Submission #154395

#	Time	Username	Problem	Language	Result	Execution time	Memory
154395		rama_pang	Rectangles (IOI19_rect)	C++14	100 / 100	4165 ms	838788 KiB

rect

#include "rect.h"
#include <bits/stdc++.h>
using namespace std;

struct bit {
    vector<int> tree;
    
    bit(int &n) {
        tree.assign(n + 1, 0);
    }

    void update(int &n, int &x) {
        for (int i = n + 1; i < tree.size(); i += (i & -i)) tree[i] += x;
    }

    int query(int n) {
        int res = 0;
        for (int i = n + 1; i > 0; i -= (i & -i)) res += tree[i];
        return res;
    }
};

void get_interval(vector<int> &a, vector<int> &L, vector<int> &R) {
    int n = a.size(); vector<int> s; s.reserve(n);
    for (int i = 0; i < n; i++) L[i] = -1, R[i] = -1;
    for (int i = 0; i < n; i++) { //find biggest on left side
        while (s.size() && a[s.back()] < a[i]) s.pop_back();
        if (s.size()) L[i] = s.back();
        s.push_back(i);
    }
    s.clear();
    for (int i = n - 1; i >= 0; i--) { //find biggest on right side
        while (s.size() && a[s.back()] < a[i]) s.pop_back();
        if (s.size()) R[i] = s.back();
        s.push_back(i);
    }
}

long long count_rectangles(vector<vector<int>> a) {
    int n = a.size(), m = a[0].size();
    vector<vector<vector<int>>> right(n, vector<vector<int>>(m)), down(n, vector<vector<int>>(m));
    vector<int> b(m), L(m), R(m);
    for (int i = 1; i < n - 1; i++) { //get valid pairs horizontally and vertically
        for (int j = 0; j < m; j++) b[j] = a[i][j];
        get_interval(b, L, R);
        for (int j = 0; j < m; j++) {
            if (L[j] != -1 && L[j] + 1 <= j - 1) right[i][L[j] + 1].push_back(j - 1);
            if (R[j] != -1 && j + 1 <= R[j] - 1 && L[R[j]] != j) right[i][j + 1].push_back(R[j] - 1); //prevent double counting, when a[i][j1] = a[i][j2]
        }
    }
    b.resize(n), L.resize(n), R.resize(n);
    for (int j = 1; j < m - 1; j++) {
        for (int i = 0; i < n; i++) b[i] = a[i][j];
        get_interval(b, L, R);
        for (int i = 0; i < n; i++) {
            if (L[i] != -1 && L[i] + 1 <= i - 1) down[L[i] + 1][j].push_back(i - 1);
            if (R[i] != -1 && i + 1 <= R[i] - 1 && L[R[i]] != i) down[i + 1][j].push_back(R[i] - 1); //prevent double counting
        }
    }
    vector<vector<int>> last_right(m, vector<int>(m, -1)), span_right(m, vector<int>(m, 0)), last_down(n, vector<int>(n, -1)), span_down(n, vector<int>(n, 0));
    vector<pair<pair<int, int>, int>> update;
    long long res = 0;
    bit cnt(m);
    for (int i = n - 1; i >= 0; i--) {
        for (int j = m - 1; j >= 0; j--) {
            for (auto &k : right[i][j]) {
                if (last_right[j][k] != i + 1) span_right[j][k] = 0;
                span_right[j][k]++;
                last_right[j][k] = i;
            }
            for (auto &k : down[i][j]) {
                if (last_down[i][k] != j + 1) span_down[i][k] = 0;
                span_down[i][k]++;
                last_down[i][k] = j;
            }
            update.clear();
            for (auto &k : right[i][j]) {
                update.push_back({{i, k}, 1}); //adding a rectangle
                update.push_back({{i + span_right[j][k], k}, -1}); //erasing a rectangle
            }
            sort(update.begin(), update.end());
            sort(down[i][j].begin(), down[i][j].end());
            int p = 0; //check if a rectangle exists if valid_down and valid_right shares a cell in the top left corner
            for (auto &k : down[i][j]) { //also count the rectangle's spanning, not just width / height 1
                while (p < update.size() && update[p].first.first <= k) { //updating cnt
                    cnt.update(update[p].first.second, update[p].second); p++;
                }
                res += cnt.query(j + span_down[i][k] - 1);
            }
            while (p < update.size()) { //restoring cnt to default
                cnt.update(update[p].first.second, update[p].second); p++;
            }    
        }
    }
    return res;
}

Compilation message (stderr)

rect.cpp: In member function 'void bit::update(int&, int&)':
rect.cpp:13:31: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
         for (int i = n + 1; i < tree.size(); i += (i & -i)) tree[i] += x;
                             ~~^~~~~~~~~~~~~
rect.cpp: In function 'long long int count_rectangles(std::vector<std::vector<int> >)':
rect.cpp:85:26: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
                 while (p < update.size() && update[p].first.first <= k) { //updating cnt
                        ~~^~~~~~~~~~~~~~~
rect.cpp:90:22: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
             while (p < update.size()) { //restoring cnt to default
                    ~~^~~~~~~~~~~~~~~

• 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