Submission #106291

#	Time	Username	Problem	Language	Result	Execution time	Memory
106291		evpipis	Aliens (IOI16_aliens)	C++11	100 / 100	183 ms	10988 KiB

aliens

//#define TEST

#ifndef TEST
#include "aliens.h"
#endif
#include <bits/stdc++.h>
using namespace std;

#define fi first
#define se second
#define pb push_back
#define mp make_pair
typedef long long ll;
typedef pair<int, int> ii;
typedef pair<ll, ll> pll;

inline ll sq(ll x){
    return x*x;
}

const int len = 1e5+5;
const ll inf = 1e15;
int n, m, k, po;
ii arr[len];
vector<ii> vec;
vector<pair<pll, int> > con;
ll com[len];
pair<ll, int> dp[len];

ll func(pll line, int x){
    return x*line.fi + line.se;
}

bool bad(pair<pll, int> a, pair<pll, int> b, pair<pll, int> c){
    if ((b.fi.se-a.fi.se)*(b.fi.fi-c.fi.fi) == (c.fi.se-b.fi.se)*(a.fi.fi-b.fi.fi))
        return (b.se >= a.se || b.se >= c.se);
    return ((b.fi.se-a.fi.se)*(b.fi.fi-c.fi.fi) > (c.fi.se-b.fi.se)*(a.fi.fi-b.fi.fi));
}

void add(ll a, ll b, int sec){
    while (con.size() >= 2 && bad(con[con.size()-2], con.back(), mp(mp(a, b), sec)))
        con.pop_back();
    con.pb(mp(mp(a, b), sec));
}

pair<ll, int> query(int x){
    if (po >= con.size())
        po = con.size()-1;

    while (po+1 < con.size() && mp(func(con[po].fi, x), con[po].se) > mp(func(con[po+1].fi, x), con[po].se))
        po++;

    return mp(func(con[po].fi, x), con[po].se);
}

int check(ll c){
    /*for (int i = 1; i <= n; i++){
        pair<ll, int> ans = mp(inf, 0);
        for (int j = 0; j < i; j++){
            ll temp = (vec[i].se-vec[j+1].fi+1)*1LL*(vec[i].se-vec[j+1].fi+1) - com[j];
            ans = min(ans, mp(dp[j].fi+temp, dp[j].se));
        }

        ans.fi += c;
        ans.se += 1;
        dp[i] = ans;

        //printf("i = %d, ans = (%lld, %d)\n", i, ans.fi, ans.se);
    }*/

    po = 0;
    con.clear();
    add(-2*(vec[1].fi-1), sq((ll)vec[1].fi-1), 0);
    for (int i = 1; i <= n; i++){
        dp[i] = query(vec[i].se);
        dp[i].fi += sq((ll)vec[i].se)+c;
        dp[i].se += 1;

        if (i != n)
            add(-2*(vec[i+1].fi-1), dp[i].fi+sq((ll)vec[i+1].fi-1)-com[i], dp[i].se);
    }

    return dp[n].se;
}

ll bs(){
    ll l = 0, r = m*1LL*m, ans;
    while (l <= r){
        ll mid = (l+r)/2;
        int cur = check(mid);

        //printf("mid = %lld, cur = %d\n", mid, cur);

        if (cur <= k)
            r = mid-1, ans = mid;
        else
            l = mid+1;
    }

    return ans;
}

ll take_photos(int N, int M, int K, vector<int> R, vector<int> C){
    n = N, m = M, k = K;

    for (int i = 0; i < n; i++){
        arr[i] = mp(R[i]+1, C[i]+1);
        if (arr[i].fi > arr[i].se)
            swap(arr[i].fi, arr[i].se);
    }

    sort(arr, arr+n);

    vec.pb(mp(1, 0));
    for (int i = 0; i < n; i++){
        while (vec.size() > 1 && vec.back().fi == arr[i].fi)
            vec.pop_back();
        if (arr[i].se > vec.back().se)
            vec.pb(arr[i]);
    }
    n = vec.size()-1;
    k = min(n, k);

    for (int i = 0; i < n; i++){
        if (vec[i].se < vec[i+1].fi)
            com[i] = 0;
        else
            com[i] = pow(vec[i].se-vec[i+1].fi+1, 2);
    }

    //for (int i = 0; i <= n; i++)
      //  printf("%d %d\n", vec[i].fi, vec[i].se);

    ll c = bs(), temp = check(c);
    //printf("c = %lld, ans = %lld\n", c, dp[n].fi - k*c);
    return dp[n].fi - k*c;
}

#ifdef TEST
int main() {
    int N, M, K;
    assert(3 == scanf("%d %d %d", &N, &M, &K));
    //printf("N = %d, M = %d, K = %d\n", N, M, K);
    vector<int> r(N), c(N);
    for (int i = 0; i < N; i++) {
        assert(2 == scanf("%d %d", &r[i], &c[i]));
    }
    long long ans = take_photos(N, M, K, r, c);


    printf("%lld\n", ans);
    return 0;
}
#endif

Compilation message (stderr)

aliens.cpp: In function 'std::pair<long long int, int> query(int)':
aliens.cpp:47:12: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
     if (po >= con.size())
         ~~~^~~~~~~~~~~~~
aliens.cpp:50:17: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
     while (po+1 < con.size() && mp(func(con[po].fi, x), con[po].se) > mp(func(con[po+1].fi, x), con[po].se))
            ~~~~~^~~~~~~~~~~~
aliens.cpp: In function 'll take_photos(int, int, int, std::vector<int>, std::vector<int>)':
aliens.cpp:134:18: warning: unused variable 'temp' [-Wunused-variable]
     ll c = bs(), temp = check(c);
                  ^~~~
aliens.cpp: In function 'll bs()':
aliens.cpp:100:12: warning: 'ans' may be used uninitialized in this function [-Wmaybe-uninitialized]
     return ans;
            ^~~

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