| # | Time | Username | Problem | Language | Result | Execution time | Memory |
|---|---|---|---|---|---|---|---|
| 394274 | Drew_ | Aliens (IOI16_aliens) | C++17 | 0 ms | 0 KiB |
This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include "aliens.h"
#include <vector>
#include <iostream>
#include <algorithm>
#include <cassert>
using namespace std;
#define ll long long
#define pb push_back
#define ii pair<int, int>
#define pl pair<ll, ll>
#define f1 first
#define s2 second
const int MAX = 1e5 + 7;
struct Line
{
ll m, c;
Line() : m(0), c(0) {}
Line(ll m, ll c) : m(m), c(c) {}
double inter(const Line &other) { return (double) (c - other.c) / (other.m - m); }
};
struct convex_hull
{
int sz = 0;
Line ar[MAX];
void clear() { sz = 0; }
bool cmp(Line a, Line b, Line c) { return a.inter(b) < b.inter(c); }
void addLine(ll m, ll c)
{
Line L(m, c);
while (sz >= 2 && !cmp(ar[sz-2], ar[sz-1], L))
sz--;
ar[sz++] = L;
}
ll query(ll x)
{
int l = 0, r = sz-1;
while (l < r)
{
int mid = (l + r) / 2;
if (ar[mid].inter(ar[mid+1]) >= x) r = mid;
else l = mid + 1;
}
return ar[l].m * x + ar[l].c;
}
} cht;
vector<pl> ivl;
//cost for interval [i, j], assuming interval [0, i-1] have been fulfilled
/*
inline ll getCost(int i, int j)
{
ll res = 1LL * (ivl[j].s2 - ivl[i].f1 + 1) * (ivl[j].s2 - ivl[i].f1 + 1);
if (i)
{
if (ivl[i-1].s2 >= ivl[i].f1)
res -= 1LL * (ivl[i-1].s2 - ivl[i].f1 + 1) * (ivl[i-1].s2 - ivl[i].f1 + 1);
}
return res;
}
*/
ll dp[2][MAX];
long long take_photos(int n, int m, int k, std::vector<int> r, std::vector<int> c) {
vector<ii> v(n);
for (int i = 0; i < n; ++i)
v[i] = {min(r[i], c[i]), max(r[i], c[i])};
sort(v.begin(), v.end(), [](const ii &x, const ii &y){
return x.f1 < y.f1 || (x.f1 == y.f1 && x.s2 > y.s2);
});
ivl.pb(v[0]);
for (int i = 1; i < n; ++i)
{
if (ivl.back().f1 <= v[i].f1 && v[i].s2 <= ivl.back().s2)
continue;
ivl.pb(v[i]);
}
for (int i = 0; i < ivl.size(); ++i)
dp[0][i] = (ivl[i].s2 - ivl[0].f1 + 1) * (ivl[i].s2 - ivl[0].f1 + 1);
k = min(k, (int)ivl.size());
for (int j = 1; j < k; ++j)
{
cht.clear();
cht.addLine(-2 * ivl[0].f1, ivl[0].f1 * ivl[0].f1);
for (int i = 1; i < ivl.size(); ++i)
{
ll m = -2 * ivl[i].f1;
ll c = (ivl[i].f1 * ivl[i].f1) + dp[~j & 1][i-1];
if (ivl[i].f1 <= ivl[i-1].s2)
c -= (ivl[i-1].s2 - ivl[i].f1 + 1) * ((ivl[i-1].s2 - ivl[i].f1 + 1));
cht.addLine(m, c);
dp[j&1][i] = cht.query(ivl[i].s2 + 1) + (ivl[i].s2 + 1) * (ivl[i].s2 + 1);
}
}
return dp[~k & 1][ivl.size() - 1];
/*
ll L = 0, R = 1e12;
for (int i = 0; i < ivl.size(); ++i)
L = max(L, getCost(i, i));
k = min(k, (int)ivl.size());
while (L < R)
{
ll mid = (L + R) / 2;
pl res = check(mid);
if (res.f1 <= k) R = mid;
else L = mid + 1;
}
pl res = check(L);
return k * L + res.s2;
*/
}
int main() {
int n, m, k;
assert(3 == scanf("%d %d %d", &n, &m, &k));
std::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;
}