E - Guard Towers

https://codeforces.com/contest/85/submission/187929986

Codeforces/85/E/E.cpp

@@ -0,0 +1,96 @@
+#include <iostream>
+#include <algorithm>
+#include <cmath>
+#include <iterator>
+#include <utility>
+#include <vector>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+const int N = 1e4 + 5;
+const int mod = 1e9 + 7;
+
+int n, color[N], ans;
+std::pair<int, int> points[N];
+
+int dis(int i, int j) {
+    return std::abs(points[i].first - points[j].first) + std::abs(points[i].second - points[j].second);
+}
+
+bool dfs(int u, int c, int limit) {
+    color[u] = c;
+
+    for (int v = 1; v <= n; v++) {
+        if (v == u || dis(u, v) <= limit) continue;
+
+        if (color[v] == -1) {
+            if (!dfs(v, c ^ 1, limit)) return false;
+        } else if (color[v] == color[u]) {
+            return false;
+        }
+    }
+
+    return true;
+}
+
+bool check(int x) {
+    std::fill(std::begin(color), std::end(color), -1);
+
+    int cnt = 0;
+
+    for (int i = 1; i <= n; i++) {
+        if (color[i] == -1) {
+            cnt++;
+            if (!dfs(i, 1, x)) return false;
+        }
+    }
+
+    ans = cnt;
+
+    return true;
+}
+
+int binpow(int a, int b) {
+    int res = 1;
+
+    while (b) {
+        if (b & 1) res = static_cast<long long>(res) * a % mod;
+        a = static_cast<long long>(a) * a % mod;
+        b >>= 1;
+    }
+
+    return res;
+}
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    cin >> n;
+
+    for (int i = 1; i <= n; i++) {
+        cin >> points[i].first >> points[i].second;
+    }
+
+    int l = 0,
+        r = 10000,
+        res = 0;
+
+    while (l <= r) {
+        int mid = (l + r) >> 1;
+
+        if (check(mid)) {
+            res = mid;
+            r = mid - 1;
+        } else {
+            l = mid + 1;
+        }
+    }
+
+    cout << res << endl
+         << binpow(2, ans) << endl;
+
+    return 0;
+}