Submission #296142

#	Time	Username	Problem	Language	Result	Execution time	Memory
296142		MoNsTeR_CuBe	Split the Attractions (IOI19_split)	C++17	53 / 100	223 ms	31352 KiB

split

#include "split.h"
#include <bits/stdc++.h>

using namespace std;

vector< int > U;
vector< int > unionSize;

int getParents(int a){
	if(U[a] == a) return a;
	else return U[a] = getParents(U[a]);
}

void Union(int a, int b){
	if(getParents(a) == getParents(b)) return;
	unionSize[getParents(b)] += unionSize[getParents(a)];
	U[getParents(a)] = getParents(b);
}

void compute_tree(int root, int last, vector< bool > &visited, vector< vector< int > > &Graph, vector< vector< int > > &Tree, vector< pair<int, int> > &back_edges){
		visited[root] = true;
		for(int a : Graph[root]){
			if(visited[a] && a != last){
				back_edges.push_back({root, a});
				continue;
			}else if(visited[a]) continue;
			Tree[root].push_back(a);
			Tree[a].push_back(root);
			compute_tree(a,root, visited, Graph, Tree, back_edges);
		}
		
}

void compute_subtrees(int root, int last, vector< vector< int > > &Tree, vector< int > &dp){
	//cout << "ROOT " << root << ' ' << last << endl;
	for(int a : Tree[root]){
		if(a == last){
			continue;
		}
		else{
			compute_subtrees(a, root, Tree, dp);
			dp[root] += dp[a];
		}
	}
}

int find_centroid(int root, int last, vector< vector< int > > &Tree, vector< int > &dp, int &n){
	
	for(int a : Tree[root]){
		if(a == last) continue;
		if(dp[a] > n/2){
			return find_centroid(a, root, Tree,dp,n);
		}
	}
	return root;
}

void compute_centroid_graph(int root, vector< vector< int > > &Tree, vector< vector< int > > &centroidGraph,vector< bool > &visitedCentroid, const int &centroid, vector< pair<int, int> > &centroidEdges){
	visitedCentroid[root] = true;
	for(int a : Tree[root]){
		if(visitedCentroid[a]) continue;
		if(a == centroid){
			centroidEdges.push_back({a,root});
			continue;
		}
		//cout << "ROOT " << root << " " << a << endl;
		centroidGraph[a].push_back(root);
		centroidGraph[root].push_back(a);
		compute_centroid_graph(a, Tree, centroidGraph, visitedCentroid, centroid, centroidEdges);
	}
}

int computeSizeSubtree(int root, vector< vector< int > > &centroidGraph, vector< bool > &visitedSubset, const int bigRoot){
	int tot = 1;
	visitedSubset[root] = true;
	Union(root, bigRoot);
	//cout << "SUBTREE " << root << endl;
	//cout << centroidGraph[root].size() << endl;
	for(int a : centroidGraph[root]){
		if(visitedSubset[a]) continue;
		//cout << root << ' ' << a << endl;
		tot += computeSizeSubtree(a, centroidGraph, visitedSubset, bigRoot);
	}
	return tot;
}

void colourGraph(int root, vector< vector< int > > &centroidGraph, vector< bool > &visitedColouring, vector< int > &ans, const int colour, int &total){
	if(total == 0) return;
	visitedColouring[root] = true;
	ans[root] = colour;
	total--;
	//cout << "COLOURING " << root << " in " << colour << endl;
	if(total == 0) return;
	for(int a : centroidGraph[root]){
		if(visitedColouring[a]) continue;
		colourGraph(a, centroidGraph, visitedColouring, ans, colour, total);
	}
}

vector<int> find_split(int n, int a, int b, int c, vector<int> p, vector<int> q) {
	
	vector< pair<int, int> > sorting = {{a,1},{b,2},{c,3}};
	sort(sorting.begin(), sorting.end());
	a = sorting[0].first;
	b = sorting[1].first;
	c = sorting[2].first;
	
	vector< vector< int > > Graph(n);
	vector< bool > visited(n,false);
	
	for(int i = 0; i < (int)p.size(); i++){
		Graph[p[i]].push_back(q[i]);
		Graph[q[i]].push_back(p[i]);
	}
	
	//TRANSFORM THE GRAPH TO A TREE
	
	vector< vector< int > > Tree(n);
	vector< pair<int, int> > back_edges;
	//cout << "OK" << endl;
	compute_tree(0,-1, visited, Graph, Tree, back_edges);
	//cout << "OK" << endl;
	//for(auto e: back_edges) cout << e.first << ' ' << e.second << endl;
	
	//COMPUTE SIZE OF SUBTREES
	
	vector< int > dp(n, 1);
	compute_subtrees(0,-1,Tree,dp);
	
	//FIND THE CENTROID
	int centroid = find_centroid(0,-1, Tree, dp,n);
	//cout << "CENTROID " << centroid << endl;
	//COMPUTE CENTROID GRAPH
	vector< vector< int > > centroidGraph(n);
	vector< bool > visitedCentroid(n,false);
	
	vector< pair<int, int> > centroidEdges;
	
	for(int i = 0; i < n; i++){
		if(!visitedCentroid[i] && i != centroid){
			compute_centroid_graph(i,Tree, centroidGraph,visitedCentroid, centroid, centroidEdges);
		}
	}
	//COMPUTE SIZE AND ROOT OF EACH SUBSET
	
	U.resize(n);
	unionSize.resize(n,1);
	for(int i = 0; i < n; i++) U[i] = i;
	
	vector< pair<int, int> > sizeAndRootOfSubset;
	vector< bool > visitedSubset(n, false);
	
	for(int i = 0; i < n; i++){
		if(!visitedSubset[i]){
			int size = computeSizeSubtree(i, centroidGraph, visitedSubset, i);
			sizeAndRootOfSubset.push_back({size,i});
			//cout << "SIZE " << size << ' ' << "ROOT " << i << endl;
		}
	}
	//cout << "OK" << endl;
	//CHECK IF ONE OF THEM IS SMALLER THAN A
	sort(sizeAndRootOfSubset.begin(), sizeAndRootOfSubset.end());
	if(sizeAndRootOfSubset.back().first >= a){
		vector< int > ans(n,-1);
		vector< bool > visitedColouring(n,false);
		colourGraph(sizeAndRootOfSubset.back().second,  centroidGraph, visitedColouring, ans, sorting[0].second, a);
		
		//ADD EDGES TO CENTROID
		for(auto e : centroidEdges){
			centroidGraph[e.first].push_back(e.second);
			centroidGraph[e.second].push_back(e.first);
		}
		int left = b;
		//cout << left << endl;
		colourGraph(centroid, centroidGraph, visitedColouring, ans, sorting[1].second, left);
		assert(left == 0);
		//REPLACE ALL -1 by 3
		for(int &A : ans){
			if(A == -1) A=sorting[2].second;
		}
		return ans;
	}
	for(auto e : back_edges){
		if(e.first == centroid || e.second == centroid) continue;
		centroidGraph[e.first].push_back(e.second);
		centroidGraph[e.second].push_back(e.first);
		if(getParents(e.first) == getParents(e.second)){
			continue;
		}
		else{
			Union(e.first, e.second);
			if(unionSize[getParents(e.first)] >= a){
				vector< int > ans(n,-1);
				vector< bool > visitedColouring(n,false);
				colourGraph(getParents(e.first),  centroidGraph, visitedColouring, ans, sorting[0].second, a);
				
				for(auto E : centroidEdges){
					centroidGraph[E.first].push_back(E.second);
					centroidGraph[E.second].push_back(E.first);
				}
				int left = b;
				colourGraph(centroid, centroidGraph, visitedColouring, ans, sorting[1].second, left);
				
				//REPLACE ALL -1 by 3
				for(int &A : ans){
					if(A == -1) A=sorting[2].second;
				}
				return ans;
			}
		}
	}
	vector< int > ans(n);
	return ans;
}

• Subtask 1: 7 / 7
• Subtask 2: 0 / 11
• Subtask 3: 22 / 22
• Subtask 4: 24 / 24
• Subtask 5: 0 / 36