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Codeforces Round 265 (Div. 1)/B. Restore Cube.cpp

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+/* Problem URL: https://codeforces.com/contest/464/problem/B */
+
+#include <bits/stdc++.h>
+#include <ext/pb_ds/assoc_container.hpp>
+#include <ext/pb_ds/tree_policy.hpp>
+
+using namespace std;
+using namespace __gnu_pbds;
+
+template <class T, class comp = less<>>
+using ordered_set = tree<T, null_type , comp , rb_tree_tag , tree_order_statistics_node_update>;
+
+#define V vector
+
+#define rmin(a, b) a = min(a, b)
+#define rmax(a, b) a = max(a, b)
+
+#define rep(i, lim) for (int i = 0; i < (lim); i++)
+#define nrep(i, s, lim) for (int i = s; i < (lim); i++)
+
+#define repv(i, v) for (auto &i : (v))
+#define fillv(v) for (auto &itr_ : (v)) { cin >> itr_; }
+#define sortv(v) sort(v.begin(), v.end())
+#define all(v) (v).begin(), (v).end()
+
+using vi = vector<int>;
+using vvi = vector<vi>;
+using vvvi = vector<vvi>;
+using vvvvi = vector<vvvi>;
+
+using ll = long long;
+
+using vl = vector<ll>;
+using vvl = vector<vl>;
+using vvvl = vector<vvl>;
+using vvvvl = vector<vvvl>;
+
+template<class v>
+auto operator<<(ostream &os, const vector<v> &vec)->ostream& {
+    os << vec[0];
+    for (size_t i = 1; i < vec.size(); i++) {
+        os << ' ' << vec[i];
+    }
+    os << '\n';
+    return os;
+}
+
+template<class v>
+auto operator>>(istream &is, vector<v> &vec)->istream& {
+    for (auto &i : vec) {
+        is >> i;
+    }
+    return is;
+}
+
+template<class v>
+auto operator<<(ostream &os, const vector<vector<v>> &vec)->ostream& {
+    for (auto &i : vec) {
+        os << i[0];
+        for (size_t j = 1; j < i.size(); j++) {
+            os << ' ' << i[j];
+        }
+        os << '\n';
+    }
+    return os;
+}
+
+template<class v>
+auto operator>>(istream  &is, vector<vector<v>> &vec)->istream& {
+    for (auto &i : vec) {
+        for (auto &j : i) {
+            is >> j;
+        }
+    }
+    return is;
+}
+
+const int oo = INT32_MAX >> 1;
+const ll OO = INT64_MAX >> 1;
+
+struct pt {
+    ll x, y, z;
+
+    pt(ll x, ll y, ll z): x(x), y(y), z(z) {}
+    pt() = default;
+    
+    friend istream &operator >> (istream &is, pt &a) {
+        is >> a.x >> a.y >> a.z;
+        return is;
+    }
+
+    friend ostream &operator << (ostream &os, pt a) {
+        os << a.x << ' ' << a.y << ' ' << a.z;
+        return os;
+    }
+
+    pt operator ^ (pt b) {
+        return pt(y * b.z- z * b.y, z * b.x - x * b.z, x * b.y - y * b.x);
+    }
+
+    ll operator * (pt b) {
+        return x * b.x + y * b.y + z * b.z;
+    }
+
+    pt operator - (pt b) {
+        return pt(x - b.x, y - b.y, z - b.z);
+    }
+
+    bool operator == (pt b) {
+        return x == b.x && y == b.y && z == b.z;
+    }
+
+    bool operator < (pt b) {
+        if (x == b.x) {
+            if (y == b.y) {
+                return z < b.z;
+            }
+            return y < b.y;
+        }
+        return x < b.x;
+    }
+};
+
+ll dis2(pt a, pt b)
+{
+    ll x = a.x - b.x;
+    ll y = a.y - b.y;
+    ll z = a.z - b.z;
+
+    return x * x + y * y + z * z;
+}
+
+void pre()
+{
+
+}
+
+#define TEST 0
+
+void solve()
+{
+    vvi pts(8, vi(3));
+    cin >> pts;
+
+    rep(i, 8) {
+        sortv(pts[i]);
+    }
+    
+    auto check = [&](){
+        V<pt> p(8);
+        rep(i, 8) {
+            p[i] = {pts[i][0], pts[i][1], pts[i][2]};
+        }
+
+        sortv(p);
+        p.erase(unique(all(p)), p.end());
+
+        if (p.size() != 8) {
+            return false;
+        }
+
+        vi dis(7);
+        nrep(i, 1, 8) {
+            dis[i - 1] = dis2(p[i], p[0]);
+        }
+
+        sortv(dis);
+
+        nrep(i, 1, 8) {
+            vi d2;
+            rep(j, 8) {
+                if (i == j) {
+                    continue;
+                }
+
+                d2.push_back(dis2(p[i], p[j]));
+            }
+
+            sortv(d2);
+            if (d2 != dis) {
+                return false;
+            }
+        }
+
+        return true;
+    };
+
+    function<bool(int)> func = [&](int i){
+        if (i >= 8) {
+            return check();
+        }
+
+        do {
+            if (func(i + 1)) {
+                return true;
+            }
+        } while (next_permutation(all(pts[i])));
+
+        return false;
+    };
+
+    if (!func(0)) {
+        cout << "NO\n";
+        return;
+    }
+
+    cout << "YES\n";
+    cout << pts;
+}
+
+int main()
+{
+    ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    pre();
+
+    int t;
+    (TEST && cin >> t) || (t = 1);
+    while (t--) {
+        solve();
+    }
+}