Stacks. Kuan-Yu Chen ( 陳冠宇 ) TR-212, NTUST
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1 Stacks Kuan-Yu Chen ( 陳冠宇 ) TR-212, NTUST
2 Review Array 2D Array = Matrix Row-Major Column-Major Upper-Triangular Lower-Triangular 2
3 Stacks. A stack is an ordered list in which insertions and deletions are made at one end called the top Given a stack SS = (aa 1, aa 2,, aa nn ) aa 1 is the bottom element aa nn is the top element aa nn aa ii is on top of element aa ii 1 add delete top aa nn aa nn aa nn 1 aa 2 aa 1 aa 2 aa 1 aa 2 aa 1 3
4 Stacks.. By the definition of stack, if we add the elements AA, BB, CC, DD, EE to the stack, in that order, then EE is the first element we delete from the stack Last-In-First-Out 4
5 Leverage Array to Implement Stack aa nn aa 2 aa 1 top aa 1 aa 2 aa 3 aa 4 aa nn 2 aa nn 1 aa nn nn 22 nn 11 nn 5
6 Stack Permutation Given a sequence of elements and a empty stack, if a permutation can be generated by these elements and the stack, the permutation is called stack permutation For a given sequence of elements {AA, BB, CC}, please write down its stack permutation AAAAAA AAAAAA BBBBBB BBBBBB CCCCCC push AA, pop AA, push BB, pop BB, push CC, pop CC Push AA, push BB, pop BB, pop AA, push CC, pop CC Push AA, push BB, push CC, pop CC, pop BB, pop AA 6
7 Expressions When pioneering computer scientists conceived the idea of higher-level programming languages, they were faced with many hurdles How to generate machine-language instructions to evaluate an arithmetic expression AA BB CC + DD EE AA CC Operator ( 運算子 ) The first problem with understanding the meaning of an expression is to decide in what order the operations are carried out Specify the order by using parentheses AA (BB CC) + DD (EE AA) CC Operand ( 運算元 ) (AA BB) CC + (DD EE) (AA CC) 7
8 Infix & Postfix Notations If ee is an expression with operators and operands, the conventional way of writing ee is called infix The operators come in-between the operands AA BB CC + DD EE AA CC The postfix form of an expression calls for each operator to appear after its operands AAAA CC DDDD +AAAA 8
9 Infix to Postfix It is simple to describe an algorithm for producing postfix from infix Take AA BB CC + DD EE AA CC for example ( AA BB CC + DD EE AA CC ) ( AA BB CC + DD EE AA CC ) AAAA CC DDDD +AAAA 9
10 Infix & Prefix Notations If ee is an expression with operators and operands, the conventional way of writing ee is called infix The operators come in-between the operands AA BB CC + DD EE AA CC In the prefix form of an expression, the operators precede their operands Take AA BB CC + DD EE AA CC for example ( AA BB CC + DD EE AA CC ) ( AA BB CC + DD EE AA CC ) + AAAACC DDDD AAAA 10
11 Examples. Given a infix expression AA + BB CC DD EE, please write down the prefix and postfix expressions AA + BB CC DD EE ( AA + BB CC DD EE ) Prefix ( AA + BB CC DD EE ) Postfix +AA BBBB DDDD ( AA + BB CC DD EE ) AABBBB +DDDD 11
12 Examples.. Given a infix expression (AA + BB) CC (DD EE FF), please write down the prefix and postfix expressions ( AA + BB CC DD (EE FF) ) Prefix +AAAAAA DD EEEE Postfix AAAA + CC DDDDDD 12
13 Examples... Given a infix expression AA (BB > CC) (DD EE), please write down the prefix and postfix expressions ((AA ( (BB > CC))) (DD ( EE))) Prefix ((AA ( (BB > CC))) (DD ( EE))) Postfix AA > BBBB DD EE ((AA ( (BB > CC))) (DD ( EE))) AAAAAA > DDDD 13
14 By Looking!. Given a infix expression (AA + BB) CC (DD EE FF), please write down the prefix and postfix expressions + CC DD prefix eeeeeeeeeeeeee infix postfix AA BB EE FF 14
15 By Looking!.. Given a infix expression (AA + BB) CC (DD EE FF), please write down the prefix and postfix expressions Prefix prefix eeeeeeeeeeeeee postfix + CC DD infix AA BB EE FF +AAAAAA DD EEEE 15
16 By Looking!... Given a infix expression (AA + BB) CC (DD EE FF), please write down the prefix and postfix expressions Postfix prefix eeeeeeeeeeeeee postfix + CC DD infix AA BB EE FF AAAA + CC DDDDDD 16
17 Examples. Given a postfix expression AAAAAAAA + EE, please write down the infix expression The pattern for postfix is < oooooooooooooo 1, oooooooooooooo 2, oooooooooooooooo > = oooooooooooooo 1 oooooooooooooooo oooooooooooooo 2 AAAAAAAA + EE AAAAAAAA + EE AAAACCCC + EE AABBBBBB + EE AABBBBBB + EE CC + DD BB (CC + DD) BB (CC + DD) EE AA BB (CC + DD) EE 17
18 Examples.. Given a prefix expression AA BB + CCCCCC, please write down the infix expression The pattern for prefix is < oooooooooooooooo, oooooooooooooo 1, oooooooooooooo 2 >= oooooooooooooo 1 oooooooooooooooo oooooooooooooo 2 AA BB + CCCCCC AA BB + CCCCCC AA BB + CCCCCC AA BB + CCCCCC AA BB + CCCCCC CC + DD BB (CC + DD) BB (CC + DD) EE AA BB (CC + DD) EE 18
19 Questions? 19
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