Submission #1029291

#	Time	Username	Problem	Language	Result	Execution time	Memory
1029291		onbert	Rectangles (IOI19_rect)	C++17	100 / 100	4019 ms	1003440 KiB

rect

#include "rect.h"
#include <bits/stdc++.h>
using namespace std;
#define ss short
#define ll long long
struct range {
    ss r, mx;
};
bool cmp0(range &a, range &b) {return a.r > b.r;}
bool cmp1(range &a, range &b) {return a.mx > b.mx;}
const int maxn = 2505, INF = 2505, lg = 12;
int n, m;
vector<vector<vector<pair<ss,ss>>>> pos[2];
vector<vector<vector<range>>> start[2];

ss fen[maxn];
void update(int id, int val) {
    while (id<maxn) {
        fen[id] += val;
        id += (id & -id);
    }
}
int qry(int id) {
    int val = 0;
    while (id >= 1) {
        val += fen[id];
        id -= (id & -id);
    }
    return val;
}

pair<int,int> st[maxn][lg];
int qry1(int l, int r) {
    int lg = log2(r-l+1);
    pair<int,int> lhs = st[l][lg], rhs = st[r-(1<<lg)+1][lg];
    if (rhs.first > lhs.first) return rhs.second;
    else return lhs.second;
}

int nn, II, ii;
void dfs(int l, int r) {
    if (l>r) return;
    int mid = qry1(l, r);
    // if (II==0 && ii==1) cout << l << " " << r << " " << mid << endl;
    if (l>=1 && r<=nn-2 && st[mid][0].first < st[l-1][0].first && st[mid][0].first < st[r+1][0].first) {
        // if (II==1) cout << ii << " " << l << " " << r << endl;
        pos[II][l][r-l].push_back({(ss)ii, -1});
        if (II==0) start[II][ii][l].push_back({(ss)r, -1});
        else start[II][l][ii].push_back({(ss)r, -1});
    }
    dfs(l, mid-1); dfs(mid+1, r);
}

long long count_rectangles(vector<vector<int32_t>> a) {
	n = a.size(), m = a[0].size();
    pos[0].resize(m);
    for (int i=0;i<m;i++) pos[0][i].resize(m - i);
    pos[1].resize(n);
    for (int i=0;i<n;i++) pos[1][i].resize(n - i);
    start[0].resize(n); start[1].resize(n);
    for (int i=0;i<n;i++) start[0][i].resize(m), start[1][i].resize(m);

    nn = m, II = 0;
    for (int i=0;i<n;i++) {
        ii = i;
        for (int j=m-1;j>=0;j--) {
            st[j][0] = {a[i][j], j};
            for (int k=1;k<lg;k++) {
                if (j+(1<<k)-1 < m) {
                    st[j][k] = st[j][k-1];
                    pair<int,int> nxt = st[j + (1 << (k-1))][k-1];
                    if (nxt.first > st[j][k].first) st[j][k] = nxt;
                } else break;
            }
        }
        dfs(0, m-1);
    }

    nn = n, II = 1;
    for (int j=0;j<m;j++) {
        ii = j;
        for (int i=n-1;i>=0;i--) {
            st[i][0] = {a[i][j], i};
            for (int k=1;k<lg;k++) {
                if (i+(1<<k)-1 < n) {
                    st[i][k] = st[i][k-1];
                    pair<int,int> nxt = st[i + (1 << (k-1))][k-1];
                    if (nxt.first > st[i][k].first) st[i][k] = nxt;
                } else break;
            }
        }
        dfs(0, n-1);
    }

    for (int I=0;I<=1;I++) {
        int nn = m;
        if (I==1) nn = n;
        for (int l=0;l<nn;l++) for (int r=l;r<nn;r++) {
            sort(pos[I][l][r-l].begin(), pos[I][l][r-l].end());
            int sz = pos[I][l][r-l].size();
            for (int i=sz-1;i>=0;i--) {
                if (i==sz-1 || pos[I][l][r-l][i+1].first!=pos[I][l][r-l][i].first+1) pos[I][l][r-l][i].second = pos[I][l][r-l][i].first;
                else pos[I][l][r-l][i].second = pos[I][l][r-l][i+1].second;
            }
        }
    }
    for (int I=0;I<=1;I++) {
        for (int i=0;i<n;i++) for (int j=0;j<m;j++) {
            for (auto &[r, mx]:start[I][i][j]) {
                ss x = j, y = i;
                if (I==1) x = i, y = j;
                mx = (*lower_bound(pos[I][x][r-x].begin(), pos[I][x][r-x].end(), make_pair(y, (ss)-1))).second;
            }
        }
    }
    ll ans = 0;
    vector<int> LOG;
    for (int i=1;i<n-1;i++) for (int j=1;j<m-1;j++) {
        sort(start[0][i][j].begin(), start[0][i][j].end(), cmp0);
        sort(start[1][i][j].begin(), start[1][i][j].end(), cmp1);
        int pt = -1;
        LOG.clear();
        for (auto [r, mx]:start[0][i][j]) {
            while (pt+1 < start[1][i][j].size() && start[1][i][j][pt+1].mx >= r) {
                pt++;
                update(start[1][i][j][pt].r, 1);
                LOG.push_back(start[1][i][j][pt].r);
            }
            ans += qry(mx);
        }
        for (int x:LOG) update(x, -1);
    }
    return ans;
}

Compilation message (stderr)

rect.cpp: In function 'long long int count_rectangles(std::vector<std::vector<int> >)':
rect.cpp:124:25: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<range>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  124 |             while (pt+1 < start[1][i][j].size() && start[1][i][j][pt+1].mx >= r) {
      |                    ~~~~~^~~~~~~~~~~~~~~~~~~~~~~

• 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