#include "aliens.h"
#include <iostream>
#include <algorithm>
#include <utility>
#include <climits>
#include <set>
using namespace std;
using ll = long long;
ll sq(ll a) {
return a * a;
}
ll sq(int a) {
return (ll)(a) * a;
}
ll getArea(pair<ll, ll> a) {
return sq(a.second - a.first + 1);
}
ll getArea(ll a, ll b) {
return sq(b - a + 1);
}
ll positiveArea(ll a, ll b) {
ll sideLength = b - a + 1;
return (sideLength > 0 ? sq(sideLength) : 0);
}
ll take_photos(int n, int m, int k, std::vector<int> r, std::vector<int> c) {
vector<pair<ll, ll>> oriPoints;
for (ll i = 0; i < n; ++i) {
if (r[i] > c[i]) swap(r[i], c[i]);
oriPoints.emplace_back(r[i], c[i]);
}
sort(oriPoints.begin(), oriPoints.end());
oriPoints.emplace_back(-1, -1);
set<pair<ll, pair<ll, ll>>> curPoints;
set<pair<ll , ll>> costs, invCosts;
pair<ll, ll> _prev = {-1, -1}, cur = {-1, -1};
ll res = 0;
for (ll i = 0; i <= n; ++i) {
if (oriPoints[i].first == cur.first) cur.second = max(oriPoints[i].second, cur.second);
else {
if (((_prev.first != -1) && (cur.second > _prev.second)) || ((_prev.first == -1) && (cur.first != -1))) {
if (_prev.first != -1) {
ll curCost = getArea(_prev.first, cur.second) - getArea(_prev) - getArea(cur) + positiveArea(cur.first, _prev.second);
costs.emplace(curPoints.size() - 1, curCost);
invCosts.emplace(curCost, curPoints.size() - 1);
res -= positiveArea(cur.first, _prev.second);
}
_prev = cur;
curPoints.insert(make_pair(curPoints.size(), cur));
res += getArea(cur);
}
cur = oriPoints[i];
}
}
while (curPoints.size() > k) {
auto cur = invCosts.begin();
res -= cur->first;
auto firstPoint = curPoints.lower_bound(make_pair(cur->second, make_pair(-1, -1))), secondPoint = next(firstPoint);
pair<int, int> newPoint = {firstPoint->second.first, secondPoint->second.second};
int newIndex = firstPoint->first;
if (firstPoint != curPoints.begin()) {
auto prevPoint = prev(firstPoint);
auto costPair = costs.lower_bound(make_pair(prevPoint->first, -1));
invCosts.erase(invCosts.lower_bound(make_pair(costPair->second, costPair->first)));
costs.erase(costPair);
int prevCost = getArea(prevPoint->second.first, newPoint.second) - getArea(prevPoint->second) - getArea(newPoint) + positiveArea(newPoint.first, prevPoint->second.second);
costs.emplace(prevPoint->first, prevCost);
invCosts.emplace(prevCost, prevPoint->first);
}
if (next(secondPoint) != curPoints.end()) {
auto nextPoint = next(secondPoint);
auto costPair = costs.lower_bound(make_pair(nextPoint->first, -1));
invCosts.erase(invCosts.lower_bound(make_pair(costPair->second, costPair->first)));
costs.erase(costPair);
int nextCost = getArea(newPoint.first, nextPoint->second.second) - getArea(newPoint) - getArea(nextPoint->second) + positiveArea(nextPoint->second.first, newPoint.second);
costs.emplace(newIndex, nextCost);
invCosts.emplace(nextCost, newIndex);
}
invCosts.erase(invCosts.lower_bound(make_pair(cur->second, cur->first)));
costs.erase(cur);
curPoints.erase(firstPoint);
curPoints.erase(secondPoint);
curPoints.insert(make_pair(newIndex, newPoint));
}
return res;
}
