Submission #368012

#	Time	Username	Problem	Language	Result	Execution time	Memory
368012		wind_reaper	Ideal city (IOI12_city)	C++17	0 / 100	35 ms	3692 KiB

city

#include <bits/stdc++.h>

using namespace std;

#define dbg(x) cout << "[" << #x << ": " << x << "] ";
const int64_t mod = 1e9;

vector<vector<int>> adj;

struct LCA{
    vector<vector<int>> up; 
    int l;
    vector<int> tin, tout; 
    vector<int64_t> depth;
    LCA(int n){
        l = 32 - __builtin_clz(n);
        up.resize(l+1, vector<int>(n));
        tin.resize(n); 
        tout.resize(n);
        depth.resize(n);
        dfs(0, 0);
    }
    int timer = 0; 
    void dfs(int node, int par){
        tin[node] = timer++; 
        depth[node] = depth[par] + 1;
        up[0][node] = par;
        for(int i = 1; i <= l; i++)
            up[i][node] = up[i-1][up[i-1][node]];

        for(int v : adj[node]){
            if(v == par)
                continue;
            dfs(v, node);
        }

        tout[node] = timer++;
    }

    bool isAncestor(int u, int v){
        return tin[u] <= tin[v] && tout[u] >= tout[v];
    }

    int lca(int u, int v){
        if(isAncestor(u, v))
            return u;
        if(isAncestor(v, u))
            return v;

        for(int i = l; i >= 0; --i)
            if(!isAncestor(up[i][u], v))
                u = up[i][u];

        return up[0][u];
    }

    int64_t dist(int u, int v){
        return depth[u] + depth[v] - 2*depth[lca(u, v)];
    }
};

vector<int64_t> c;
vector<pair<int, int>> del = {{-1, 0}, {0, -1}, {1, 0}, {0, 1}};

int64_t ans = 0;
void dfs(int node, int par, int N){
	for(int v : adj[node]){
		if(v == par)
			continue;
		dfs(v, node, N);
		c[node] += c[v];
	}
	c[node]++;
	ans += (c[node]*(N-c[node])) % mod;
	ans %= mod;
}


int DistanceSum(int N, int *X, int *Y) {
	adj.resize(N);
	vector<array<int, 2>> P(N);
	for(int i = 0; i < N; i++)
		P[i] = {X[i], Y[i]};

	sort(P.begin(), P.end());
	vector<int> vis(N, 0);

	queue<array<int, 3>> q;
	q.push({P[0][0], P[0][1], 0});
	vis[0] = 1;
	while(!q.empty()){
		array<int, 3> cur = q.front();
		int x = cur[0], y = cur[1], idx = cur[2];
		q.pop();

		for(auto &[dx, dy] : del){
			array<int, 2> t = {x+dx, y+dy};
			auto it = lower_bound(P.begin(), P.end(), t);
			if(it == P.end() || *it != t) 
				continue;
			int tmp = it - P.begin();
			if(!vis[tmp]){
				vis[tmp] = 1;
				adj[tmp].push_back(idx);
				adj[idx].push_back(tmp);
				// array<int, 3> p = {temp[0], temp[1], tmp};
				// q.push(p);
				q.push({t[0], t[1], tmp});
			}
		}
	}

	c.resize(N);

	dfs(0, 0, N);
	LCA D(N);

	ans = (ans + ans) % mod;
	
	for(int i = 0; i < N; i++){
		auto [x, y] = P[i];
		for(auto& [dx, dy] : del){
			array<int, 2> t = {x+dx, y+dy};
			auto it = lower_bound(P.begin(), P.end(), t);
			if(it == P.end() || *it != t)
				continue;
			ans = (ans - D.dist(it - P.begin(), i) + 1 + mod) % mod;
		}
	}
		
	ans /= 2;
	ans %= mod;
	
	return ans;
}

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