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Twenty Questions

                                 Twenty Questions

                                                 DP + bitmasking


#include <iostream>
#include <cstring>
#include <string>
#include <algorithm>

using namespace std;

int F[128]; //feature set
int dp[1 << 11][1 << 11]; //set of question and answer
//denotes bitmask of question and answer

int n, m;

int solve(int Q, int A)
{
    if(dp[Q][A] != -1)
        return dp[Q][A];

    int nObjects = 0; //number of objects remaining after asking Q

    for(int i = 0; i < n; i++)
    {
        if((F[i] & Q) == A)
            nObjects++;
    }

    if(nObjects <= 1)
    {
        return dp[Q][A] = 0;
    }

    int nQuestions = m + 1;

    //one by one ask each question and take the min number o question required to identify each object
    for(int i = 0; i < m; i++)
    {
        if((Q & (1 << i)) == 0) //ith question is not yet asked
        {
            nQuestions = min(nQuestions, 1 + max(solve(Q | (1 << i), A),solve(Q | (1 << i), A | (1 << i))));
            //solve(Q | (1 << i), A) denotes number of objects which 0 at ith position after asking ith uestion
            //solve(Q | (1 << i), (A | (1 << i))) denotes number of objects which 1 at ith positoin after asking ith question
        }
    }

    return dp[Q][A] = nQuestions;
}
int main()
{
   while(cin >> m >> n, !(m == 0 && n == 0))
   {
       for(int i = 0; i < n; i++)
       {
           string s;
           cin >> s;

           int feature = 0;

           for(int j = 0; j < m; j++)
           {
               feature |= (s[j] - '0') << j;
           }

           F[i] = feature;
       }

       memset(dp, -1, sizeof(dp));

       cout << solve(0, 0) << endl;
   }
    return 0;
}

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