k in this array that

k is larger than all the numbers before it and smaller than all the numbers after it?

[1,2,3,4,5] -> true

[6,2,3,8,10,9] -> true

[4,3,5,2] -> false

[2] -> true

extra practice

Return all balance numbers

Homework 6.1

Simplify Path

http://www.zhitongguigu.com

Homework 6.2

Implementing Stack using Queues

http://www.zhitongguigu.com

Homework 6.3

Trapping Rain Water

http://www.zhitongguigu.com

Explain

Homework 6 (optional)

Container With Most Water

http://www.zhitongguigu.com

Explain

Homework 6 (more)

http://www.zhitongguigu.com

Basic Calculator
Evaluate Reverse Polish Notation
Flatten Nested List Iterator
132 Pattern (optional)
Q -> S; S -> Q; Array -> Q, S
Implement Java LL with Node
- Front & Rear
  - popFront, popRear
  - pushFront, pushRear
  - peekFront, peekRear
  - isEmpty, size

Stack & Queue

Stack & Queue

Stack: LIFO

Queue: FIFO

Queue: FIFO

Stack

Basic Operation

Stack

How to use Array to implement a stack?

Array -> Stack

Memory Leak

When to use Stack?

Stack in Operating System

Stack in Operating System

Stack in Operating System

Queue

Basic Operations

Queue

How to use Array to implement a queue?

Array => Queue

Array => Queue (Cont.d)

When to use Queue?

LinkedList Rule Them All

Practice 1

Implement Queue using Stacks

Implement Queue using Stacks

Implement Queue using Stacks

Implement Queue using Stacks

Implement Queue using Stacks

Implement Queue using Stacks

Practice 2

a stack with max()

a stack with max()

Practice 3

Valid Parentheses

Valid Parentheses

Practice 4

Bad Hair Day

How to use Stack?

How to use Stack?

Monotonic Stack

Practice 5

Largest Rectangle in Histogram

Largest Rectangle in Histogram

Largest Rectangle in Histogram

Largest Rectangle in Histogram

Largest Rectangle in Histogram

Homework 6.1

Simplify Path

Homework 6.2

Implementing Stack using Queues

Homework 6.3

Trapping Rain Water

Homework 6 (optional)

Container With Most Water

Homework 6 (more)

[GoValley-201612] Stack & Queue

More from govalley201612