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describes data structures

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  1. 1. AData Structure
  2. 2.  What is a Stack Stack Operations LIFO Stack Animation Depicting Push Operation Animation Depicting Pop Operation Array Implementation of Stack Applications of stack Checking for balanced braces Converting Infix Expression to Postfix Postfix calculator
  3. 3. What is a Stack?A stack is a Last In, First Out (LIFO) datastructure,objects inserted last are the first tocome out of the stackAnything added to the stack goes on the “top”of the stackAnything removed from the stack is taken fromthe “top” of the stackThings are removed in the reverse order fromthat in which they were inserted
  4. 4. Stack Operations PUSH Adds the object to the top of the stack POP Removes the object at the top of the stack and returns it PEEK Returns the top object of the stack but does not remove it from the stack ISEMPTY Returns True if Stack is empty
  5. 5. A LIFO Stack Push PopStack Pointer Top Bottom
  6. 6. array Implementation of Stack A[1] A[2] …. …. …. A[n]Push X w y x Stack pointer Stack pointer After many Stack pointer J=2 J=3 Push Ops J=n Before Push After Push Stack FullPop w yAfter many Pop ops Stack Pointer Stack Pointer Stack Pointer J=0 J=2 J=3 Stack Empty After Pop Before Pop
  7. 7. Checking for Balanced Braces ([]({()}[()])) is balanced; ([]({()}[())]) is not Simple counting is not enough to check balance You can do it with a stack: going left to right,  If you see a (, [, or {, push it on the stack  If you see a ), ], or }, pop the stack and check whether you got the corresponding (, [, or {  When you reach the end, check that the stack is empty
  8. 8. Converting Infix Expressions to Equivalent Postfix Expressions Infix Expression a+b Postfix Expression ab+ An infix expression can be evaluated by first being converted into an equivalent postfix expression Facts about converting from infix to postfix  Operands always stay in the same order with respect to one another  All parentheses are removed
  9. 9. Algorithm : Converting Infix Expression to Postfix using stack Suppose X is an arithmetic expression written in infix notation. This algorithm finds the equivalent postfix expression Y. 1. Push "(" onto STACK, and add ")" to the end of X. 2. Scan X from left to right and REPEAT Steps 3 to 6 for each element of X UNTIL the STACK is empty : 3. If an operand is encountered, add it to Y. 4. If a left parenthesis is encountered, push it onto STACK. 5. If an operator is encountered, then : (a) Repeatedly pop from STACK and add to Y each operator (on the top of STACK) which has the same precedence as or higher precedence than operator. (b) Add operator to STACK. /* End of If structure * / 6. If a right parenthesis is encountered, then : (a) Repeatedly pop from STACK and add to Y each operator (on the top of STACK) until a left parenthesis is encountered. (b) Remove the left parenthesis. [Do not add the left parenthesis to Y]. /* End of If structure * / /* End of Step 2 loop * / 7. END.
  10. 10. A trace of the algorithm that converts the infix expression a - (b + c * d)/e to postfix form
  11. 11. A postfix calculator When an operand is entered, the calculator  Pushes it onto a stack When an operator is entered, the calculator  Applies it to the top (one or two, depending on unary or binary operator) operand(s) of the stack  Pops the operands from the stack  Pushes the result of the operation on the stack
  12. 12. The action of a postfix calculator when evaluating the expression 2 * (3 + 4) Postfix Notation--- 2 3 4 + *
  13. 13. Acknowledgement Data Structures BY Tanenbaum Internet Computer Science C++ A textbook for class XII -By Sumita Arora prepared by- Seema kaushik, Computer science department, DAV public school, sector-14, gurgaon