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03 Stacks

Data is stored one over the other

\(t\) is a variable that refers to the top. Initial value is -1 (stack empty)

Operation Return Type Function
push(element) void inserts element at top position
pop() element removes topmost element and returns the removed element
top() element returns the topmost element
size() int returns no of elements
isEmpty() boolean checks if empty 
Algorithm push(element)
        if t = n-1
            overflow
        t = t + 1
        a[t] = element

Algorithm pop()
        if t = -1
            underflow
        t = t - 1
        return a[t]

Algorithm size()
    return (t+1)

Algorithm top()
    return a[t]

Algorithm isEmpty()
    if t = -1
        return true

Applications

  1. browsing history
  2. undo sequence
  3. chain of method calls in JVM (java virtual machine)
  4. Evaluation and conversion of expressions (infix, post-fix, pre-fix)

Infix \(\to\) PostFix

Token Stack Output
a a
+ + a
c ac
- - ac+

Rules

Input Output
HIN \(\leftarrow\) LCIN HOUT, ALL OUT
LIN \(\leftarrow\) HCIN No change

Priority

Arithmetic Logical
\(()\) NOT
^ AND
\(*/\) OR
\(+-\)

If what is coming in and what is already in have the same priority, then the one inside is considered as the higher priority

PostFix \(\to\) Infix

Simple rules

Token Stack Action
3 3 Push 3
2 3, 2 Push 2
5 3, 2, 5 Push 5
^ 3, 32 Pop \(2, 5\); Push \(2^5\)
+ 35 Pop \(3, 32\); Push \(3+32\)

Balancing of Symbols

We’re basically checking if all the brackets are matched

while there are symbols in the expression do
    if symbol is variable
        do nothing
    if symbol is opening
        push it to the stack
    if symbol is closing symbol
        if stack is empty
            invalid
        else
            valid

if stack is empty   // once evaluation of expression is over
    valid
else
    invalid
Token Stack Reason
Last Updated: 2023-01-25 ; Contributors: AhmedThahir

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