Summat

#include <bits/stdc++.h>
using namespace std;
 
typedef long long ll;

int b[10101];
int ans[1010];
map<int,int> m;

bool check(int ind, int n) {
    int N = n*(n-1)/2;
    ans[2] = (b[ind] + b[1] - b[0])/2;
    ans[0] = b[1] - ans[2];
    ans[1] = ans[2] - (b[1] - b[0]);
    if (ans[0] < 1 || ans[1] < 1 || ans[2] < 1) return false;
    for (int i = 3; i <= ind; i++) {
        ans[i] = b[i-1]-ans[0];
    }
    m.clear();
    for (int i = 0; i <= ind; i++) {
        for (int j = i+1; j <= ind; j++) {
            m[ans[i]+ans[j]]++;
        }
    }
    for (int i = 0; i <= ind; i++) m[b[i]]--;
    int mones = ind+1;
    for (int i = ind+1; i < N; i++) {
        if (m[b[i]] > 0) {
            m[b[i]]--;
        } else {
            if (mones == n) return false;
            ans[mones] = b[i]-ans[0];
            if (ans[mones] < 1) return false;
            for (int j = 1; j < mones; j++) m[ans[j]+ans[mones]]++;
            mones++;
        }
    }
    return true;
}
 
int main() {
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    
    int n;
    cin >> n;
    int N = n*(n-1)/2;
    for (int i = 0; i < N; i++) cin >> b[i];
    sort(b,b+N);
    for (int i = 2; i < 101; i++) {
        if (check(i,n)) break;
    }
    for (int i = 0; i < n; i++) cout << ans[i] << " ";
    cout << "\n";
}

Test 1

Group: 1, 2, 3

Verdict: ACCEPTED

Test 2

Group: 1, 2, 3

Verdict: ACCEPTED

Test 3

Group: 1, 2, 3

Verdict: ACCEPTED

Test 4

Group: 1, 2, 3

Verdict: ACCEPTED

Test 5

Group: 1, 2, 3

Verdict: ACCEPTED

Test 6

Group: 2, 3

Verdict: ACCEPTED

Test 7

Group: 2, 3

Verdict: ACCEPTED

Test 8

Group: 2, 3

Verdict: ACCEPTED

Test 9

Group: 2, 3

Verdict: ACCEPTED

Test 10

Group: 2, 3

Verdict: ACCEPTED

Test 11

Group: 3

Verdict: ACCEPTED

Test 12

Group: 3

Verdict: ACCEPTED

Test 13

Group: 3

Verdict: ACCEPTED

Test 14

Group: 3

Verdict: ACCEPTED

Test 15

Group: 3

Verdict: ACCEPTED