Submission #666882

#	Time	Username	Problem	Language	Result	Execution time	Memory
666882		Lobo	Aliens (IOI16_aliens)	C++17	100 / 100	192 ms	6760 KiB

aliens

#include<bits/stdc++.h>
#include "aliens.h"
using namespace std;
#define int long long
#define dbl long double
#define fr first
#define sc second
#define mp make_pair
#define pb push_back
#define all(x) x.begin(),x.end()
const int inf = 1e18+10;
int n;
vector<pair<int,int>> pts;
deque<pair<pair<int,int>,int>> cht;

dbl intx(int a1, int b1, int a2, int b2) {
    // x*a1 + b1 = x*a2 + b2
    // x*(a1-a2) = b2-b1
    // x = (b2-b1)/(a1-a2)
    return ((dbl) b2-b1)/((dbl) a1-a2);
}

int func(int a, int b, int x) {
    return a*x+b;
}

void chtclear() {
    cht.clear();
}

void chtadd(int a, int b, int k) {
    while(cht.size() >= 2 && (intx(a,b,cht[1].fr.fr,cht[1].fr.sc) > intx(cht[0].fr.fr,cht[0].fr.sc,cht[1].fr.fr,cht[1].fr.sc) || (intx(a,b,cht[1].fr.fr,cht[1].fr.sc) == intx(cht[0].fr.fr,cht[0].fr.sc,cht[1].fr.fr,cht[1].fr.sc) && k <= cht[0].sc))) {
        cht.pop_front();
    }
    cht.push_front(mp(mp(a,b),k));
}

pair<int,int> chtqry(int x) {
    while(cht.size() >= 2 && (func(cht.back().fr.fr,cht.back().fr.sc,x) > func(cht[cht.size()-2].fr.fr,cht[cht.size()-2].fr.sc,x) || (func(cht.back().fr.fr,cht.back().fr.sc,x) == func(cht[cht.size()-2].fr.fr,cht[cht.size()-2].fr.sc,x) && cht[cht.size()-2].sc <= cht.back().sc))) {
        cht.pop_back();
    }
    return mp(func(cht.back().fr.fr,cht.back().fr.sc,x),cht.back().sc);
}

pair<int,int> sol(int p) {
    pair<int,int> dp[n];

    chtclear();
    for(int i = 0; i < n; i++) {
        int xi = pts[i].fr;
        int yi = pts[i].sc;

        if(i == 0) {
            int xj = pts[i].fr;
            int yj = pts[i].sc;
            chtadd(yj,yj*yj - 2*yj,0);
        }
        else {
            int j = i;
            int xj = pts[i].fr;
            int yj = pts[i].sc;
            int xj1 = pts[i-1].fr;
            int yj1 = pts[i-1].sc;
            chtadd(yj,(dp[j-1].fr + yj*yj - 2*yj - max((int)0,xj1-yj+1)*max((int) 0,xj1-yj+1)),dp[j-1].sc);
        }

        pair<int,int> anshere = chtqry(-2*xi);
        dp[i] = mp(anshere.fr + (xi*xi + 2*xi + 1) + p, anshere.sc+1);
    }
    return dp[n-1];
}

int take_photos(int32_t N, int32_t m, int32_t k, vector<int32_t> rw, vector<int32_t> cl) {
    for(int i = 0; i < N; i++) {
        int x = cl[i];
        int y = rw[i];
        if(x < y) swap(x,y);
        pts.pb(mp(x,-y));
    }

    sort(all(pts));

    stack<pair<int,int>> prt;
    for(auto X : pts) {
        int x = X.fr;
        int y = -X.sc;

        while(prt.size() && prt.top().sc >= y) prt.pop();
        prt.push(mp(x,y));
    }
    pts.clear();
    while(prt.size()) {
        pts.pb(prt.top());
        prt.pop();
    }
    sort(all(pts));
    n = pts.size();

    int l = 0;
    int r = (int) m*m;
    int ans = -1;
    while(l <= r) {
        int mid = (l+r)>>1;
        auto dp = sol(mid);
        if(dp.sc > k) {
            l = mid+1;
        }
        else {
            ans = dp.fr-k*mid;
            r = mid-1;
        }
    }

    return ans;
}

Compilation message (stderr)

aliens.cpp: In function 'std::pair<long long int, long long int> sol(long long int)':
aliens.cpp:54:17: warning: unused variable 'xj' [-Wunused-variable]
   54 |             int xj = pts[i].fr;
      |                 ^~
aliens.cpp:60:17: warning: unused variable 'xj' [-Wunused-variable]
   60 |             int xj = pts[i].fr;
      |                 ^~
aliens.cpp:63:17: warning: unused variable 'yj1' [-Wunused-variable]
   63 |             int yj1 = pts[i-1].sc;
      |                 ^~~
aliens.cpp:51:13: warning: unused variable 'yi' [-Wunused-variable]
   51 |         int yi = pts[i].sc;
      |             ^~

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