HELP : Game Theory / Grundy Number

general
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I am trying to solve this problem :

I read all the available entries. I can’t figure out where is mistake in my code.

Strategy used:

  1. Calculated grundy value for each possible cell entry

void solve() {

grundy[0] = 0;

for(int i = 1; i <= 51; ++i) {

    memset(used, false, sizeof(used));

    int mex = 0;
    for(int j = 1; j <= i; ++j)
        used[grundy[i - j]] = true;

    while(used[mex])
        ++mex;

    grundy[i] = mex;
    for(int j = i + 1; j <= 51; ++j)
        grundy[j] = grundy[i];
}

}

  1. Then for each row calculated it’s grundy number and xor-ed them.

int main() {

solve();

int test, n, m, item;                           // n rows, m columns
scanf("%d", &test);

while(test--) {

    scanf("%d%d", &n, &m);                   
    int gr_overall = 0;                        // NIM sum

    for(int i = 0; i < n; ++i) {

        int mex = 1;                          // Tried mex = 0 also gives WA
        memset(used, false, sizeof(used));

        for(int j = 0; j < m; ++j) {
            scanf("%d", &item);
            used[grundy[item]] = true;         // Marking grundy number for each cell
        }

        while(used[mex]) ++mex;                // Calculating minimum value

        gr_overall ^= mex;                     // Calcualting NIM sum

    }

    if(gr_overall) cout << "FIRST" << endl;
    else cout << "SECOND" << endl;

}

return 0;

}

Please help. Thank you.

2

What about this case?

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