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  • [Algorithm -- Dynamic programming] 91. Decode Ways <How Many Ways to Decode This Message?>

    For example we have

    'a' -> 1

    'b' -> 2

    ..

    'z' -> 26

    By given "12", we can decode the string to give result "ab" or 'L', 2 ways to decode, your function should return 2 as an answer.

    Now asking by given "1246", what should be the return number; 

    The thinking process is somehow like this:

    by given "1" -> we got 'a'

    by given "" -> we got ""

    by given "12345" -> 'a' + decode('2345') or 'L' + decode('345'), therefore number of ways to decode "12345"is the same of decode(2345)+decode(345).

    Somehow we can see that this is a recursion task, therefore we can use Dynamice Programming + memo way to solve the problem.

    const data = "1246";
    
    function num_ways(data) {
      // k : count from last to beginning
      function helper(data, k, memo) {
        if (k === 0) {
          // if k equals 0, mean only one single digital number left
          // means there must be one char
          return 1;
        }
    
        if (data === "") {
          // if data equals empty, then return 1
          return 1;
        }
    
        if (memo[k] != null) {
          return memo[k];
        }
    
        const start = data.length - k;
        if (data[start] === "0") {
          // if sth start as 0, then no char
          return 0;
        }
    
        let result = helper(data, k - 1, memo);
    
        if (k >= 2 && parseInt(data.slice(start, start + 2), 10) <= 26) {
          result += helper(data, k - 2, memo);
        }
    
        memo[k] = result;
    
        return result;
      }
    
      let memo = [];
      return helper(data, data.length, memo);
    }
    
    const res = num_ways(data);
    console.log(res); // 3
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  • 原文地址:https://www.cnblogs.com/Answer1215/p/10468653.html
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