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| 1 | +// Status: unfinished and I think the idea is wrong |
| 2 | + |
| 3 | +#include <bits/stdc++.h> |
| 4 | + |
| 5 | +using namespace std; |
| 6 | + |
| 7 | + |
| 8 | +template<typename A> |
| 9 | +ostream& operator<<(ostream& os, vector<A> v) { |
| 10 | + os << "{"; |
| 11 | + for (size_t i = 0; i < v.size(); ++i) { |
| 12 | + if (i) |
| 13 | + os << ", "; |
| 14 | + os << v[i]; |
| 15 | + } |
| 16 | + return os << "}"; |
| 17 | +} |
| 18 | + |
| 19 | +template<typename A, typename B> |
| 20 | +ostream& operator<<(ostream& os, pair<A, B> p) { |
| 21 | + return os << "(" << p.first << ", " << p.second << ")"; |
| 22 | +} |
| 23 | + |
| 24 | +template<typename A, typename B, typename C> |
| 25 | +ostream& operator<<(ostream& os, tuple<A, B, C> t) { |
| 26 | + return os << "(" << get<0>(t) << ", " << get<1>(t) << ", " << get<2>(t) << ")"; |
| 27 | +} |
| 28 | + |
| 29 | +template<typename A, typename B, typename C, typename D> |
| 30 | +ostream& operator<<(ostream& os, tuple<A, B, C, D> t) { |
| 31 | + return os << "(" << get<0>(t) << ", " << get<1>(t) << ", " << get<2>(t) << ", " << get<3>(t) << ")"; |
| 32 | +} |
| 33 | + |
| 34 | +template <size_t N> |
| 35 | +ostream& operator<<(ostream& os, bitset<N> b) { |
| 36 | + for (size_t i = 0; i < N; ++i) { |
| 37 | + os << static_cast<char>('0' + b[i]); |
| 38 | + } |
| 39 | + return os; |
| 40 | +} |
| 41 | +#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:" << (__VA_ARGS__) << endl |
| 42 | + |
| 43 | + |
| 44 | +long long gcd(long long a, long long b) { |
| 45 | + return a ? gcd(b % a, a) : b; |
| 46 | +} |
| 47 | + |
| 48 | +void solve() { |
| 49 | + int n, d; |
| 50 | + scanf("%d %d", &n, &d); |
| 51 | + vector<int> x(n), y(n); |
| 52 | + vector<int> p(n), q(n); |
| 53 | + for (int i = 0; i < n; ++i) { |
| 54 | + scanf("%d %d", &x[i], &y[i]); |
| 55 | + p[i] = x[i] + y[i]; |
| 56 | + q[i] = x[i] - y[i]; |
| 57 | + } |
| 58 | + vector<int> add = p, sub = q; |
| 59 | + vector<int> vp, vq; |
| 60 | + for (int i = 0; i < n; ++i) { |
| 61 | + add.emplace_back(p[i] + d); |
| 62 | + add.emplace_back(p[i] - d); |
| 63 | + sub.emplace_back(q[i] + d); |
| 64 | + sub.emplace_back(q[i] - d); |
| 65 | + } |
| 66 | + auto make_distinct = [](vector<int> & v) { |
| 67 | + sort(v.begin(), v.end()); |
| 68 | + v.erase(unique(v.begin(), v.end()), v.end()); |
| 69 | + }; |
| 70 | + make_distinct(vp); |
| 71 | + make_distinct(vq); |
| 72 | + while (true) { |
| 73 | + bool ok = true; |
| 74 | + for (int i = 0; i < n; ++i) { |
| 75 | + for (int dp : vp) { |
| 76 | + add.emplace_back(p[i] + dp); |
| 77 | + } |
| 78 | + for (int dq : vq) { |
| 79 | + sub.emplace_back(q[i] + dq); |
| 80 | + } |
| 81 | + } |
| 82 | + } |
| 83 | + make_distinct(add); |
| 84 | + make_distinct(sub); |
| 85 | + vector<vector<pair<int, int>>> dir(add.size() * sub.size()); |
| 86 | + int tot = (int)add.size() * sub.size(); |
| 87 | + vector<pair<int, int>> sz(tot); |
| 88 | + long long up = 0, down = 0; |
| 89 | + for (int i = 0; i + 1 < (int)add.size(); ++i) { |
| 90 | + for (int j = 0; j + 1 < (int)sub.size(); ++j) { |
| 91 | + int id = i * (int)sub.size() + j; |
| 92 | + int pp = add[i] + add[i+1]; |
| 93 | + int qq = sub[j] + sub[j+1]; |
| 94 | + sz[id] = {add[i+1] - add[i], sub[j+1] - sub[j]}; |
| 95 | + for (int k = 0; k < n; ++k) { |
| 96 | + if (max(abs(2 * p[k] - pp), abs(2 * q[k] - qq)) <= 2 * d) |
| 97 | + dir[id].emplace_back(4 * x[k] - (pp + qq), 4 * y[k] - (pp - qq)); |
| 98 | + } |
| 99 | + if (dir[id].size() > 0) { |
| 100 | + down += 1LL * (add[i+1] - add[i]) * (sub[j+1] - sub[j]); |
| 101 | + // sort(dir[id].begin(), dir[id].end()); |
| 102 | + cerr << id << " " << pp << " " << qq << " " << sz[id] << " " << dir[id] << endl; |
| 103 | + } |
| 104 | + } |
| 105 | + } |
| 106 | + vector<bool> dup(tot, false); |
| 107 | + for (int i = 0; i < tot; ++i) { |
| 108 | + if (dir[i].empty()) continue; |
| 109 | + for (int j = i+1; j < tot; ++j) { |
| 110 | + if (dir[j].empty()) continue; |
| 111 | + if (dir[i] == dir[j]) { |
| 112 | + dup[i] = dup[j] = true; |
| 113 | + } |
| 114 | + } |
| 115 | + } |
| 116 | + |
| 117 | + for (int i = 0; i + 1 < (int)add.size(); ++i) { |
| 118 | + for (int j = 0; j + 1 < (int)sub.size(); ++j) { |
| 119 | + int id = i * (int)sub.size() + j; |
| 120 | + if (dir[id].empty()) continue; |
| 121 | + if (!dup[id]) continue; |
| 122 | + up += 1LL * (add[i+1] - add[i]) * (sub[j+1] - sub[j]); |
| 123 | + } |
| 124 | + } |
| 125 | + if (down == 0) |
| 126 | + down = 1; |
| 127 | + cerr << up << " " << down << endl; |
| 128 | + long long g = gcd(up, down); |
| 129 | + up /= g; |
| 130 | + down /= g; |
| 131 | + printf("%lld %lld\n", up, down); |
| 132 | +} |
| 133 | + |
| 134 | +int main() { |
| 135 | +#ifdef LOCAL |
| 136 | + time_t starttime = clock(); |
| 137 | +#endif |
| 138 | + int tt; |
| 139 | + scanf("%d", &tt); |
| 140 | + for (int tc = 1; tc <= tt; tc++) { |
| 141 | + printf("Case #%d: ", tc); |
| 142 | + solve(); |
| 143 | +#ifdef LOCAL |
| 144 | + cerr << "~ TC#" << tc << " done! execution time: " << |
| 145 | + (double)(clock()-starttime) / CLOCKS_PER_SEC << " s" << endl; |
| 146 | +#endif |
| 147 | + } |
| 148 | + return 0; |
| 149 | +} |
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