Valid Number

描述

Validate if a given string is numeric.

Some examples:

  1. "0" => true
  2. " 0.1 " => true
  3. "abc" => false
  4. "1 a" => false
  5. "2e10" => true

Note: It is intended for the problem statement to be ambiguous. You should gather all requirements up front before implementing one.

分析

细节实现题。

本题的功能与标准库中的strtod()功能类似。

有限自动机

  1. // Valid Number
  2. // @author 龚陆安 (http://weibo.com/luangong)
  3. // finite automata，时间复杂度O(n)，空间复杂度O(n)
  4. class Solution {
  5. public:
  6.     bool isNumber(const string& s) {
  7.         enum InputType {
  8.             INVALID,    // 0
  9.             SPACE,      // 1
  10.             SIGN,       // 2
  11.             DIGIT,      // 3
  12.             DOT,        // 4
  13.             EXPONENT,   // 5
  14.             NUM_INPUTS  // 6
  15.         };
  16.         const int transitionTable[][NUM_INPUTS] = {
  17.                 -1, 0, 3, 1, 2, -1, // next states for state 0
  18.                 -1, 8, -1, 1, 4, 5,     // next states for state 1
  19.                 -1, -1, -1, 4, -1, -1,     // next states for state 2
  20.                 -1, -1, -1, 1, 2, -1,     // next states for state 3
  21.                 -1, 8, -1, 4, -1, 5,     // next states for state 4
  22.                 -1, -1, 6, 7, -1, -1,     // next states for state 5
  23.                 -1, -1, -1, 7, -1, -1,     // next states for state 6
  24.                 -1, 8, -1, 7, -1, -1,     // next states for state 7
  25.                 -1, 8, -1, -1, -1, -1,     // next states for state 8
  26.                 };
  28.         int state = 0;
  29.         for (auto ch : s) {
  30.             InputType inputType = INVALID;
  31.             if (isspace(ch))
  32.                 inputType = SPACE;
  33.             else if (ch == '+' || ch == '-')
  34.                 inputType = SIGN;
  35.             else if (isdigit(ch))
  36.                 inputType = DIGIT;
  37.             else if (ch == '.')
  38.                 inputType = DOT;
  39.             else if (ch == 'e' || ch == 'E')
  40.                 inputType = EXPONENT;
  42.             // Get next state from current state and input symbol
  43.             state = transitionTable[state][inputType];
  45.             // Invalid input
  46.             if (state == -1) return false;
  47.         }
  48.         // If the current state belongs to one of the accepting (final) states,
  49.         // then the number is valid
  50.         return state == 1 || state == 4 || state == 7 || state == 8;
  52.     }
  53. };

原文: https://soulmachine.gitbooks.io/algorithm-essentials/content/cpp/string/valid-number.html