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The program mainly includes: basic structure definition, lexical analysis, syntax analysis, arithmetic operation
Basic structure definition: enumeration (operand types, operator types, token types, finite state automata);
Structure (operands, operators, tokens, token chains).
Lexical analysis: Decompose a string into valid tokens (valid operands and operators), and generate a linked list of tokens.
Syntax analysis: Analyze the validity of parentheses, the validity of the arrangement of operands and operators, and the matching relationship between operators and operand types.
Arithmetic operation: Use the postfix expression operation rules to evaluate according to the postfix expression linked list. First convert the infix expressions we use every day into postfix expressions. For example: 6*(5-3) converts to 6 5 3 - *, 6-2+5*2 converts to 6 2 - 5 2 * +
Here is a description of the conversion of postfix expressions, each operator has an operation priority (oper_PRI), but when the expression contains parentheses, the operation priority of the operators in the parentheses will change. So a bracket depth priority (deep_PRI) is added. Using the two-level approach is simpler and easier to read than using the stack.
| operator | oper_PRI |
| + | 7 |
| - | 7 |
| * | 9 |
When converting, the operator has two priorities, expressed as: operator (deep_PRI, oper_PRI)
Input each token of the expression 5+(8-2*3)*4 in turn and finally output 5 8 2 3 * - 4 * +.
| enter | temporary space When entering an operator, put a temporary empty time, trigger the action at the same time. operator(deep_PRI,oper_PRI) Initial deep_PRI=0 |
action When '(' is entered, deep_PRI++ When entering ')', deep_PRI-- When entering an operator, the previous operator is compared to it Priority, if true, output the previous operator. Comparison rules: deep_PRI > deep_PRI || (deep_PRI == deep_PRI && oper_PRI >= oper_PRI) |
output operand directly output |
| 5 | 5 | ||
| + | +(0,7) | ||
| ( | +(0,7) | deep_PRI++ | |
| 8 | +(0,7) | 8 | |
| - | +(0,7) -(1,7) |
+(0,7) compared to -(1,7) 0>1||(0==1&&7>=7) is false, no output |
|
| 2 | +(0,7) -(1,7) |
2 | |
| * | +(0,7) -(1,7) *(1,9) |
-(1,7) compared with *(1,9) 1>1||(1==1&&7>=9) is false, no output |
|
| 3 | +(0,7) -(1,7) *(1,9) |
3 | |
| ) | +(0,7) -(1,7) *(1,9) |
deep_PRI-- | |
| * | +(0,7) -(1,7) *(1,9) *(0,9) |
*(1,9) compared with *(0,9) 1>0||(1==0&&9>=9) is true output *(1,9) |
* |
| +(0,7) -(1,7) *(0,9) |
-(1,7) compared with *(0,9) 1>0||(1==0&&7>=9) is true output -(1,7) |
- | |
| +(0,7) *(0,9) |
+(0,7) compared with *(0,9) 0>0||(0==0&&7>=9) is false, no output |
||
| 4 | +(0,7) *(0,9) |
4 | |
| +(0,7) *(0,9) |
No operator: output temporary space values in reverse order | * | |
| +(0,7) | + |