Submission #529177

#	Time	Username	Problem	Language	Result	Execution time	Memory
529177		vuavisao	Discharging (NOI20_discharging)	C++17	100 / 100	134 ms	22464 KiB

Discharging

#include<bits/stdc++.h>
#define ll long long
#define ld long double
#define fi first
#define se second
#define pb push_back
#define all(c) c.begin(), c.end()
#define pii pair<int, int>
#define pll pair<long long, long long>
using namespace std;

const int N = 1e6 + 10;

struct line
{
    ll a, b;

    line() {};
    line(ll a, ll b) : a(a), b(b) {};
};

int n;
ll a[N], dp[N];

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);
}

void addLine(vector<line> &memo, line cur)
{
    int k = memo.size();
    while(k >= 2 && bad(memo[k - 2], memo[k - 1], cur))
    {
        memo.pop_back();
        k--;
    }
    memo.pb(cur);
}

ll Fn(line A, ll x)
{
    return A.a * x + A.b;
}

ll Query(vector<line> &memo, ll x)
{
    int l = 0, r = memo.size() - 1;
    if(r == - 1) return 0ll;

    while(l < r)
    {
        int mid = l + r >> 1;
        if(Fn(memo[mid], x) < Fn(memo[mid + 1], x)) r = mid;
        else l = mid + 1;
    }
    return Fn(memo[l], x);
}

vector<line> memo;

int main()
{
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
    //freopen("DISCHARG.inp", "r", stdin);
    //freopen("DISCHARG.out", "w", stdout);
    cin >> n;
    for(int i = 1; i <= n; i++) cin >> a[i];
    reverse(a + 1, a + 1 + n);
    vector<int> pos;
    for(int i = 1; i <= n; i++)
    {
        while(!pos.empty() && a[pos.back()] <= a[i]) pos.pop_back();
        pos.pb(i);
    }
    for(int i = 1; i <= pos.size(); i++)
    {
        addLine(memo, line(a[pos[i - 1]], dp[i - 1]));
        dp[i] = Query(memo, pos[i - 1]);
//        cout << dp[i] << '\n';
    }
    cout << dp[pos.size()];
    return 0;
}

Compilation message (stderr)

Discharging.cpp: In function 'long long int Query(std::vector<line>&, long long int)':
Discharging.cpp:53:21: warning: suggest parentheses around '+' inside '>>' [-Wparentheses]
   53 |         int mid = l + r >> 1;
      |                   ~~^~~
Discharging.cpp: In function 'int main()':
Discharging.cpp:78:22: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   78 |     for(int i = 1; i <= pos.size(); i++)
      |                    ~~^~~~~~~~~~~~~

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