P1337 [JSOI2004] 平衡点 / 吊打XXX

https://www.luogu.com.cn/record/87691240

Luogu/P1337/P1337.cpp

@@ -0,0 +1,82 @@
+#include <iostream>
+#include <chrono>
+#include <cmath>
+#include <iomanip>
+#include <random>
+#include <tuple>
+#include <utility>
+#include <vector>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    int n;
+
+    cin >> n;
+
+    std::vector<std::tuple<int, int, int>> a(n);
+
+    for (auto &o : a) {
+        cin >> std::get<0>(o) >> std::get<1>(o) >> std::get<2>(o);
+    }
+
+    std::mt19937 gen(std::chrono::system_clock::now().time_since_epoch().count());
+
+    auto random = [&](int low, int high) -> int {
+        std::uniform_int_distribution<> dist(low, high);
+        return dist(gen);
+    };
+
+    auto potential_energy = [&](double x, double y) -> double {
+        double res = 0;
+
+        for (auto &o : a) {
+            double xx = x - std::get<0>(o),
+                   yy = y - std::get<1>(o);
+
+            res += std::sqrt(std::pow(xx, 2) + std::pow(yy, 2)) * std::get<2>(o);
+        }
+
+        return res;
+    };
+
+    double ans_x = 0,
+           ans_y = 0,
+           ans = 1e18;
+
+    for (int i = 1; i <= 10; i++) {
+        double xx = ans_x,
+               yy = ans_y;
+
+        double t = 21000;
+
+        while (t > 1e-15) {
+            double tmp_x = ans_x + random(-100000, 100000) * t,
+                   tmp_y = ans_y + random(-100000, 100000) * t;
+
+            double tmp_ans = potential_energy(tmp_x, tmp_y);
+            double delta = tmp_ans - ans;
+
+            if (delta < 0) {
+                ans_x = xx = tmp_x;
+                ans_y = yy = tmp_y;
+                ans = tmp_ans;
+            } else if (std::exp(-delta / t) * 10000 > random(0, 10000)) {
+                xx = tmp_x;
+                yy = tmp_y;
+            }
+
+            t *= 0.998;
+        }
+    }
+
+    cout << std::fixed << std::setprecision(3) << ans_x << ' '
+         << std::fixed << std::setprecision(3) << ans_y << endl;
+
+    return 0;
+}