请实现一个函数用来判断字符串是否表示数值(包括整数和小数)。例如,字符串"+100","5e2","-123","3.1416"和"-1E-16"都表示数值。 但是"12e","1a3.14","1.2.3","+-5"和"12e+4.3"都不是。
题目是要判断一个表达式是否满足预设规则。其实就是正则匹配。正则匹配的原理,编译原理课上有讲过,用NFA/DFA来判定即可。
class Solution {
private:
enum STATUS{ END = 0, START, SIGNED1, INTEGER, POINT, FLOAT, EXPONENT, SIGNED2, SCIENCE };
STATUS dfa[256][9] = { END };
public:
Solution(){
for (int i = 0; i < 256; ++i){
for (int j = 0; j < 9; ++j){
dfa[i][j] = END;
}
}
initDFA();
}
bool isNumeric(char* string){
STATUS current = START;
while (*string && current != END){
current = DFA(current, *string);
++string;
}
switch (current){
case INTEGER:
case FLOAT:
case SCIENCE:
return true;
}
return false;
}
private:
void initDFA(){
char d = '0';
// 1. START 变迁
dfa['+'][START] = SIGNED1;
dfa['-'][START] = SIGNED1;
dfa['.'][START] = POINT;
for (d = '0'; d <= '9'; ++d){
dfa[d][START] = INTEGER;
}
// 2. SIGNED1 变迁
for (d = '0'; d <= '9'; ++d){
dfa[d][SIGNED1] = INTEGER;
}
dfa['.'][SIGNED1] = POINT;
// 3. INTEGER 变迁
for (d = '0'; d <= '9'; ++d){
dfa[d][INTEGER] = INTEGER;
}
dfa['.'][INTEGER] = FLOAT;
dfa['E'][INTEGER] = EXPONENT;
dfa['e'][INTEGER] = EXPONENT;
// 4. POINT 变迁
for (d = '0'; d <= '9'; ++d){
dfa[d][POINT] = FLOAT;
}
// 5. FLOAT 变迁
for (d = '0'; d <= '9'; ++d){
dfa[d][FLOAT] = FLOAT;
}
dfa['E'][FLOAT] = EXPONENT;
dfa['e'][FLOAT] = EXPONENT;
// 6. EXPONENT 变迁
for (d = '0'; d <= '9'; ++d){
dfa[d][EXPONENT] = SCIENCE;
}
dfa['+'][EXPONENT] = SIGNED2;
dfa['-'][EXPONENT] = SIGNED2;
// 7. SIGNED2 变迁
for (d = '0'; d <= '9'; ++d){
dfa[d][SIGNED2] = SCIENCE;
}
// 8. SCIENCE 变迁
for (d = '0'; d <= '9'; ++d){
dfa[d][SCIENCE] = SCIENCE;
}
// 其余情况均变迁到 END
}
STATUS DFA(STATUS current, char input){
STATUS ret = START;
return dfa[input][current];
}
};