Submission #803194

#	Time	Username	Problem	Language	Result	Execution time	Memory
803194		pavement	Ideal city (IOI12_city)	C++17	23 / 100	54 ms	10740 KiB

city

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

#define mp make_pair
#define eb emplace_back

using ll = long long;
using ii = pair<int, int>;

const int MOD = (int)1e9;
int rep[100005];
vector<ii> row[100005], col[100005];

namespace ufds {
	int lnk[100005], sz[100005];
	
	void init(int n) {
		iota(lnk, lnk + n, 0);
		fill(sz, sz + n, 1);
	}
	int find(int x) {
		if (x == lnk[x]) return x;
		return lnk[x] = find(lnk[x]);
	}
	void unite(int a, int b) {
		a = find(a);
		b = find(b);
		if (a == b) return;
		if (sz[b] > sz[a]) swap(a, b);
		sz[a] += sz[b];
		lnk[b] = a;
	}
};

int DistanceSum(int N, int X[], int Y[]) {
	int ans = 0, min_X = *min_element(X, X + N), min_Y = *min_element(Y, Y + N);
	for (int i = 0; i < N; i++) {
		X[i] -= min_X;
		Y[i] -= min_Y;
		assert(0 <= X[i] && X[i] < N && 0 <= Y[i] && Y[i] < N);
		row[X[i]].eb(Y[i], i);
		col[Y[i]].eb(X[i], i);
	}
	for (int i = 0; i < N; i++) {
		sort(row[i].begin(), row[i].end());
		sort(col[i].begin(), col[i].end());
	}
	for (auto dim : {row, col}) {
		ufds::init(N);
		int cnt = 0, ccs = 0, cur_prod = 0, tot_sz = 0;
		for (int i = 0; i < N; i++) {
			int prv_j = -1, prv_idx = -1;
			for (auto [j, cur] : dim[i]) {
				int upper = -1, idx;
				if (i + 1 < N) {
					auto it = lower_bound(dim[i - 1].begin(), dim[i - 1].end(), mp(j, 0));
					if (it != dim[i - 1].end() && it->first == j) {
						upper = ufds::find(rep[it->second]);
					}
				}
				if (upper == -1) {
					idx = cnt++;
					ccs++;
					cur_prod += tot_sz;
					cur_prod %= MOD;
					tot_sz++;
				} else {
					idx = upper;
					cur_prod += tot_sz - ufds::sz[upper];
					cur_prod %= MOD;
					ufds::sz[upper]++;
					tot_sz++;
				}
				rep[cur] = idx;
				if (prv_j != -1 && prv_j + 1 == j) {
					if (ufds::find(prv_idx) != ufds::find(idx)) {
						ccs--;
						cur_prod -= (ll)ufds::sz[ufds::find(prv_idx)] * (tot_sz - ufds::sz[ufds::find(prv_idx)]) % MOD;
						cur_prod %= MOD;
						if (cur_prod < 0) cur_prod += MOD;
						tot_sz -= ufds::sz[ufds::find(prv_idx)];
						cur_prod -= (ll)ufds::sz[ufds::find(idx)] * (tot_sz - ufds::sz[ufds::find(idx)]) % MOD;
						cur_prod %= MOD;
						if (cur_prod < 0) cur_prod += MOD;
						tot_sz -= ufds::sz[ufds::find(idx)];
						ufds::unite(prv_idx, idx);
						cur_prod += (ll)tot_sz * ufds::sz[ufds::find(prv_idx)] % MOD;
						cur_prod %= MOD;
						if (cur_prod < 0) cur_prod += MOD;
						tot_sz += ufds::sz[ufds::find(prv_idx)];
					}
				}
				prv_j = j;
				prv_idx = idx;
			}
			//~ cout << "@ " << i << ' ' << cur_prod << ' ' << tot_sz << endl;
			ans += (2 * cur_prod % MOD + (ll)tot_sz * (N - tot_sz) % MOD) % MOD;
			ans %= MOD;
		}
	}
	for (auto dim : {row, col}) {
		ufds::init(N);
		int cnt = 0, ccs = 0, cur_prod = 0, tot_sz = 0;
		for (int i = N - 1; i >= 0; i--) {
			int prv_j = -1, prv_idx = -1;
			for (auto [j, cur] : dim[i]) {
				int upper = -1, idx;
				if (i + 1 < N) {
					auto it = lower_bound(dim[i + 1].begin(), dim[i + 1].end(), mp(j, 0));
					if (it != dim[i + 1].end() && it->first == j) {
						upper = ufds::find(rep[it->second]);
					}
				}
				if (upper == -1) {
					idx = cnt++;
					ccs++;
					cur_prod += tot_sz;
					cur_prod %= MOD;
					tot_sz++;
				} else {
					idx = upper;
					cur_prod += tot_sz - ufds::sz[upper];
					cur_prod %= MOD;
					ufds::sz[upper]++;
					tot_sz++;
				}
				rep[cur] = idx;
				if (prv_j != -1 && prv_j + 1 == j) {
					if (ufds::find(prv_idx) != ufds::find(idx)) {
						ccs--;
						cur_prod -= (ll)ufds::sz[ufds::find(prv_idx)] * (tot_sz - ufds::sz[ufds::find(prv_idx)]) % MOD;
						cur_prod %= MOD;
						if (cur_prod < 0) cur_prod += MOD;
						tot_sz -= ufds::sz[ufds::find(prv_idx)];
						cur_prod -= (ll)ufds::sz[ufds::find(idx)] * (tot_sz - ufds::sz[ufds::find(idx)]) % MOD;
						cur_prod %= MOD;
						if (cur_prod < 0) cur_prod += MOD;
						tot_sz -= ufds::sz[ufds::find(idx)];
						ufds::unite(prv_idx, idx);
						cur_prod += (ll)tot_sz * ufds::sz[ufds::find(prv_idx)] % MOD;
						cur_prod %= MOD;
						if (cur_prod < 0) cur_prod += MOD;
						tot_sz += ufds::sz[ufds::find(prv_idx)];
					}
				}
				prv_j = j;
				prv_idx = idx;
			}
			ans += 2 * cur_prod % MOD;
			ans %= MOD;
		}
	}
	return ans;
}

• Subtask 1: 0 / 11
• Subtask 2: 0 / 21
• Subtask 3: 23 / 23
• Subtask 4: 0 / 45