Submission #764667

#	Time	Username	Problem	Language	Result	Execution time	Memory
764667		mousebeaver	Aliens (IOI16_aliens)	C++14	100 / 100	1055 ms	8124 KiB

aliens

#include "aliens.h"
#include <bits/stdc++.h>
#define ll long long
#define INF numeric_limits<ll>::max()/2
#define pll pair<ll, ll>
using namespace std;

ll cost(ll i, ll j, vector<pll>& a)
{
    ll root = a[j-1].second - a[i-1].first+1;
    ll area = root*root; //Area of the necessary square to cover the given cells
    if(i > 1 && a[i-1].first <= a[i-2].second)
    {
        //Calculate the overlap with the previous square
        root = a[i-2].second-a[i-1].first+1;
        area -= root*root;
    }
    return area;
}

void calc(vector<vector<ll>>& dp, ll j, ll left, ll right, ll optl, ll optr, vector<pll>& a)
{
    if(left > right)
    {
        return;
    }

    ll mid = (left+right)/2;
    ll opt = -1;
    for(ll b = optl; b <= min(optr, mid); b++)
    {
        ll val = dp[b-1][j-1]+cost(b, mid, a);

        if(val < dp[mid][j])
        {
            dp[mid][j] = val;
            opt = b;
        }
    }
    dp[mid][j] = min(dp[mid][j], dp[mid][j-1]);

    calc(dp, j, left, mid-1, optl, opt, a);
    calc(dp, j, mid+1, right, opt, optr, a);
}

ll f(ll i, ll j, vector<ll>& dp, vector<pll>& a) //First index with j better as i
{
    ll n = a.size();
    if(dp[i-1]+cost(i, n, a) <= dp[j-1]+cost(j, n, a))
    {
        return n+1;
    }

    ll left = j;
    ll right = n;
    while(left < right)
    {
        ll mid = (left+right)/2;
        if(dp[j-1]+cost(j, mid, a) < dp[i-1]+cost(i, mid, a))
        {
            right = mid;
        }
        else
        {
            left = mid+1;
        }
    }
    return left;
}

void calcDP(vector<pll>& a, ll delt, ll& cnt, ll& val)
{
    ll n = a.size();
    vector<ll> dp(n+1, INF);
    vector<ll> counter(n+1, 0);
    dp[0] = 0;
    deque<pll> q = {{1, 1}}; //index of point, starting being the best

    for(ll i = 1; i <= n; i++)
    {
        pll t = q.front();
        q.pop_front();
        while(q.size() && q.front().second <= i)
        {
            t = q.front();
            q.pop_front();
        }

        dp[i] = dp[t.first-1]+cost(t.first, i, a)+delt;
        counter[i] = counter[t.first-1]+1;
        q.push_front(t);

        if(i == n)
        {
            break;
        }
        while(q.size() && f(q.back().first, i+1, dp, a) <= q.back().second)
        {
            q.pop_back();
        }
        ll start = 1;
        if(q.size())
        {
            start = f(q.back().first, i+1, dp, a);
        }
        q.push_back({i+1, start});
    }

    val = dp[n];
    cnt = counter[n];
}

long long take_photos(int n, int m, int k, std::vector<int> r, std::vector<int> c)
{
    vector<pll> a(n);
    for(ll i = 0; i < n; i++)
    {
        a[i] = {r[i], c[i]};
        if(c[i] < r[i]) //Mirror to diagonal or above
        {
            swap(a[i].first, a[i].second);
        }
    }

    sort(a.begin(), a.end());
    vector<pll> b(0);
    for(ll i = 0; i < n; i++)
    {
        if((i == n-1 || a[i].first != a[i+1].first) && (b.empty() || a[i].second > b.back().second))
        {
            b.push_back(a[i]);
        }
    }
    a = b;
    n = a.size();
    k = min(k, n);

    if(false)
    {
        vector<vector<ll>> dp(n+1, vector<ll> (k+1, INF));
        dp[0][0] = 0;
        for(ll i = 1; i <= n; i++)
        {
            for(ll j = 1; j <= k; j++)
            {
                dp[i][j] = dp[i][j-1];
                for(ll b = 1; b <= i; b++)
                {
                    ll val = dp[b-1][j-1]+cost(b, i, a);
                    dp[i][j] = min(dp[i][j], val);
                }
            }
        }

        return dp[n][k];
    }

    if(false)
    {
        vector<vector<ll>> dp(n+1, vector<ll> (k+1, INF));
        dp[0][0] = 0;

        for(ll j = 1; j <= k; j++)
        {
            calc(dp, j, j, n, 1, n, a);
        }

        return dp[n][k];
    }

    ll left = 0;
    ll right = (ll) m * (ll) m;
    ll val = 0; ll cnt;
    while(left < right)
    {
        ll mid = (left+right)/2;
        calcDP(a, mid, cnt, val);

        if(cnt > k)
        {
            left = mid+1;
        }
        else
        {
            right = mid;
        }
    }

    calcDP(a, left, cnt, val);
    return val-left*k;
}

• Subtask 1: 4 / 4
• Subtask 2: 12 / 12
• Subtask 3: 9 / 9
• Subtask 4: 16 / 16
• Subtask 5: 19 / 19
• Subtask 6: 40 / 40