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/*
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Max Possible combination of characters in the string has followig parts(stages)
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:
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            +/- number . number e/E +/- number
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stages: 0 1 2 3 4 5 6 7
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Now check each characters at there correct stages or not and increament the
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stage as per the character found at ith position.
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*/
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class Solution {
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 public:
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  bool isNumber(string s) {
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    char stage = 0;
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    for (int i = 0; i < s.size(); ++i) {
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      if ((s[i] == '+' || s[i] == '-') && (stage == 0 || stage == 5)) {
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        stage++;
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      } else if ((s[i] == 'e' || s[i] == 'E') && stage > 1 && stage < 5) {
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        stage = 5;
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      } else if (s[i] == '.' && stage < 3) {
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        // both side of '.' do not have any digit then return false
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        if (stage <= 1 && (i + 1 >= s.size() || !(s[i + 1] >= '0' && s[i + 1] <= '9')))
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          return false;
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        stage = 3;
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      } else if (s[i] >= '0' && s[i] <= '9') {
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        if (!(stage == 2 || stage == 4 || stage == 7)) stage++;
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        if (stage == 1 || stage == 6) stage++;
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      } else
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        return false;
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    }
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    if (stage <= 1 || stage == 5 || stage == 6) return false;
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    return true;
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  }
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};