DP/tests/aizu_dpl_1_d_lis.test.cpp

View this file on GitHub
Last update: 2022-11-29 22:46:48+08:00
Problem: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=DPL_1_D

Depends on

Code

#define PROBLEM "http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=DPL_1_D"

#include "../../template.h"
#include "../lis.h"

void solve() {
    int n; cin >> n;
    vector<int> a(n); for(int& x : a) cin >> x;
    cout << lis_strict(a) << endl;
}

#line 1 "DP/tests/aizu_dpl_1_d_lis.test.cpp"
#define PROBLEM "http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=DPL_1_D"

#line 1 "template.h"
#include <bits/stdc++.h>
using namespace std;

#define FOR(i,a,b) for(int i=(a),_b=(b); i<=_b; i++)
#define FORD(i,a,b) for(int i=(a),_b=(b); i>=_b; i--)
#define REP(i,a) for(int i=0,_a=(a); i<_a; i++)
#define EACH(it,a) for(__typeof(a.begin()) it = a.begin(); it != a.end(); ++it)

#define DEBUG(x) { cout << #x << " = "; cout << (x) << endl; }
#define PR(a,n) { cout << #a << " = "; FOR(_,1,n) cout << a[_] << ' '; cout << endl; }
#define PR0(a,n) { cout << #a << " = "; REP(_,n) cout << a[_] << ' '; cout << endl; }

#define sqr(x) ((x) * (x))

// For printing pair, container, etc.
// Copied from https://quangloc99.github.io/2021/07/30/my-CP-debugging-template.html
template<class U, class V> ostream& operator << (ostream& out, const pair<U, V>& p) {
    return out << '(' << p.first << ", " << p.second << ')';
}

template<class Con, class = decltype(begin(declval<Con>()))>
typename enable_if<!is_same<Con, string>::value, ostream&>::type
operator << (ostream& out, const Con& con) {
    out << '{';
    for (auto beg = con.begin(), it = beg; it != con.end(); it++) {
        out << (it == beg ? "" : ", ") << *it;
    }
    return out << '}';
}
template<size_t i, class T> ostream& print_tuple_utils(ostream& out, const T& tup) {
    if constexpr(i == tuple_size<T>::value) return out << ")"; 
    else return print_tuple_utils<i + 1, T>(out << (i ? ", " : "(") << get<i>(tup), tup); 
}
template<class ...U> ostream& operator << (ostream& out, const tuple<U...>& t) {
    return print_tuple_utils<0, tuple<U...>>(out, t);
}

mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
long long get_rand(long long r) {
    return uniform_int_distribution<long long> (0, r-1)(rng);
}

template<typename T>
vector<T> read_vector(int n) {
    vector<T> res(n);
    for (int& x : res) cin >> x;
    return res;
}

void solve();

int main() {
    ios::sync_with_stdio(0); cin.tie(0);
    solve();
    return 0;
}
#line 1 "DP/lis.h"
// Source: http://codeforces.com/blog/entry/13225
// Non-strict.

int lis_non_strict(const vector<int>& a) {
    multiset<int> s;
    for (int x : a) {
        s.insert(x);
        auto it = s.upper_bound(x);

        if (it != s.end())
            s.erase(it);
    }
    return s.size();
}

// Strict.
int lis_strict(const vector<int>& a) {
    multiset<int> s;
    for (int x : a) {
        s.insert(x);
        auto it = s.lower_bound(x);
        it++;
        
        if (it != s.end())
            s.erase(it);
    }
    return s.size();
}

// Return indices of LIS (strict)
vector<int> lis_strict_trace(const vector<int>& a) {
    int n = (int) a.size();
    vector<int> b(n+1, 0), f(n, 0);
    int answer = 0;
    for (int i = 0; i < n; i++) {
        f[i] = lower_bound(b.begin() + 1, b.begin()+answer+1, a[i]) - b.begin();
        answer = max(answer, f[i]);
        b[f[i]] = a[i];
    }

    int require = answer;
    vector<int> T;
    for (int i = n-1; i >= 0; i--) {
        if (f[i] == require) {
            T.push_back(i);
            require--;
        }
    }
    reverse(T.begin(), T.end());
    return T;
}

// Count number of LIS
using mint = long long;  // Cnt is exponential. Check if statement says ModInt here?
// Returns: (length of LIS, number of LIS)
pair<int,mint> count_lis(const vector<int>& a) {
    if (a.empty()) {
        return {0, 1};
    }

    // dp[i] = [ (last value, accumulate count) ] for increasing seq of
    //                                            length i+1
    //         last value are decreasing
    vector<vector<pair<int,mint>>> dp(a.size() + 1);
    int max_len = 0;

    // returns true if we can append `val` to LIS stored at `cur`.
    auto pred_len = [] (const vector<pair<int, mint>>& cur, int val) {
        return !cur.empty() && cur.back().first < val;
    };
    // returns true if we can append `val` after the LIS represented with `p`.
    auto pred_val = [] (int val, const pair<int,mint>& p) { return val > p.first; };

    for (int x : a) {
        int len = lower_bound(dp.begin(), dp.end(), x, pred_len) - dp.begin();

        mint cnt = 1;
        if (len >= 1) {
            int pos = upper_bound(dp[len-1].begin(), dp[len-1].end(), x, pred_val) - dp[len-1].begin();
            cnt = dp[len-1].back().second;
            cnt -= (pos == 0) ? 0 : dp[len-1][pos-1].second;
        }
        dp[len].emplace_back(x, cnt + (dp[len].empty() ? 0 : dp[len].back().second));
        max_len = max(max_len, len + 1);
    }
    assert(max_len > 0);
    return {
        max_len,
        dp[max_len-1].back().second,
    };
}
#line 5 "DP/tests/aizu_dpl_1_d_lis.test.cpp"

void solve() {
    int n; cin >> n;
    vector<int> a(n); for(int& x : a) cin >> x;
    cout << lis_strict(a) << endl;
}