oj.uz

Submission #167807

# Submission time Handle Problem Language Result Execution time Memory
167807 2019-12-10T08:04:51 Z oolimry Split the Attractions (IOI19_split) C++14
100 / 100
 241 ms 26360 KB 
#include "split.h"
#include <bits/stdc++.h>

using namespace std;

typedef vector<int> vi;
typedef pair<int,int> ii;

static vi answer;
static vi adj[100005];
static vi child[100005];
static vi tree[100005];
static int sz[100005];
static int pa[100005];
static bool vis[100005];

class UFDS {
public:
    vi p, rak, setSize;
    int numSets;

    void create(int n){
        setSize.assign(n, 1);
        numSets = n;
        rak.assign(n, 0);
        p.assign(n, 0);
        for(int i =0;i < n;i++){
            p[i] = i;
        }
    }

    int findSet(int i){
        return (p[i] == i) ? i : (p[i] = findSet(p[i]));
    }

    bool isSameSet(int i, int j){
        return findSet(i) == findSet(j);
    }

    int unionSet(int i, int j){
        if(isSameSet(i,j))
            return 0;
        numSets--;
        int x = findSet(i);
        int y = findSet(j);

        if(rak[x] > rak[y]) {
            p[y] = x; setSize[x] += setSize[y];
        }

        else {
            p[x] = y; setSize[y] += setSize[x];
            if(rak[x] == rak[y]) rak[y]++;
        }
		return max(setSize[x],setSize[y]);
    }
};

void dfs(int u){
	vis[u] = true;
	sz[u] = 1;
	for(int v : adj[u]){
		if(!vis[v]){
			child[u].push_back(v);
			tree[u].push_back(v);
			tree[v].push_back(u);
			pa[v] = u;
			dfs(v);
			sz[u] += sz[v];
		}	
	}
}

void bfs(int root, int number){
	if(number == 0) return;
	queue<int> bf;
	bf.push(root);
	while(!bf.empty()){
		int u = bf.front(); bf.pop();
		for(int v : tree[u]){
			if(answer[v] == 0){
				answer[v] = answer[u];
				number--; ///We fill only the required number of nodes
				if(number == 0) return;
				bf.push(v);
			}
		}
	}
}
vi find_split(int n, int aaa, int bbb, int ccc, vi p, vi q) {
	
	///WLOG, let A <= B <= C. A <= N/3, B <= N/2
	vector<ii> v = {ii(aaa,1),ii(bbb,2),ii(ccc,3)};
	sort(v.begin(),v.end());
	int A = v[0].first;
	int B = v[1].first;
	int AColour = v[0].second;
	int BColour = v[1].second;
	int CColour = v[2].second;
	answer.assign(n,0);
	
	for(int i = 0;i < (int) p.size();i++){
		int x = p[i], y = q[i];
		adj[y].push_back(x);
		adj[x].push_back(y);
	}
	
	///Generate an arbitrary spanning tree T
	dfs(0);
	
	///Check if there exists an edge which splits T into 2 parts which fit both A and B
	for(int i = 0;i < (int) p.size();i++){
		int x = p[i], y = q[i];
		if(sz[y] < sz[x]) swap(x,y); ///x is child of y
		
		int l = sz[x], r = n - sz[x];
		if(l > r) swap(l,r), swap(x,y);
		
		///A split is found, bfs to find nodes to put in set A and set B
		if(l >= A && r >= B){
			answer[x] = AColour;
			answer[y] = BColour;
			bfs(x,A-1); 
			bfs(y,B-1);
			for(int i = 0;i < n;i++){
				if(answer[i] == 0) answer[i] = CColour;
			}
			return answer;
		}
	}
	
	///There must exist only one vertex R such that all of it's subtrees have a size smaller than A
	int R = -1;
	for(int u = 0;u < n;u++){
		bool can = true;
		for(int v : child[u]){
			if(sz[v] >= A){
				can = false;
				break;
			}
		}
		if(n - sz[u] >= A) can = false;
		if(can){
			R = u;
			break;
		}
	}
	
	assert(R != -1);
	
	///For all edges in our spanning tree not connected to R, we merge them using UFDS
	UFDS uf;
	uf.create(n);
	for(int i = 0;i < (int) p.size();i++){
		int u = p[i]; int v = q[i];
		if(u == R || v == R) continue;
		if(pa[u] == v || pa[v] == u){
			uf.unionSet(u,v);
		}
	}

	///For all edges not in the spanning tree not connected to R, we merge them using UFDS
	///If this creates a connected component not connected to R that is at least size A, we use that for set A
	///The other set is connected via the Root R.
	for(int i = 0;i < (int) p.size();i++){
		int u = p[i]; int v = q[i];
		if(u == R || v == R) continue;
		if(pa[u] == v || pa[v] == u) continue;
			
		tree[u].push_back(v);
		tree[v].push_back(u);
		///A split is found, find the stuff to put in set A and set B using bfs
		if(uf.unionSet(u,v) >= A){ ///uf.unionSet returns the new set size of that set
			int x = u;
			int y = R;
			answer[x] = AColour;
			answer[y] = BColour;
			bfs(x,A-1);
			bfs(y,B-1);
			for(int i = 0;i < n;i++){
				if(answer[i] == 0) answer[i] = CColour;
			}
			return answer;
		}
	}
	
	///There is no answer. We have exhausted all edges and we're left with a graph with root R, and subtrees of size < A.
	///To make a set greater than A, we need to pass through R, which means we can't make sets for B.
	return answer;
}

Subtask #1
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 8 ms 7416 KB ok, correct split
2 Correct 8 ms 7416 KB ok, correct split
3 Correct 8 ms 7412 KB ok, correct split
4 Correct 8 ms 7416 KB ok, correct split
5 Correct 8 ms 7464 KB ok, correct split
6 Correct 8 ms 7416 KB ok, correct split
7 Correct 146 ms 25984 KB ok, correct split
8 Correct 142 ms 24184 KB ok, correct split
9 Correct 145 ms 23516 KB ok, correct split
10 Correct 134 ms 26360 KB ok, correct split
11 Correct 144 ms 26204 KB ok, correct split

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 8 ms 7416 KB ok, correct split
2 Correct 8 ms 7416 KB ok, correct split
3 Correct 8 ms 7420 KB ok, correct split
4 Correct 159 ms 23032 KB ok, correct split
5 Correct 134 ms 18808 KB ok, correct split
6 Correct 142 ms 26232 KB ok, correct split
7 Correct 148 ms 24028 KB ok, correct split
8 Correct 173 ms 21364 KB ok, correct split
9 Correct 132 ms 20216 KB ok, correct split
10 Correct 87 ms 18260 KB ok, correct split
11 Correct 84 ms 18224 KB ok, correct split
12 Correct 85 ms 18288 KB ok, correct split

Subtask #3
22.0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 8 ms 7416 KB ok, correct split
2 Correct 125 ms 18708 KB ok, correct split
3 Correct 48 ms 11900 KB ok, correct split
4 Correct 8 ms 7416 KB ok, correct split
5 Correct 154 ms 22136 KB ok, correct split
6 Correct 143 ms 21880 KB ok, correct split
7 Correct 136 ms 21752 KB ok, correct split
8 Correct 157 ms 22776 KB ok, correct split
9 Correct 148 ms 21664 KB ok, correct split
10 Correct 46 ms 11640 KB ok, no valid answer
11 Correct 68 ms 13688 KB ok, no valid answer
12 Correct 116 ms 19444 KB ok, no valid answer
13 Correct 143 ms 19852 KB ok, no valid answer
14 Correct 96 ms 19180 KB ok, no valid answer

Subtask #4
24.0 / 24.0

# Verdict Execution time Memory Grader output
1 Correct 8 ms 7288 KB ok, correct split
2 Correct 8 ms 7416 KB ok, no valid answer
3 Correct 8 ms 7288 KB ok, correct split
4 Correct 8 ms 7416 KB ok, correct split
5 Correct 8 ms 7416 KB ok, correct split
6 Correct 8 ms 7416 KB ok, correct split
7 Correct 8 ms 7416 KB ok, correct split
8 Correct 8 ms 7416 KB ok, correct split
9 Correct 11 ms 7804 KB ok, correct split
10 Correct 11 ms 7696 KB ok, correct split
11 Correct 8 ms 7416 KB ok, correct split
12 Correct 11 ms 7800 KB ok, correct split
13 Correct 8 ms 7416 KB ok, correct split
14 Correct 8 ms 7388 KB ok, correct split
15 Correct 8 ms 7416 KB ok, correct split
16 Correct 8 ms 7416 KB ok, correct split
17 Correct 8 ms 7416 KB ok, correct split
18 Correct 8 ms 7416 KB ok, correct split
19 Correct 8 ms 7416 KB ok, correct split
20 Correct 9 ms 7544 KB ok, correct split
21 Correct 10 ms 7672 KB ok, correct split
22 Correct 10 ms 7748 KB ok, correct split
23 Correct 10 ms 7800 KB ok, correct split
24 Correct 10 ms 7800 KB ok, correct split
25 Correct 10 ms 7672 KB ok, correct split
26 Correct 11 ms 7672 KB ok, correct split
27 Correct 10 ms 7800 KB ok, correct split
28 Correct 11 ms 7804 KB ok, correct split
29 Correct 8 ms 7416 KB ok, correct split
30 Correct 11 ms 7672 KB ok, correct split
31 Correct 9 ms 7416 KB ok, correct split
32 Correct 8 ms 7416 KB ok, correct split
33 Correct 8 ms 7416 KB ok, correct split
34 Correct 10 ms 7672 KB ok, correct split
35 Correct 11 ms 7800 KB ok, correct split
36 Correct 10 ms 7672 KB ok, correct split
37 Correct 12 ms 7800 KB ok, correct split
38 Correct 13 ms 7800 KB ok, correct split
39 Correct 11 ms 7800 KB ok, correct split
40 Correct 11 ms 7672 KB ok, correct split
41 Correct 9 ms 7544 KB ok, correct split
42 Correct 11 ms 7672 KB ok, correct split
43 Correct 13 ms 7800 KB ok, correct split
44 Correct 11 ms 7804 KB ok, correct split
45 Correct 11 ms 7800 KB ok, correct split
46 Correct 10 ms 7800 KB ok, correct split
47 Correct 10 ms 7800 KB ok, no valid answer
48 Correct 10 ms 7672 KB ok, correct split
49 Correct 10 ms 7800 KB ok, correct split
50 Correct 8 ms 7416 KB ok, no valid answer
51 Correct 8 ms 7416 KB ok, no valid answer
52 Correct 10 ms 7672 KB ok, no valid answer
53 Correct 12 ms 7800 KB ok, no valid answer
54 Correct 10 ms 7676 KB ok, no valid answer
55 Correct 10 ms 7800 KB ok, no valid answer
56 Correct 10 ms 7672 KB ok, no valid answer

Subtask #5
36.0 / 36.0

# Verdict Execution time Memory Grader output
1 Correct 8 ms 7416 KB ok, correct split
2 Correct 8 ms 7416 KB ok, correct split
3 Correct 8 ms 7412 KB ok, correct split
4 Correct 8 ms 7416 KB ok, correct split
5 Correct 8 ms 7464 KB ok, correct split
6 Correct 8 ms 7416 KB ok, correct split
7 Correct 146 ms 25984 KB ok, correct split
8 Correct 142 ms 24184 KB ok, correct split
9 Correct 145 ms 23516 KB ok, correct split
10 Correct 134 ms 26360 KB ok, correct split
11 Correct 144 ms 26204 KB ok, correct split
12 Correct 8 ms 7416 KB ok, correct split
13 Correct 8 ms 7416 KB ok, correct split
14 Correct 8 ms 7420 KB ok, correct split
15 Correct 159 ms 23032 KB ok, correct split
16 Correct 134 ms 18808 KB ok, correct split
17 Correct 142 ms 26232 KB ok, correct split
18 Correct 148 ms 24028 KB ok, correct split
19 Correct 173 ms 21364 KB ok, correct split
20 Correct 132 ms 20216 KB ok, correct split
21 Correct 87 ms 18260 KB ok, correct split
22 Correct 84 ms 18224 KB ok, correct split
23 Correct 85 ms 18288 KB ok, correct split
24 Correct 8 ms 7416 KB ok, correct split
25 Correct 125 ms 18708 KB ok, correct split
26 Correct 48 ms 11900 KB ok, correct split
27 Correct 8 ms 7416 KB ok, correct split
28 Correct 154 ms 22136 KB ok, correct split
29 Correct 143 ms 21880 KB ok, correct split
30 Correct 136 ms 21752 KB ok, correct split
31 Correct 157 ms 22776 KB ok, correct split
32 Correct 148 ms 21664 KB ok, correct split
33 Correct 46 ms 11640 KB ok, no valid answer
34 Correct 68 ms 13688 KB ok, no valid answer
35 Correct 116 ms 19444 KB ok, no valid answer
36 Correct 143 ms 19852 KB ok, no valid answer
37 Correct 96 ms 19180 KB ok, no valid answer
38 Correct 8 ms 7288 KB ok, correct split
39 Correct 8 ms 7416 KB ok, no valid answer
40 Correct 8 ms 7288 KB ok, correct split
41 Correct 8 ms 7416 KB ok, correct split
42 Correct 8 ms 7416 KB ok, correct split
43 Correct 8 ms 7416 KB ok, correct split
44 Correct 8 ms 7416 KB ok, correct split
45 Correct 8 ms 7416 KB ok, correct split
46 Correct 11 ms 7804 KB ok, correct split
47 Correct 11 ms 7696 KB ok, correct split
48 Correct 8 ms 7416 KB ok, correct split
49 Correct 11 ms 7800 KB ok, correct split
50 Correct 8 ms 7416 KB ok, correct split
51 Correct 8 ms 7388 KB ok, correct split
52 Correct 8 ms 7416 KB ok, correct split
53 Correct 8 ms 7416 KB ok, correct split
54 Correct 8 ms 7416 KB ok, correct split
55 Correct 8 ms 7416 KB ok, correct split
56 Correct 8 ms 7416 KB ok, correct split
57 Correct 9 ms 7544 KB ok, correct split
58 Correct 10 ms 7672 KB ok, correct split
59 Correct 10 ms 7748 KB ok, correct split
60 Correct 10 ms 7800 KB ok, correct split
61 Correct 10 ms 7800 KB ok, correct split
62 Correct 10 ms 7672 KB ok, correct split
63 Correct 11 ms 7672 KB ok, correct split
64 Correct 10 ms 7800 KB ok, correct split
65 Correct 11 ms 7804 KB ok, correct split
66 Correct 8 ms 7416 KB ok, correct split
67 Correct 11 ms 7672 KB ok, correct split
68 Correct 9 ms 7416 KB ok, correct split
69 Correct 8 ms 7416 KB ok, correct split
70 Correct 8 ms 7416 KB ok, correct split
71 Correct 10 ms 7672 KB ok, correct split
72 Correct 11 ms 7800 KB ok, correct split
73 Correct 10 ms 7672 KB ok, correct split
74 Correct 12 ms 7800 KB ok, correct split
75 Correct 13 ms 7800 KB ok, correct split
76 Correct 11 ms 7800 KB ok, correct split
77 Correct 11 ms 7672 KB ok, correct split
78 Correct 9 ms 7544 KB ok, correct split
79 Correct 11 ms 7672 KB ok, correct split
80 Correct 13 ms 7800 KB ok, correct split
81 Correct 11 ms 7804 KB ok, correct split
82 Correct 11 ms 7800 KB ok, correct split
83 Correct 10 ms 7800 KB ok, correct split
84 Correct 10 ms 7800 KB ok, no valid answer
85 Correct 10 ms 7672 KB ok, correct split
86 Correct 10 ms 7800 KB ok, correct split
87 Correct 8 ms 7416 KB ok, no valid answer
88 Correct 8 ms 7416 KB ok, no valid answer
89 Correct 10 ms 7672 KB ok, no valid answer
90 Correct 12 ms 7800 KB ok, no valid answer
91 Correct 10 ms 7676 KB ok, no valid answer
92 Correct 10 ms 7800 KB ok, no valid answer
93 Correct 10 ms 7672 KB ok, no valid answer
94 Correct 151 ms 21172 KB ok, correct split
95 Correct 190 ms 25208 KB ok, correct split
96 Correct 186 ms 23928 KB ok, correct split
97 Correct 48 ms 12024 KB ok, correct split
98 Correct 53 ms 12152 KB ok, correct split
99 Correct 73 ms 13460 KB ok, correct split
100 Correct 209 ms 21712 KB ok, correct split
101 Correct 172 ms 20968 KB ok, correct split
102 Correct 197 ms 20592 KB ok, correct split
103 Correct 147 ms 20336 KB ok, correct split
104 Correct 137 ms 20248 KB ok, correct split
105 Correct 85 ms 15096 KB ok, correct split
106 Correct 152 ms 21640 KB ok, correct split
107 Correct 146 ms 19960 KB ok, correct split
108 Correct 147 ms 19984 KB ok, correct split
109 Correct 196 ms 22616 KB ok, correct split
110 Correct 214 ms 23280 KB ok, correct split
111 Correct 190 ms 23280 KB ok, correct split
112 Correct 193 ms 22132 KB ok, correct split
113 Correct 186 ms 22000 KB ok, correct split
114 Correct 22 ms 9080 KB ok, correct split
115 Correct 21 ms 8824 KB ok, correct split
116 Correct 178 ms 23084 KB ok, correct split
117 Correct 190 ms 23152 KB ok, correct split
118 Correct 150 ms 20088 KB ok, correct split
119 Correct 146 ms 20088 KB ok, correct split
120 Correct 149 ms 23288 KB ok, correct split
121 Correct 140 ms 20012 KB ok, no valid answer
122 Correct 131 ms 19704 KB ok, no valid answer
123 Correct 241 ms 24724 KB ok, no valid answer
124 Correct 241 ms 24440 KB ok, no valid answer
125 Correct 130 ms 20620 KB ok, no valid answer
126 Correct 101 ms 17972 KB ok, no valid answer
127 Correct 144 ms 21200 KB ok, no valid answer