stack application

100
50 25 12 6 3 1 0 0 0 1 0
• print the remainders in backward order.
Stack is an ideal structure to implement this process.
2 2
0
1 1
e.g Convert decimal number to octal number
Algorithm DecimaltoBinary
Parsing
Parsing is any logic that breaks data into
independent pieces for further processing.
For example: to translate a source program
Transform expression with stack
A*B AB*
1.Read and copy the first operand A to the result, we get “A”. 2.Read the operator “*” and push it into a stack for later use. 3.Read and copy the second operand B to the result, we can get “AB”. 4.Finish scanning the source expression, pop up the operator and concatenate it to the result, we get “AB*”
to machine language
括弧匹配检验
假设表达式中允许包含两种括号：圆括号和 方括号，其嵌套的顺序随意，如: （［ ］（））或［（［ ］［ ］）］等为正确 的匹配 ［（ ]）或（［ ］（ ）或 ( ( ) ) ）均为错误的匹 配。
要求检验一个给定表达式中的括 弧是否正确匹配？
检验括号是否匹配的方法可用“期待的急迫程度”这个概
Fill stack
4
loop(not end of data AND not fullStack(stack)) stack(statements 4-5), then pop 1 pushStack(stack, number) 2 prompt (Enter nextthem out successively number: <EOF> to stop) 3 read(number) (statements 6-7) . Because stack 5 end loop is a LIFO data structure, the Now print numbers in reverse order of the item has been 6 Loop (not emptyStack(stack)) reversed. 1 popStack(stack dataOut) 2 print(dataOut) 7 end loop end reverseNumber
Precedence rule
the priority of an operator pushed into the
stack is higher than the operator at the top of the stack -------push it into the stack. the operator at the top of the stack has a higher priority than or equal to the current operator -------it is popped and placed in the output expression.
Examples of manual transformation
A+B*C (A+(B*C)) (A+B)*C+D+E*F-G
(((((A+B)*C)+D)+(E*F))-G)
(A+(BC *))
(A(BC *) +)
(((((AB+)C*)D+)(EF*)+)G-)
AB+C*D+EF*+GABC*+
expression.
Stack can hold the left parts of these segments while
scanning an expression or a statement for the later comparing.
Algorithm parseParens
Reverse a List
algorithm reverseNumber This program reverses a list of integers read from the keyboard by pushing them into a stack and retrieving them one by one. 1 createStack( stack) 2 prompt (Enter a number) The idea lies in reversing data iserstand. First,
显然，必须将先后出现的左括弧依次保存，为了反映这
个优先程度，保存左括弧的结构用栈最合适。这样对出 现的右括弧来说，只要"栈顶元素"相匹配即可。如果在 栈顶的那个左括弧正好和它匹配，就可将它从栈顶删除 。
Unmatched Parentheses Example
Parentheses must be matched in an algebraic
Stack Applications
Typical stack applications can be classified into four broad categories: Reversing data Reverse a List Convert decimal to binary Parsing data Parse parentheses Postponing data usage Infix to postfix transformation Evaluating postfix expressions Backtracking steps goal seeking Eight Queens Problem
Parse parentheses
This algorithm reads a source program and parses it to make sure all opening-closing parentheses are paired. 1 loop (more data) 1 read (character) 2 if (character is an opening parenthesis) 1 pushStack (stack, character) 3 else 1 if (character is closing parenthesis) 1 if (emptyStack (stack)) 1 print (Closing parenthesis not matched alert) 2 else 1 popStack(stack,token) and to match 3 end if 2 end if 4 end if 2 end loop 3 if (not emptyStack(stack)) 1 print (Opening parenthesis not matched alert) 4 end if end parseParens
Manual transformation
Fully parenthesize the expression using any
explicit parentheses Changing all infix notations in each parenthesis to postfix notation, starting from the innermost expressions Remove all parentheses.
postfix notation: 也叫逆波兰式（Reverse Polish notation, RPN，或逆波兰记法），
Infix to postfix transformation
Infix: a+b Prefix: +ab Postfix: ab+
High-level language use the infix convert it to postfix
push each item one by one into
Convert decimal to binary
•divide decimal number by 2 continuously
• record the remainders until the quotient becomes 0
2
2 2 2 2
念来描述。 例如考虑下列括号序列： [ ( [ ][ ] ) ] 12 345 6 78 即后出现的“左括弧”，它等待与其匹配的“右括弧”出现 的“急迫”心情要比先出现的左中括弧高。对“左括弧”来 说，后出现的比先出现的“优先”等待检验。 对“右括弧”来说，每个出现的右括弧要去找在它之前“ 最后”出现的那个左括弧去匹配。
Postponing data usage
Postponement means deferring data usage until
some later point(or something happens). An arithmetic expression can be expressed in three different ways: Infix, prefix, and postfix. In source program, it is often expressed with infix format, but before an expression is calculated in computer, it is usually transformed into postfix expressions.