Submission #1197291

#TimeUsernameProblemLanguageResultExecution timeMemory
1197291polarityZoltan (COCI16_zoltan)C++20
140 / 140
244 ms24532 KiB
/** * Solution by Charles Ran (polarity.sh) * Date: 2025-05-06 * Contest: COCI 2016 * Problem: zoltan **/ #include <bits/stdc++.h> using namespace std; using ull = unsigned long long; using ll = long long; using vi = vector<int>; using vl = vector<ll>; using pii = pair<int, int>; #define pb push_back #define rep(i, a, b) for(int i = (a); i < (b); ++i) #define all(x) begin(x), end(x) #define sz(x) (int)(x).size() const int MAX_N = 1e5 + 1; const ll MOD = 1e9 + 7; /** * DATASTRUCTURE: Segment Tree * PURPOSE: Range Updates and Queries * TIME: O(log n) to update and query */ template <class T> class SegmentTree { private: const T UNIT = {0, 0}; T combine(T a, T b){ if (a.first == b.first){ return {a.first, (a.second + b.second) % MOD}; } return max(a, b); } vector<T> segtree; int len; public: SegmentTree(int len) : len(len), segtree(len * 2, UNIT) {} void set(int ind, T val) { ind += len; segtree[ind] = val; for (; ind > 1; ind /= 2) { segtree[ind / 2] = combine(segtree[ind], segtree[ind ^ 1]); } } // [start, end) T query(int start, int end) { T ans = UNIT; for (start += len, end += len; start < end; start /= 2, end /= 2) { if (start % 2 == 1) { ans = combine(ans, segtree[start++]); } if (end % 2 == 1) { ans = combine(ans, segtree[--end]); } } return ans; } }; /** * ALGORITHM: Modular Exponentiation * PURPOSE: Computes x^n (mod m) * CONSTRAINT: m * m <= LLONG_MAX to prevent overflow * TIME: O(log n) */ ll mod_exp(ll x, ll n, ll m) { x %= m; ll res = 1; while (n > 0) { if (n % 2 == 1) { res = res * x % m; } x = x * x % m; n /= 2; } return res; } /** TOOL: Debug * PURPOSE: Prints various data types to terminal * SOURCE: tourist */ template <typename A, typename B> string to_string(pair<A, B> p); template <typename A, typename B, typename C> string to_string(tuple<A, B, C> p); template <typename A, typename B, typename C, typename D> string to_string(tuple<A, B, C, D> p); string to_string(const string& s) { return '"' + s + '"'; } string to_string(const char* s) { return to_string((string) s); } string to_string(bool b) { return (b ? "true" : "false"); } string to_string(vector<bool> v) { bool first = true; string res = "{"; for (int i = 0; i < static_cast<int>(v.size()); i++) { if (!first) { res += ", "; } first = false; res += to_string(v[i]); } res += "}"; return res; } template <size_t N> string to_string(bitset<N> v) { string res = ""; for (size_t i = 0; i < N; i++) { res += static_cast<char>('0' + v[i]); } return res; } template <typename A> string to_string(A v) { bool first = true; string res = "{"; for (const auto &x : v) { if (!first) { res += ", "; } first = false; res += to_string(x); } res += "}"; return res; } template <typename A, typename B> string to_string(pair<A, B> p) { return "(" + to_string(p.first) + ", " + to_string(p.second) + ")"; } template <typename A, typename B, typename C> string to_string(tuple<A, B, C> p) { return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " + to_string(get<2>(p)) + ")"; } template <typename A, typename B, typename C, typename D> string to_string(tuple<A, B, C, D> p) { return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " + to_string(get<2>(p)) + ", " + to_string(get<3>(p)) + ")"; } void debug_out() { cerr << endl; } template <typename Head, typename... Tail> void debug_out(Head H, Tail... T) { cerr << " " << to_string(H); debug_out(T...); } void solve(){ int n; cin >> n; vi a(n); rep(i, 0, n){ cin >> a[i]; } vi aa = a; sort(all(aa)); int cnt = 1; map<int, int> b; rep(i, 0, n){ if (i != 0 && aa[i] != aa[i - 1]){ cnt++; } b[aa[i]] = cnt; } rep(i, 0, n){ a[i] = b[a[i]]; } vi ra = a; reverse(all(ra)); vector<pii> arr(n + 2, {0, 0}); arr[n + 1] = {0, 1}; SegmentTree<pii> st(n + 2), nst(n + 2); st.set(n + 1, {0, 1}); rep(i, 0, n){ int x = ra[i]; pii amt = st.query(x + 1, n + 2); amt.first++; if (arr[x].first == amt.first){ arr[x].second += amt.second; arr[x].second %= MOD; } else { arr[x] = amt; } st.set(x, arr[x]); if (i == n - 2){ rep(j, 0, n + 2){ nst.set(j, arr[j]); } } } pii nlis = nst.query(0, n + 2); pii lis = st.query(0, n + 2); int mx = lis.first; auto mult = [&](pii lis, pii nlis, int rem) -> ll { if (nlis.first == lis.first || lis.first == 0){ ll ans = (ll) nlis.second * mod_exp(2, rem - lis.first - 1, MOD) % MOD; ans += (ll) (lis.second + MOD - nlis.second) * mod_exp(2, rem - lis.first, MOD) % MOD; return ans % MOD; } return (ll) lis.second * mod_exp(2, rem - lis.first, MOD) % MOD; }; ll num = mult(lis, nlis, n); vector<pii> arr2(n + 1, {0, 0}); arr2[0] = {0, 1}; SegmentTree<pii> st2(n + 1); st2.set(0, {0, 1}); rep(i, 0, n - 1){ int j = n - 1 - i; int x = ra[i]; pii amt = st2.query(0, x); amt.first++; pii li = st.query(x + 1, n + 2); pii nli = nst.query(x + 1, n + 2); // debug_out(amt); // debug_out(nli); // debug_out(li); if (li.first + amt.first > mx){ mx = li.first + amt.first; num = (mult(li, nli, n - amt.first) * (ll) amt.second) % MOD; } else if (li.first + amt.first == mx){ num += (mult(li, nli, n - amt.first) * (ll) amt.second) % MOD; num %= MOD; } if (arr2[x].first == amt.first){ arr2[x].second += amt.second; arr2[x].second %= MOD; } else { arr2[x] = amt; } st2.set(x, arr2[x]); } cout << mx << " " << num << endl; } int main(){ ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0); solve(); return 0; }
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