All we need is to have a couple of flags so we can process the string in linear time:

```
public boolean isNumber(String s) {
s = s.trim();
boolean pointSeen = false;
boolean eSeen = false;
boolean numberSeen = false;
boolean numberAfterE = true;
for(int i=0; i<s.length(); i++) {
if('0' <= s.charAt(i) && s.charAt(i) <= '9') {
numberSeen = true;
numberAfterE = true;
} else if(s.charAt(i) == '.') {
if(eSeen || pointSeen) {
return false;
}
pointSeen = true;
} else if(s.charAt(i) == 'e') {
if(eSeen || !numberSeen) {
return false;
}
numberAfterE = false;
eSeen = true;
} else if(s.charAt(i) == '-' || s.charAt(i) == '+') {
if(i != 0 && s.charAt(i-1) != 'e') {
return false;
}
} else {
return false;
}
}
return numberSeen && numberAfterE;
}
```

We start with trimming.

- If we see
`[0-9]`

we reset the number flags. - We can only see
`.`

if we didn't see`e`

or`.`

. - We can only see
`e`

if we didn't see`e`

but we did see a number. We reset numberAfterE flag. - We can only see
`+`

and`-`

in the beginning and after an`e`

- any other character break the validation.

At the and it is only valid if there was at least 1 number and if we did see an `e`

then a number after it as well.

So basically the number should match this regular expression:

`[-+]?(([0-9]+(.[0-9]*)?)|.[0-9]+)(e[-+]?[0-9]+)?`