// moreflags=grader.cpp
// 13
// an insignificant optimization.
#include "rect.h"
#include<vector>
#include<set>
#include<algorithm>
#if not LOCAL
#define NDEBUG
#endif
#include<cassert>
#include<climits>
struct T{
short right, depth;
T& operator=(T) && = delete;
};
struct Vector{
struct Node{T t; int next;};
static std::vector<Node> data;
int node;
int back;
Vector(): node(-1)
, back(-1)
{}
bool empty()const{return node<0;}
//struct Sentinel{};
struct Iterator: std::iterator<std::forward_iterator_tag, T>{
//using iterator_category=std::forward_iterator_tag;
int node;
Iterator(int node): node(node){} // because of the inheritance...
//bool operator==(Sentinel) const{return node<0;}
bool operator==(Iterator other) const{return node==other.node;}
bool operator!=(Iterator other) const{return node!=other.node;}
T& operator*() const{return data[node].t;} // too lazy to implement const-correctness correctly
T* operator->() const{return &data[node].t;}
Iterator& operator++(){ node=data[node].next; return *this; }
};
Iterator begin()const{ return {node}; }
Iterator end()const{ return {-1}; }
//Sentinel end(){ return {}; }
void push_back(T value){
if(node<0){
node=back=(int)data.size();
data.push_back({value, -1});
return;
}
assert(data[back].next<0);
back=data[back].next=(int)data.size();
data.push_back({value, -1});
}
void push_front(T value){
auto const newNode=(int)data.size();
data.push_back({value, node});
node=newNode;
}
};
std::vector<Vector::Node> Vector::data; // ...
long long count_rectangles(std::vector<std::vector<int> > a) {
using std::begin; using std::end;
if(a.size()<3 or a[0].size()<3) return 0;
Vector::data.reserve(2*a.size()*a[0].size());
struct Set{
std::vector<bool> data;
Set(int number): data(number*2){}
int offset() const{return int(data.size()/2); }
void add(int index){
auto node=index+offset();
for(; node; node>>=1) data[node]=true;
}
int minimum(int node)const{
assert(data[node]);
while(node<offset()){
node<<=1;
if(not data[node]) ++node;
}
return node-offset();
}
int maximum(int node)const{
assert(data[node]);
while(node<offset()){
node<<=1;
if(data[node+1]) ++node;
}
return node-offset();
}
int getMinimum(int first, int sec)const{
first+=offset(); sec+=offset();
int best=-1;
for(; first<sec; first>>=1, sec>>=1){
if(first&1) {
if(data[first]) return minimum(first);
first++;
}
if(sec&1){
--sec;
if(data[sec]) best=sec;
}
}
return best<0 ? -1: minimum(best);
}
int getMaximum(int first, int sec)const{
first+=offset(); sec+=offset();
int best=-1;
for(; first<sec; first>>=1, sec>>=1){
if(first&1) {
if(data[first]) best=first;
first++;
}
if(sec&1){
--sec;
if(data[sec]) return maximum(sec);
}
}
return best<0 ? -1: maximum(best);
}
};
using Segments=std::vector<Vector>;
auto const getSegments=[&](std::vector<int> const& data)->Segments{
Segments result(data.size()-1); // [l] -> list of valid r in reverse sorted order
struct Item{int value, index;};
std::vector<Item> items(data.size());
for(int index=0; index<(int)items.size(); ++index)
items[index]={data[index], index};
std::sort(begin(items), end(items),[&](Item first, Item sec){return first.value>sec.value;});
Set done((int)items.size());
for(auto [value, index]: items){
done.add(index);
auto const next=done.getMinimum(index+1, (int)items.size());
if(next>=0){
auto const prev=done.getMaximum(0, index);
if(prev>=0){
assert(prev<index); assert(index<next);
if(value<data[prev] and value<data[next]){
result[prev+1].push_back(T{next, 1});
}
}
}
}
for(auto& it: result)
assert(std::is_sorted(begin(it), end(it), [&](T first, T sec){return first.right>sec.right;}));
return result;
};
std::vector<Segments> rows(a.size()-1), cols(a[0].size()-1);
for(int row=1; row<(int)a.size()-1; ++row)
rows[row]=getSegments(a[row]);
{
std::vector<int> tmp(a.size());
for(int col=1; col<(int)a[0].size()-1; ++col){
std::transform(begin(a), end(a), tmp.begin(),[&](std::vector<int> const& it){return it[col];});
cols[col]=getSegments(tmp);
}
}
auto const computeDepth=[&](std::vector<Segments>& data)->void{
if(data.size()<=2) return;
assert(data[0].empty());
for(int row=(int)data.size()-1; --row;){
for(int left=0; left<(int)data[row].size(); ++left){
auto const& v=data[row+1][left];
if(not v.empty()){
auto iterator=v.begin();
for(auto& [right, depth]: data[row][left]){
assert(depth==1);
while(true){
if(iterator==v.end()) goto break_outer;
if(iterator->right<=right) break;
++iterator;
}
if(iterator->right==right)
depth=iterator->depth+1;
else{
assert(iterator==v.end() or iterator->right<right);
assert(iterator==v.begin() or iterator->right>right);
assert(std::is_sorted(begin(v), end(v), [&](T first, T sec){return first.right>sec.right;}));
}
}
break_outer:;
}
}
}
};
computeDepth(rows);
computeDepth(cols);
struct Bit{
std::vector<int> data;
Bit(int number): data(number){}
void add(int index, int value){
for(; index>=0; index=(index&(index+1))-1)
data[index]+=value;
}
int sumSuffix(int index) const{
int result{};
for(; index<(int)data.size(); index|=index+1)
result+=data[index];
return result;
}
};
Bit bit((int)a[0].size()-1);
enum class EventType{ add, get };
struct Event{ EventType type; int x, y;
bool operator<(Event other) const{return std::tie(y, type)<std::tie(other.y, other.type);}
};
std::vector<Event> events;
int64_t result{};
for(int up=1; up<(int)a.size()-1; ++up)
for(int left=1; left<(int)a[0].size()-1; ++left){
if(rows[up][left].empty() or cols[left][up].empty()) continue;
events.clear();
for(auto [right, depthDown]: rows[up][left])
events.push_back({EventType::get, right-left, depthDown});
for(auto [down, depthRight]: cols[left][up])
events.push_back({EventType::add, depthRight, down-up});
std::sort(begin(events), end(events));
for(auto [type, x, y]: events)
if(type==EventType::add){
bit.add(x, 1);
}else{
result+=bit.sumSuffix(x);
}
for(auto [type, x, y]: events)
if(type==EventType::add){
bit.add(x, -1);
}
}
return result;
}
