Peli

#include <bits/stdc++.h>

using namespace std;
using ll = long long;

int n;

int ans[2001][2001];
bool col_has_other[2001];
bool row_has_other[2001];
bool diag_has_other[4002];

const int SELF = 1;
const int OTHER = 2;

const int MAX = 2000;

inline int mini(int a, int b) {
    return a < b ? a : b;
}

inline int maxi(int a, int b) {
    return a > b ? a : b;
}

void set_other(int a, int b) {
    ans[a][b] = OTHER;
    col_has_other[a] = true;
    row_has_other[b] = true;
    diag_has_other[a-b+MAX] = true;
}

bool has_other(int a, int b) {
    return col_has_other[a] || row_has_other[b] || diag_has_other[a-b+MAX];
}

int main() {
    cin.tie(NULL);
    ios_base::sync_with_stdio(false);

    cin >> n;

    for (int a = 0; a <= MAX; a++) {
        for (int b = 0; b <= MAX; b++) {
            if (a == 0 || b == 0) {
                ans[a][b] = SELF;
            } else if (a == b) {
                ans[a][b] = SELF;
            } else if ((a == 1 && b == 2) || (a == 2 && b == 1)) { 
                set_other(a, b);
            } else if (has_other(a, b)) {
                ans[a][b] = SELF;
            } else {
                set_other(a, b);
            }
        }
    }

    // tilanne 1, 1 on voittava sille kuka pelaa seuraavaksi
    // kaikki tilanteet n, n myös voittavia
    // tilanteet 1, 2 ja 2, 1 ovat häviäviä
    // n, 2 pakottaa voittavan tilanteen (n >= 3) jos tekee tilanteen 1, 2
    // n, 3 pakottaa voittavan tilanteen (n >= 3): 4, 1
    


    for (int i = 0; i < n; i++) {
        int a, b;
        cin >> a >> b;

        //if (b < a) swap(a, b);
        
        cout << (ans[a][b] == SELF ? "first\n" : "second\n");
    }

    return 0;
}

Test 1 (public)

Group: 1, 2, 3

Verdict: ACCEPTED

Test 2

Group: 1, 2, 3

Verdict: ACCEPTED

Test 3

Group: 2, 3

Verdict: ACCEPTED

Test 4

Group: 3

Verdict: ACCEPTED

Test 5

Group: 2, 3

Verdict: ACCEPTED

Test 6

Group: 3

Verdict: ACCEPTED