Very concise C++ solution with explaination. No DP

  • 17

    Since * can be used as 3 kinds of char, if we do backtrack the complexity can blow up if the string is *****.... We need to find a non-trivial method.
    Without *, we can just use a number to indicate the unmatch (, ( will increment it and ) will decrement it. We don't want this number less than 0 all the time and it should be 0 when all the string has been matched.
    When * is introduced, the number becomes a range, indicating the number of possible unmatched ( found. One * just expand the range by 1. And we can use the same principle to check if the criteria above is within the range.

    class Solution {
        bool checkValidString(string s) {
            int lower = 0, upper = 0;
            for (char c : s) {
                if (c=='(') {
                } else if (c==')') {
                } else { // * encountered
                lower = max(lower, 0);
                if (upper<0) // unmatched ')' found in the middle of string
                    return false;
            return lower==0;

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