#include "seats.h"
#include <bits/stdc++.h>
#define pii pair<int, int>
#define INF numeric_limits<int>::max()/2
using namespace std;
struct inf
{
int r1;
int r2;
int c1;
int c2;
bool possible;
};
inf combine(inf a, inf b)
{
return {min(a.r1, b.r1), max(a.r2, b.r2), min(a.c1, b.c1), max(a.c2, b.c2)};
}
int area(inf dat)
{
return ((1+dat.r2-dat.r1)*(1+dat.c2-dat.c1));
}
int left(int i)
{
return 2*i;
}
int right(int i)
{
return 2*i+1;
}
int par(int i)
{
return i/2;
}
inf query(int i, vector<inf>& s, int a, int b, int l, int r)
{
if(l <= a && b <= r)
{
return s[i];
}
if(r < a || b < l)
{
return {INF, 0, INF, 0};
}
int mid = (a+b)/2;
inf q1 = query(left(i), s, a, mid, l, r);
inf q2 = query(right(i), s, mid+1, b, l, r);
return {min(q1.r1, q2.r1), max(q1.r2, q2.r2), min(q1.c1, q2.c1), max(q1.c2, q2.c2)};
}
void update(int i, vector<inf>& s, inf val)
{
s[i] = val;
i = par(i);
while(i > 0)
{
s[i] = {min(s[left(i)].r1, s[right(i)].r1), max(s[left(i)].r2, s[right(i)].r2), min(s[left(i)].c1, s[right(i)].c1), max(s[left(i)].c2, s[right(i)].c2)};
i = par(i);
}
}
vector<inf> s(0);
vector<pii> p(0);
vector<inf> a(0);
int segnodes = 1;
int counter = 1;
int n = 1;
bool sub3 = false;
void give_initial_chart(int H, int W, std::vector<int> R, std::vector<int> C)
{
if(H <= 1000 && W <= 1000)
{
sub3 = true;
}
if(sub3)
{
n = H*W;
while(2*n > segnodes)
{
segnodes *= 2;
}
s.assign(segnodes, {INF, 0, INF, 0});
p.assign(n, {-1, -1});
for(int i = 0; i < n; i++)
{
s[i+segnodes/2] = {R[i], R[i], C[i], C[i]};
p[i] = {R[i], C[i]};
}
for(int i = segnodes/2-1; i > 0; i--)
{
s[i] = {min(s[left(i)].r1, s[right(i)].r1), max(s[left(i)].r2, s[right(i)].r2), min(s[left(i)].c1, s[right(i)].c1), max(s[left(i)].c2, s[right(i)].c2)};
}
}
else
{
n = H*W;
for(int i = 0; i < n; i++)
{
p.push_back({R[i], C[i]});
}
a = {{p[0].first, p[0].first, p[0].second, p[0].second, true}};
for(int i = 1; i < n; i++)
{
a.push_back(a.back());
a.back().r1 = min(a.back().r1, p[i].first);
a.back().r2 = max(a.back().r2, p[i].first);
a.back().c1 = min(a.back().c1, p[i].second);
a.back().c2 = max(a.back().c2, p[i].second);
a.back().possible = ((1+a.back().r2-a.back().r1)*(1+a.back().c2-a.back().c1) == i+1);
counter += a.back().possible;
}
}
}
int swap_seats(int d, int b)
{
if(sub3)
{
swap(p[d], p[b]);
update(segnodes/2+d, s, {p[d].first, p[d].first, p[d].second, p[d].second});
update(segnodes/2+b, s, {p[b].first, p[b].first, p[b].second, p[b].second});
int output = 1;
int ar = 1;
while(ar < n)
{
int i = segnodes/2;
inf dat = s[i];
while(area(dat) <= ar)
{
i = par(i);
dat = s[i];
}
dat = s[left(i)];
i = right(i);
//Now, we are in the lowest node that contains enough area! => Going back down
while(left(i) < segnodes)
{
if(area(combine(s[left(i)], dat)) > ar)
{
i = left(i);
}
else
{
dat = combine(dat, s[left(i)]);
i = right(i);
}
}
dat = combine(dat, s[i]);
ar = area(dat);
output += (ar == area(query(1, s, 1, segnodes/2, 1, ar)));
}
return output;
}
else
{
if(d > b)
{
swap(d, b);
}
swap(p[d], p[b]);
for(int i = d; i <= b; i++)
{
counter -= a[i].possible;
if(i == 0)
{
a[i] = {p[0].first, p[0].first, p[0].second, p[0].second, true};
}
else
{
a[i] = a[i-1];
}
a[i].r1 = min(a[i].r1, p[i].first);
a[i].r2 = max(a[i].r2, p[i].first);
a[i].c1 = min(a[i].c1, p[i].second);
a[i].c2 = max(a[i].c2, p[i].second);
a[i].possible = ((1+a[i].r2-a[i].r1)*(1+a[i].c2-a[i].c1) == i+1);
counter += a[i].possible;
}
return counter;
}
}
