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Here is the lecture on stacks by Prof Naveen Garg.

A very simple implementation of a Stack in Python is explained below.

#class for defining a stack class Stack: def __init__(self): self.items = [] #method for pushing an item on a stack def push(self,item): self.items.append(item) #method for popping an item from a stack def pop(self): return self.items.pop() #method to check whether the stack is empty or not def isEmpty(self): return (self.items == []) #method to get the top of the stack def topOfStack(self): return len(self.items) def __str__(self): return str(self.items) if __name__ == "__main__": stck = Stack() stck.push(5) stck.push(10) stck.push(15) stck.push(20) print stck #Output = [5, 10, 15, 20] stck.pop() print stck #Output = [5, 10, 15] print stck.topOfStack() #Output = 3

We will learn about how to implement stacks using Linked Lists later, when we cover Linked Lists. At this moment we will use the stack created above for solving most of the problems related to Stacks.

**1. Write a code for showing how stacks can be used for checking balancing of symbols.**

Sample Input: “([)]”

Sample Output: False

Sample Input : “{{([][])}()}”

Sample Output : True

Soln: The algorithm is as follows:

Step 1. Create a stack.

Step 2. Scan the input and while the end is not reached perform the following steps:

Step 2a. If the character read is not a symbol to be balanced then ignore it.

Step 2b. If the character is an opening symbol like “(,{ or [” then push it onto the stack.

Step 2c. If the character is a closing symbol like “), } or ]” then if the stack is empty then return that the given input is unbalanced, else pop the symbol from the top of the stack.

Step 2d. If the symbol popped is not the corresponding opening symbol of the closing symbol currently being scanned then return that the given input is unbalanced.

The Python program implementing the problem is as follows:

class Stack: def __init__(self): self.items = [] #method for pushing an item on a stack def push(self,item): self.items.append(item) #method for popping an item from a stack def pop(self): return self.items.pop() #method to check whether the stack is empty or not def isEmpty(self): return (self.items == []) #method to get the top of the stack def topOfStack(self): return len(self.items) def __str__(self): return str(self.items) def matches(top,symbol): openingSymbols = "({[" closingSymbols = ")}]" return openingSymbols.index(top) == closingSymbols.index(symbol) def checkBalance(input): symbolstack = Stack() balanced = False for symbols in input: if symbols in ["(","{","["]: symbolstack.push(symbols) else: if symbolstack.isEmpty(): balanced = False else: topSymbol = symbolstack.pop() if not matches(topSymbol,symbols): balanced = False else: balanced = True return balanced print checkBalance("([)]") '''Output: False''' print checkBalance("{{([][])}()}") '''Output: True'''

**2. Convert a decimal number into the number of a particular given base.**

Sample Input: decimal = 25 base = 2

Sample Output: 11001

Soln:

class Stack: def __init__(self): self.items = [] #method for pushing an item on a stack def push(self,item): self.items.append(item) #method for popping an item from a stack def pop(self): return self.items.pop() #method to check whether the stack is empty or not def isEmpty(self): return (self.items == []) #method to get the top of the stack def topOfStack(self): return len(self.items) def __str__(self): return str(self.items) def baseConversion(decimalNum,base): digits = "0123456789ABCDEF" remainderStack = Stack() while (decimalNum > 0): remainderStack.push(decimalNum % base) decimalNum //= base convertedString = "" while not remainderStack.isEmpty(): convertedString = convertedString + digits[remainderStack.pop()] return convertedString print baseConversion(25,2) '''Output 11001''' print baseConversion(1000,16) '''Output 3E8'''

**3. Check whether a given string is a palindrome or not?**

Sample Input: “madam”

Sample Output: True

Soln:

class Stack: def __init__(self): self.items = [] #method for pushing an item on a stack def push(self,item): self.items.append(item) #method for popping an item from a stack def pop(self): return self.items.pop() #method to check whether the stack is empty or not def isEmpty(self): return (self.items == []) #method to get the top of the stack def topOfStack(self): return len(self.items) def __str__(self): return str(self.items) def isPalindrome(str): strStack = Stack() palindrome = False for char in str: strStack.push(char) for char in str: if char == strStack.pop(): palindrome = True else: palindrome = False return palindrome print isPalindrome("madam")