feat(cf/895): nonlazy prop soln

codeforces/886/e.cc

@@ -0,0 +1,150 @@
+#include <bits/stdc++.h>  // {{{
+
+// https://codeforces.com/blog/entry/96344
+
+#pragma GCC optimize("O2,unroll-loops")
+#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
+
+using namespace std;
+
+template <typename T>
+[[nodiscard]] static T MIN() {
+  return std::numeric_limits<T>::min();
+}
+
+template <typename T>
+[[nodiscard]] static T MAX() {
+  return std::numeric_limits<T>::max();
+}
+
+template <typename T>
+[[nodiscard]] static T sc(auto&& x) {
+  return static_cast<T>(x);
+}
+
+template <typename T>
+[[nodiscard]] static T sz(auto&& x) {
+  return static_cast<T>(x.size());
+}
+
+#define prln(...) std::println(__VA_ARGS__)
+#define pr(...) std::print(__VA_ARGS__)
+
+#ifdef LOCAL
+#define dbgln(...) std::println(__VA_ARGS__)
+#define dbg(...) std::print(__VA_ARGS__)
+#endif
+
+inline static void NO() {
+  prln("NO");
+}
+
+inline static void YES() {
+  prln("YES");
+}
+
+using ll = long long;
+using ld = long double;
+template <typename T>
+using ve = std::vector<T>;
+template <typename T, size_t N>
+using ar = std::array<T, N>;
+template <typename T1, typename T2>
+using pa = std::pair<T1, T2>;
+template <typename... Ts>
+using tu = std::tuple<Ts...>;
+template <typename... Ts>
+using dq = std::deque<Ts...>;
+template <typename... Ts>
+using qu = std::queue<Ts...>;
+template <typename... Ts>
+using pq = std::priority_queue<Ts...>;
+template <typename... Ts>
+using st = std::stack<Ts...>;
+auto lb = [](auto... args) {
+  return std::lower_bound(args...);
+};
+auto ub = [](auto... args) {
+  return std::upper_bound(args...);
+};
+
+#define ff first
+#define ss second
+#define eb emplace_back
+#define pb push_back
+#define all(x) (x).begin(), (x).end()
+#define rall(x) (x).rbegin(), (x).rend()
+//  }}}
+
+void solve() {
+  ll n, c;
+  cin >> n >> c;
+  ll sum = 0, sumsq = 0;
+  ll s;
+  for (int i = 0; i < n; ++i) {
+    cin >> s;
+    sum += s;
+    sumsq += s * s;
+  }
+
+  ld C = sumsq - c;
+
+  ld A = 4 * n;
+  // NOTE: tbh, look back at solutions,m not sure what went exactly wrong here.
+  // most definitely just not taking my time
+  // NOTE: didn't check WHY round down/why is this right, just that it *looked* right in the examples
+  // this logic is a surefire way to skip certainty and absolutely confuse yourself
+
+  ld B = 4 * sum;
+
+  ll root = (-B + sqrtl(B * B - 4 * A * C)) / (2 * A);
+  prln("{}", root);
+
+  // NOTE: tbh, look back at solutions,m not sure what went exactly wrong here.
+  // most definitely just not taking my time
+  // NOTE: didn't check WHY round down/why is this right, just that it *looked* right in the examples
+  // this logic is a surefire way to skip certainty and absolutely confuse yourself
+
+  /*
+     p ez, if anything should've just been locked and written the equation
+     division and long double - fucked
+
+     say paintings are a, b, c
+
+     ax^2+bx+c
+
+     area c= (a + 2w) ^ 2 + ...
+    =a^2+4w^2+4aw + ...
+
+     c = a^2+b^2+...+4(a+b+...) * w + 4nw^2
+     0 = sumsq - c
+
+
+     a^2+b^2+c^2=sum of painting area
+     (a+2w)^2+(b+2w)^2+...= c; find w quickly
+
+      a^2+2aw+4w^2+...
+
+      c = = a^2 + 4w^2+2aw + ...
+      =a^2+b^2+c^2 + ... 2aw + 2bw + 2cw + ... + 4nw^2
+      0 = sumsq + 4nw^2 + 2w(a+b+c+d+....) - c
+      quadratic formula
+      = 4nw^2+2w(a+b+c+d)
+      = 4nw^2+2w(a+b+...) - c +a^2+b^2+c^2+...
+     */
+}
+
+int main() {  // {{{
+  cin.tie(nullptr)->sync_with_stdio(false);
+  cin.exceptions(cin.failbit);
+
+  int t = 1;
+  cin >> t;
+
+  while (t--) {
+    solve();
+  }
+
+  return 0;
+}
+// }}}