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Question

I\'m trying to solve a question and my question here is why doesn\'t my solution work?. Here\'s the question and below\'s the answer.

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Answer 1

Here is an O(N) C++ DP implementation.

int numDecodings(string s) {

    if(s[0] == '0') return 0; // Invalid Input
        
    int n = s.length();

    // dp[i] denotes the number of ways to decode the string of length 0 to i
    vector<int> dp(n+1, 0);
        
    // base case : string of 0 or 1 characters will have only 1 way to decode
    dp[0] = dp[1] = 1; 
        
    for(int i = 2; i <= n; i++) {
        // considering the previous number
        if(s[i-1] > '0') dp[i] += dp[i-1];
        // considering the previous two numbers
        if(s[i-2] == '1' || (s[i-2] == '2' && s[i-1] < '7')) dp[i] += dp[i-2];
    }
        
    return dp[n];
}