Submission #671107

#	Time	Username	Problem	Language	Result	Execution time	Memory
671107		vuavisao	Discharging (NOI20_discharging)	C++14	100 / 100	100 ms	19484 KiB

Discharging

#include<bits/stdc++.h>
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#define ll long long
#define ld long double
using namespace std;

const ll N = 1e6 + 10;
const ll INF = 1e18;

struct line {
    ll a = 0, b = 0;
    line() {};
    line(ll _a, ll _b) { a = _a; b = _b; }

    ll Fn(const ll& x) { return this -> a * x + this -> b; }
};

bool bad(line A, line B, line C) {
    return (ld) (C.b - A.b) / (A.a - C.a) < (ld) (B.b - A.b) / (A.a - B.a);
}

struct CHT {
    vector<line> memo = {};
    ll ptr = 0; /// for a query where x has been sorted

    void add_line(const line& cur) {
        ll k = memo.size();
        while(k >= 2 && bad(memo[k - 2], memo[k - 1], cur)) {
            memo.pop_back();
            -- k;
        }
        memo.push_back(cur); ++ k;
        if(ptr >= k) ptr = k - 1;
    }

    ll Query_bs(const ll& x) {
        if(memo.empty()) return INF;
        ll l = 0, r = memo.size() - 1;
        while(l < r) {
            ll mid = (l + r) >> 1;
            if(memo[mid].Fn(x) < memo[mid + 1].Fn(x)) r = mid;
            else l = mid + 1;
        }
        return memo[l].Fn(x);
    }

    ll Query_ptr(const ll& x) {
        if(memo.empty()) return INF;
        while(ptr < memo.size() - 1 && memo[ptr].Fn(x) > memo[ptr + 1].Fn(x)) ++ ptr;
        return memo[ptr].Fn(x);
    }

    void clear() {
        this -> memo.clear();
        this -> ptr = 0;
    }
};

ll n, a[N];

ll dp[N];

int32_t main() {
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
    if (fopen("Discharging.inp", "r")) {
        freopen("Discharging.inp", "r", stdin);
        freopen("Discharging.out", "w", stdout);
    }
    cin >> n;
    for(ll i = 1; i <= n; ++ i) cin >> a[i];
    reverse(a + 1, a + 1 + n);
    deque<ll> dq = {};
    for(ll i = 1; i <= n; ++ i) {
        while(!dq.empty() && a[dq.back()] <= a[i]) dq.pop_back();
        dq.push_back(i);
    }
    CHT cht = {};
    cht.add_line(line(a[dq[0]], 0));
    for(ll i = 1; i <= (ll) dq.size(); ++ i) {
        dp[i] = cht.Query_ptr(dq[i - 1]);
        if(i < (ll) dq.size()) cht.add_line(line(a[dq[i]], dp[i]));
    }
    cout << dp[dq.size()];
    return 0;
}

/// Code by vuavisao

Compilation message (stderr)

Discharging.cpp: In member function 'long long int CHT::Query_ptr(const long long int&)':
Discharging.cpp:50:19: warning: comparison of integer expressions of different signedness: 'long long int' and 'std::vector<line>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   50 |         while(ptr < memo.size() - 1 && memo[ptr].Fn(x) > memo[ptr + 1].Fn(x)) ++ ptr;
      |               ~~~~^~~~~~~~~~~~~~~~~
Discharging.cpp: In function 'int32_t main()':
Discharging.cpp:69:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
   69 |         freopen("Discharging.inp", "r", stdin);
      |         ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Discharging.cpp:70:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
   70 |         freopen("Discharging.out", "w", stdout);
      |         ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

• Subtask 1: 9 / 9
• Subtask 2: 13 / 13
• Subtask 3: 25 / 25
• Subtask 4: 11 / 11
• Subtask 5: 14 / 14
• Subtask 6: 28 / 28