#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);
}
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(n <= 500)
{
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(n <= 4000 || k <= 100)
{
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];
}
return 0;
}
