Submission #296828

#	Time	Username	Problem	Language	Result	Execution time	Memory
296828		rqi	Split the Attractions (IOI19_split)	C++14	100 / 100	293 ms	29004 KiB

split

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

typedef vector<int> vi;
typedef pair<int, int> pi;
typedef vector<pi> vpi;

#define pb push_back
#define sz(x) (int)(x).size()
#define mp make_pair
#define f first
#define s second
#define all(x) begin(x), end(x)

const int mx = 100005;

struct DSU{
	vi e;
	void init(int n){
		e = vi(n, -1);
	}
	int get(int a){
		if(e[a] < 0) return a;
		e[a] = get(e[a]);
		return e[a];
	}
	int getSz(int a){
		return -e[get(a)];
	}
	bool sameSet(int a, int b){
		return get(a) == get(b);
	}
	bool unite(int a, int b){
		a = get(a);
		b = get(b);
		if(a == b) return 0;
		if(-e[a] < -e[b]) swap(a, b); //a now has bigger size
		e[a]+=e[b];
		e[b] = a;
		return 1;
	}
};



int n, a, b, c;
vi L;
vi res;

vi oadj[mx];

vi tadj[mx]; //tree edges

DSU dsu;
vpi extr;

int sub[mx];

void genSub(int node, int prv = -1){
	sub[node] = 1;
	for(auto u: tadj[node]){
		if(u == prv) continue;
		genSub(u, node);
		sub[node]+=sub[u];
	}
}

int getCen(int node, int prv = -1){
	for(auto u: tadj[node]){
		if(u == prv) continue;
		if(sub[u] >= n-sub[u]) return getCen(u, node);
	}
	return node;
}

int und[mx]; //underneath a node under cen
vi rund[mx];

vi sadj[mx]; //adjacent things in cnt graph

void genUnd(int node, int val, int prv = -1){
	und[node] = val;
	rund[val].pb(node);
	for(auto u: tadj[node]){
		if(u == prv) continue;
		genUnd(u, val, node);
	}
}

bool good[mx];
int curw;
bool inSet[mx];

void getW(int node){
	if(!good[node]) return;
	if(inSet[node]) return;
	if(curw >= L[0]) return;

	inSet[node] = 1;
	curw+=sub[node];

	for(auto u: sadj[node]){
		getW(u);
	}
}

int ocount = 0;

void getOnes(int node){
	if(und[node] == -1) return;
	if(!inSet[und[node]]) return;
	if(ocount >= L[0]) return;
	if(res[node] == 1) return;
	//cout << node << "\n";
	ocount++;
	res[node] = 1;
	for(auto u: oadj[node]){
		getOnes(u);
	}
}

int tcount = 0;

void assign2(int node){
	if(tcount >= L[1]) return;
	if(res[node] != 0) return;
	//cout << node << "\n";
	res[node] = 2;
	tcount++;
	for(auto u: tadj[node]){
		assign2(u);
	}
}

void adjustRes(){
	vi to(4, 0);
	vi vals(4, 0);
	for(auto u: res) vals[u]++;
	vpi cnt1, cnt2;
	cnt1.pb(mp(a, 1)); cnt1.pb(mp(b, 2)); cnt1.pb(mp(c, 3));
	cnt2.pb(mp(vals[1], 1)); cnt2.pb(mp(vals[2], 2)); cnt2.pb(mp(vals[3], 3));
	sort(all(cnt1));
	sort(all(cnt2));
	for(int i = 0; i < 3; i++){
		to[cnt2[i].s] = cnt1[i].s;
	}
 
	for(auto &u: res) u = to[u];
}

bool visited[mx];

void crvisit(int node){
	if(visited[node]) return;
	visited[node] = 1;
	for(auto u: oadj[node]){
		if(res[node] == res[u]){
			crvisit(u);
		}
	}
}

bool checkRes(){
	vector<bool> works = vector<bool>(4, 1);
	for(int j = 1; j <= 3; j++){
		for(int i = 0; i < n; i++){
			if(res[i] == j){
				crvisit(i);
				break;
			}
		}
	}
	for(int i = 0; i < n; i++){
		if(!visited[i]){
			works[res[i]] = 0;
		}
	}

	int cnt = 0;
	for(int j = 1; j <= 3; j++){
		if(works[j]) cnt++;
	}
	if(cnt >= 2) return 1;
	return 0;
}

vi find_split(int _n, int _a, int _b, int _c, vi p, vi q) {
	n = _n, a = _a, b = _b, c = _c;
	L = vi{a, b, c};
	sort(all(L));
	res = vi(n, 0);

	dsu.init(n);
	for(int i = 0; i < sz(p); i++){
		oadj[p[i]].pb(q[i]);
		oadj[q[i]].pb(p[i]);
		if(dsu.unite(p[i], q[i])){
			tadj[p[i]].pb(q[i]);
			tadj[q[i]].pb(p[i]);
			//cout << p[i] << " " << q[i] << "\n";
		}
		else{
			extr.pb(mp(p[i], q[i]));
			//cout << p[i] << " " << q[i] << "\n";
		}
	}

	genSub(0);
	int cen = getCen(0);

	und[cen] = -1;
	for(auto u: tadj[cen]){
		genUnd(u, u, cen);
		//cout << u << " " << u << "\n";
	}

	//cout << cen << "\n";
	genSub(cen);

	dsu.init(n);

	for(auto u: tadj[cen]){
		dsu.e[u] = -sub[u];
		//cout << u << " " << dsu.e[u] << "\n";
	}

	for(auto u: extr){
		if(u.f == cen || u.s == cen) continue;
		dsu.unite(und[u.f], und[u.s]);
		sadj[und[u.f]].pb(und[u.s]);
		sadj[und[u.s]].pb(und[u.f]);
		// cout << und[u.f] << " " << und[u.s] << "\n";
	}

	for(auto u: tadj[cen]){
		if(dsu.getSz(u) >= L[0]){
			//cout << u << "\n";
			for(auto x: tadj[cen]){
				if(dsu.sameSet(u, x)){
					//cout << x << "\n";
					good[x] = 1;
				}
			}

			curw = 0;
			getW(u);

			//for(int i = 0; i < n; i++) if(inSet[i]) cout << i << "\n";

			ocount = 0;
			getOnes(u);

			assign2(cen);
			for(auto &u: res) if(u == 0) u = 3;
				// for(auto u: res) cout << u << " ";
				// cout << "\n";
			adjustRes();

			// for(auto u: res) cout << u << " ";
			// cout << "\n";
			assert(checkRes());
			
			return res;
		}
	}

	// for(auto u: res) cout << u << " ";
	// cout << "\n";

	return res;

}

• Subtask 1: 7 / 7
• Subtask 2: 11 / 11
• Subtask 3: 22 / 22
• Subtask 4: 24 / 24
• Subtask 5: 36 / 36