IOI '04 P1 - Artemis

#include <iostream>
#include <vector>
#include <algorithm>

using namespace std;

void compress(vector<int> &v) {
    vector<int> v2 = v;
    sort(v2.begin(), v2.end());
    // do not need to remove duplicates since there are no duplicates
    for (int &x : v) x = 1+lower_bound(v2.begin(), v2.end(), x)-v2.begin();
}

struct Point {
    int x, y, id;
    bool operator < (const Point &p2) const {
        return pair<int, int>(x, y) < pair<int, int>(p2.x, p2.y);;
    }
};

int main() {
    ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
    int n, t; cin >> n >> t;
    vector<int> x(n), y(n);
    for (int i = 0; i < n; ++i) cin >> x[i] >> y[i];
    compress(x);
    compress(y);

    vector<Point> points(n);
    for (int i = 0; i < n; ++i) points[i].x = x[i], points[i].y = y[i], points[i].id = i+1;
    sort(points.begin(), points.end());

    vector<int> treesDL(n); // trees down and left (excluding itself)
    for (int i = 0; i < n; ++i) {
        for (int j = 0; j < n; ++j) {
            if (points[j].x < points[i].x && points[j].y < points[i].y) ++treesDL[i];
        }
    }

    int minTrees = n+1, bestI = 0, bestJ = 0;
    for (int i = 0; i < n && minTrees > t; ++i) { // fix one end tree
        int treesBelow = 0;
        vector<int> treesLeft(1+n); // number of trees at each y-value
        for (int j = 0; j < i; ++j) {
            if (points[j].y < points[i].y) ++treesBelow;
            ++treesLeft[points[j].y];
        }
        // convert treesLeft into prefix sums
        for (int yy = 1; yy <= n; ++yy) treesLeft[yy] += treesLeft[yy-1];

        for (int j = i+1; j < n; ++j) {
            // find number of trees enclosed by trees i and j
            int trees;
            if (points[j].y > points[i].y) {
                trees = treesDL[i] + treesDL[j] - treesBelow - treesLeft[points[j].y] + 1; // add tree i
            } else {
                trees = treesBelow + treesLeft[points[j].y] - treesDL[i] - treesDL[j] + 2; // add trees i and j
            }
            if (trees >= t && trees < minTrees) minTrees = trees, bestI = points[i].id, bestJ = points[j].id;

            if (points[j].y < points[i].y) ++treesBelow;
        }
    }
    cout << bestI << ' ' << bestJ << endl;
    return 0;
}