149 lines
3.0 KiB
C++
149 lines
3.0 KiB
C++
/* Problem URL: https://codeforces.com/gym/102644/problem/A */
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#include <bits/stdc++.h>
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#include <ext/pb_ds/assoc_container.hpp>
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#include <ext/pb_ds/tree_policy.hpp>
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using namespace std;
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using namespace __gnu_pbds;
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template <class T, class comp = less<>>
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using ordered_set = tree<T, null_type , comp , rb_tree_tag , tree_order_statistics_node_update>;
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#define V vector
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#define rmin(a, b) a = min(a, b)
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#define rmax(a, b) a = max(a, b)
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#define rep(i, lim) for (int i = 0; i < (lim); i++)
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#define nrep(i, s, lim) for (int i = s; i < (lim); i++)
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#define repv(i, v) for (auto &i : (v))
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#define fillv(v) for (auto &itr_ : (v)) { cin >> itr_; }
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#define sortv(v) sort(v.begin(), v.end())
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#define all(v) (v).begin(), (v).end()
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using vi = vector<int>;
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using vvi = vector<vi>;
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using vvvi = vector<vvi>;
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using vvvvi = vector<vvvi>;
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using ll = long long;
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using vl = vector<ll>;
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using vvl = vector<vl>;
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using vvvl = vector<vvl>;
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using vvvvl = vector<vvvl>;
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template<class v>
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auto operator<<(ostream &os, const vector<v> &vec)->ostream& {
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os << vec[0];
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for (size_t i = 1; i < vec.size(); i++) {
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os << ' ' << vec[i];
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}
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os << '\n';
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return os;
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}
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template<class v>
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auto operator>>(istream &is, vector<v> &vec)->istream& {
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for (auto &i : vec) {
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is >> i;
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}
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return is;
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}
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template<class v>
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auto operator<<(ostream &os, const vector<vector<v>> &vec)->ostream& {
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for (auto &i : vec) {
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os << i[0];
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for (size_t j = 1; j < i.size(); j++) {
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os << ' ' << i[j];
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}
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os << '\n';
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}
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return os;
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}
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template<class v>
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auto operator>>(istream &is, vector<vector<v>> &vec)->istream& {
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for (auto &i : vec) {
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for (auto &j : i) {
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is >> j;
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}
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}
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return is;
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}
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const int oo = INT32_MAX >> 1;
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const ll OO = INT64_MAX >> 1;
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void pre()
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{
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}
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#define TEST 0
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void solve()
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{
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ll n;
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long double p;
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cin >> n >> p;
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// long double h = 1;
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// long double s = 1;
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//
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// rep(i, n) {
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// long double th = h * (1 - p) + s * p;
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// long double ts = h * p + s * (p - 1);
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// h = th;
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// s = ts;
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// }
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V<V<long double>> mat = {{1},
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{0}};
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auto mul = [&](V<V<long double>> &a, V<V<long double>> &b) {
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V<V<long double>> c(a.size(), V<long double>(b[0].size()));
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rep(i, c.size()) {
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rep(j, c[0].size()) {
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rep(k, b.size()) {
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c[i][j] += a[i][k] * b[k][j];
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}
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}
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}
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return c;
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};
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V<V<long double>> prob = {{1 - p, p},
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{p, 1 - p}};
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rep(i, 30) {
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if ((n >> i) & 1) {
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mat = mul(prob, mat);
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}
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prob = mul(prob, prob);
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}
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cout << fixed << setprecision(10) << mat[0][0] << '\n';
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}
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int main()
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{
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ios::sync_with_stdio(false);
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cin.tie(nullptr);
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pre();
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int t;
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(TEST && cin >> t) || (t = 1);
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while (t--) {
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solve();
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}
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}
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