1003. Check If Word Is Valid After Substitutions

We are given that the string "abc" is valid.

From any valid string V, we may split V into two pieces X and Y such that X + Y (X concatenated with Y) is equal to V. (X or Y may be empty.) Then, X + "abc" + Y is also valid.

If for example S = "abc", then examples of valid strings are: "abc", "aabcbc", "abcabc", "abcabcababcc". Examples of invalid strings are: "abccba", "ab", "cababc", "bac".

Return true if and only if the given string S is valid.

Example 1:

Input: "aabcbc"
Output: true
Explanation: 
We start with the valid string "abc".
Then we can insert another "abc" between "a" and "bc", resulting in "a" + "abc" + "bc" which is "aabcbc".

Example 2:

Input: "abcabcababcc"
Output: true
Explanation: 
"abcabcabc" is valid after consecutive insertings of "abc".
Then we can insert "abc" before the last letter, resulting in "abcabcab" + "abc" + "c" which is "abcabcababcc".

Example 3:

Input: "abccba"
Output: false

Example 4:

Input: "cababc"
Output: false

Note:

1. 1 <= S.length <= 20000

2. S[i] is 'a', 'b', or 'c'

// Stack
bool isValid(string S) { // time: O(n); space: O(n)
    vector<char> st;
    for (char ch : S) {
        if (ch == 'c') {
            int n = st.size();
            if (n < 2 || st[n - 1] != 'b' || st[n - 2] != 'a') return false;
            st.pop_back(), st.pop_back();
        } else {
            st.push_back(ch);
        }
    }
    return st.empty();
}