P2421 [NOI2002] 荒岛野人

https://www.luogu.com.cn/record/76652453

Luogu/P2421/P2421.cpp

@@ -0,0 +1,71 @@
+#include <algorithm>
+#include <iostream>
+#include <tuple>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+const int N = 20;
+
+int n, max, ans;
+std::tuple<int, int, int> a[N];
+
+int exgcd(int a, int b, int& x, int& y) {
+    if (!b) {
+        x = 1, y = 0;
+        return a;
+    }
+
+    int g = exgcd(b, a % b, y, x);
+    y -= a / b * x;
+    return g;
+}
+
+bool check(int k) {
+    for (int i = 1; i < n; i++) {
+        for (int j = i + 1; j <= n; j++) {
+            int c1, p1, l1, c2, p2, l2;
+            std::tie(c1, p1, l1) = a[i];
+            std::tie(c2, p2, l2) = a[j];
+
+            int a = p1 - p2,
+                b = k,
+                c = c2 - c1;
+
+            int x, y,
+                g = exgcd(a, b, x, y);
+
+            if (c % g) continue;
+
+            a /= g, b = std::abs(b / g), c /= g;
+            x = (x * c % b + b) % b;
+
+            if (x <= std::min(l1, l2)) return false;
+        }
+    }
+
+    return true;
+}
+
+int main() {
+    std::ios::sync_with_stdio(false);
+
+    cin >> n;
+
+    for (int i = 1, c, p, l; i <= n; i++) {
+        cin >> std::get<0>(a[i]) >> std::get<1>(a[i]) >> std::get<2>(a[i]);
+
+        max = std::max(max, std::get<0>(a[i]));
+    }
+
+    for (int i = max; i <= 1000000; i++) {
+        if (check(i)) {
+            cout << i << endl;
+
+            exit(0);
+        }
+    }
+
+    return 0;
+}