Submission #937444

#	Time	Username	Problem	Language	Result	Execution time	Memory
937444		GrindMachine	Rectangles (IOI19_rect)	C++17	100 / 100	2731 ms	659332 KiB

rect

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

using namespace std;
using namespace __gnu_pbds;

template<typename T> using Tree = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
typedef long long int ll;
typedef long double ld;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;

#define fastio ios_base::sync_with_stdio(false); cin.tie(NULL)
#define pb push_back
#define endl '\n'
#define sz(a) (int)a.size()
#define setbits(x) __builtin_popcountll(x)
#define ff first
#define ss second
#define conts continue
#define ceil2(x,y) ((x+y-1)/(y))
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define yes cout << "Yes" << endl
#define no cout << "No" << endl

#define rep(i,n) for(int i = 0; i < n; ++i)
#define rep1(i,n) for(int i = 1; i <= n; ++i)
#define rev(i,s,e) for(int i = s; i >= e; --i)
#define trav(i,a) for(auto &i : a)

template<typename T>
void amin(T &a, T b) {
    a = min(a,b);
}

template<typename T>
void amax(T &a, T b) {
    a = max(a,b);
}

#ifdef LOCAL
#include "debug.h"
#else
#define debug(x) 42
#endif

/*

read some solutions long back, remember some ideas from there

*/

const int MOD = 1e9 + 7;
const int N = 1e5 + 5;
const int inf1 = int(1e9) + 5;
const ll inf2 = ll(1e18) + 5;

#include "rect.h"
 
template<typename T>
struct fenwick {
    int siz;
    vector<T> tree;
 
    fenwick() {
 
    }
 
    fenwick(int n) {
        siz = n;
        tree = vector<T>(n + 1);
    }
 
    int lsb(int x) {
        return x & -x;
    }
 
    void build(vector<T> &a, int n) {
        for (int i = 1; i <= n; ++i) {
            int par = i + lsb(i);
            tree[i] += a[i];
 
            if (par <= siz) {
                tree[par] += tree[i];
            }
        }
    }
 
    void pupd(int i, T v) {
        i++;
        while (i <= siz) {
            tree[i] += v;
            i += lsb(i);
        }
    }
 
    T sum(int i) {
        i++;
        T res = 0;
 
        while (i) {
            res += tree[i];
            i -= lsb(i);
        }
 
        return res;
    }
 
    T query(int l, int r) {
        if (l > r) return 0;
        T res = sum(r) - sum(l - 1);
        return res;
    }
};
 
long long count_rectangles(std::vector<std::vector<int> > a) {
    int n = sz(a), m = sz(a[0]);
    if(n <= 2 or m <= 2) return 0;
 
    vector<pii> up[n][m];
    int ptr = 0;
 
    rep(j,m){
        stack<int> st;
        rep(i,n){
            bool eq = false;
            while(!st.empty() and a[i][j] >= a[st.top()][j]){
                int k = st.top();
                st.pop();
                if(a[i][j] == a[k][j]){
                    eq = true;
                }
                if(i-k >= 2){
                    up[i][j].pb({k,ptr++});
                }
            }
 
            if(!st.empty() and !eq){
                int k = st.top();
                if(i-k >= 2){
                    up[i][j].pb({k,ptr++});
                }
            }
 
            st.push(i);
        }
    }
 
    vector<int> farthest(ptr);
    int seg_ptr[n][n];
    memset(seg_ptr,-1,sizeof seg_ptr);

    rev(j,m-1,0){
        if(j+2 < m){
            rep(i,n){
                for(auto [k,ptr] : up[i][j+2]){
                    seg_ptr[k][i] = -1;
                }
            }   
        }

        if(j+1 < m){
            rep(i,n){
                for(auto [k,ptr] : up[i][j+1]){
                    seg_ptr[k][i] = ptr;
                }
            }   
        }

        rep(i,n){
            for(auto [k,ptr] : up[i][j]){
                if(seg_ptr[k][i] != -1){
                    farthest[ptr] = farthest[seg_ptr[k][i]];
                }
                else{
                    farthest[ptr] = j;
                }
            }
        }
    }
 
    int prev_occ[m][m], first_occ[m][m];
    memset(prev_occ,-1,sizeof prev_occ);
    memset(first_occ,-1,sizeof first_occ);
 
    ll ans = 0;
    vector<int> queries[ptr];
 
    rep1(i,n-2){
        stack<int> st;
        vector<pii> good;
        rep(j,m){
            bool eq = false;
            while(!st.empty() and a[i][j] >= a[i][st.top()]){
                int k = st.top();
                st.pop();
                if(a[i][j] == a[i][k]){
                    eq = true;
                }
                if(j-k >= 2){
                    good.pb({k,j});
                }
            }
 
            // cout << j << endl;
            // cout << eq << endl;
            // auto st_copy = st;
            // while(!st_copy.empty()){
            //  cout << st_copy.top() << " ";
            //  st_copy.pop();
            // }
            // cout << endl;
 
            if(!st.empty() and !eq){
                int k = st.top();
                if(j-k >= 2){
                    // cout << k << " " << j << endl;
                    good.pb({k,j});
                }
            }
 
            st.push(j);
        }
 
        for(auto [l,r] : good){
            if(prev_occ[l][r] != i-1){
                first_occ[l][r] = i;
            }
 
            prev_occ[l][r] = i;
 
            int lo = 0, hi = sz(up[i+1][l+1])-1;
            int pos = -1;
 
            while(lo <= hi){
                int mid = (lo+hi) >> 1;
                if(up[i+1][l+1][mid].ff >= first_occ[l][r]-1){
                    pos = mid;
                    lo = mid+1;
                }
                else{
                    hi = mid-1;
                }
            }
 
            if(pos != -1){
                int ind = up[i+1][l+1][pos].ss;
                queries[ind].pb(r);
            }
 
            /*
 
            for(auto [k,ptr] : up[i+1][l+1]){
                if(k >= first_occ[l][r]-1){
                    if(farthest[ptr] >= r-1){
                        ans++;
                    }
                }
                else{
                    break;
                }
            }
 
            */
        }
    }
 
    fenwick<int> fenw(m);
 
    rep(i,n){
        rep(j,m){
            for(auto [k,ptr] : up[i][j]){
                fenw.pupd(farthest[ptr],1);
                trav(r,queries[ptr]){
                    ans += fenw.query(r-1,m-1);
                }
            }
 
            for(auto [k,ptr] : up[i][j]){
                fenw.pupd(farthest[ptr],-1);
            }
        }
    }
 
    /*
 
    int oans = 0;
 
    rep1(i1,n-2){
        rep1(j1,m-2){
            for(int i2 = i1; i2 < n-1; ++i2){
                for(int j2 = j1; j2 < m-1; ++j2){
                    bool ok = true;
                    for(int r = i1; r <= i2; ++r){
                        for(int c = j1; c <= j2; ++c){
                            if(a[r][c] >= min({a[i1-1][c],a[i2+1][c],a[r][j1-1],a[r][j2+1]})){
                                ok = false;
                                break;
                            }
                        }
                        if(!ok) break;
                    }
 
                    if(ok){
                        oans++;
                        cout << i1 << " " << j1 << " " << i2 << " " << j2 << endl;
                    }
                }
            }
        }
    }
    
    */
    
    // cout << ans << endl;
    // cout << oans << endl;
    // cout << endl;
 
    // assert(ans == oans);
 
    return ans;
}

• Subtask 1: 8 / 8
• Subtask 2: 7 / 7
• Subtask 3: 12 / 12
• Subtask 4: 22 / 22
• Subtask 5: 10 / 10
• Subtask 6: 13 / 13
• Subtask 7: 28 / 28