Summary:

You will be given a string containing capital letters and 0 or more '?' question marks. You can substitute '?' with vowel or consonant. A string is considered as BAD if it contains 3 vowels or 5 consonants in a row otherwise it is GOOD. It is MIXED if it can be made both good and bad by substituting '?' with consonant or vowel. You have to find whether a string is GOOD or BAD or MIXED.

Observations:

• If there is no '?' question mark in string and the string contains 3 vowels or 5 consonant in a row then it is BAD otherwise it is GOOD.
• If the string contains '?' then it can be GOOD or BAD or MIXED.
• If the string contains 3 vowels or 5 consonants after substituting one or more '?' then it is BAD. If the string does not contain 3 vowels or 5 consonants in a row after substituting all '?' then it is GOOD.
• If all '?' can be substituted in such a way that it can be GOOD and also can be BAD based on substituted letters in place of '?' then it is MIXED.

You can make decision only at the positions containing '?'. You have two choices:

• Replace it by a vowel or,
• Replace it by a consonant.

Solution:

Use recursion to solve this problem. Iterate from first position to the last position of the string and in each position check if it contains 3 vowels or 5 consonants in a row from first position to current position. If any position contains '?' then -

1. Replace it by vowel and check if it holds the condition to be BAD. If holds then it is BAD and return BAD, else continue like this till the last position.
2. Replace it by consonant and check if it holds the condition to be BAD. If holds then it is BAD and return BAD, else continue like this till the last position.

If you reach the last position of the string and does not hold the condition to be BAD then it is GOOD and return GOOD.

If choice 1 and 2 both return BAD then the string is BAD.If both of them return GOOD then it is GOOD. If one of them return GOOD and another one of them return BAD then it is MIXED. If any one of them return MIXED then it is MIXED.

It is better to keep track of the number of vowels and consonants in a row from first position to current position instead of replacing '?' every time.

Algorithm:

S is the given string. vowel and cons are the number of vowels and consonants in a row.

Start from i=0 and continue till the last position of the string.

GOOD_OR_BAD(S , i , vowel , cons)

1.  if vowel == 3 or cons == 5 then,  //base case
       return BAD
2.  if i >= s.size() then,    //base case,if it cross the last position of the string
       return GOOD    

3.  if s[i] == '?' then,    //if s[i] contains '?' then make decision
        v = GOOD_OR_BAD(s,i+1,vowel+1,0) //replacing '?' with vowel will increase the vowels count in a row and make consonant 0      
        c = GOOD_OR_BAD(s,i+1,0,cons+1) //replacing '?' with consonant will increase the consonants count in a row and make vowel 0

4.      if v!=c or v == MIXED or c == MIXED then, //if one is good and one is bad or anyone of them is mixed
            return  MIXED
5.      else
            return v

6.  else if isVowel( s[i] ) == true then,    //if s[i] is vowel
        return GOOD_OR_BAD(s,i+1,vowel+1,0)
7.  else
      return GOOD_OR_BAD(s,i+1,0,cons+1) //if s[i] is consonant

This solution will cause TLE. To reduce the time complexity apply dynamic programming. Take a 3D array say dp. dp[i][vowel][cons] contains number of vowels and consonants in a row from position 0 to i for position i. Whenever it finds the optimal solution for position i it stores the result and the number of vowel and consonant for which it gets optimal result in dp[i][vowel][cons]. Later, when an optimal solution is found in dp it returns the solution.

Code(C++):

#include<bits/stdc++.h>
#define vi vector<int>
#define vvi vector<vi>
using namespace std;

bool isVowel(char c){
    if(c=='A' or c=='E' or c=='I' or c=='O' or c=='U')
        return true;
    return false;
}
int goodBad(const string& s,int i,int vowel,int cons,vector<vvi>&dp)
{

    if(vowel == 3 or cons == 5)
        return 1;
    if(i>=s.size())
        return 0;
    if(dp[i][vowel][cons]!=-1)
        return dp[i][vowel][cons];
    if(s[i] == '?')
    {
        int v = goodBad(s,i+1,vowel+1,0,dp);
        int c = goodBad(s,i+1,0,cons+1,dp);
        if(v!=c or v == 2 or c == 2)
            return dp[i][vowel][cons] = 2;
        else
            return dp[i][vowel][cons] = v;
    }
    else if(isVowel(s[i]))
        return dp[i][vowel][cons] = goodBad(s,i+1,vowel+1,0,dp);
    else
        return dp[i][vowel][cons] = goodBad(s,i+1,0,cons+1,dp);

}
int main()
{
    vector<string>ans = {"GOOD","BAD","MIXED"};
    int t,cs=1;
    cin>>t;
    while(t--)
    {
        string s;
        cin>>s;
        vector<vvi>dp(s.size(),vvi(s.size(),vi(s.size(),-1)));

        int res = goodBad(s,0,0,0,dp);
        cout<<"Case "<<cs++<<": "<<ans[res]<<endl;
    }  
    return 0;
}

Tutorial source