oj.uz

Submission #447695

# Submission time Handle Problem Language Result Execution time Memory
447695 2021-07-27T10:54:10 Z blue Keys (IOI21_keys) C++17
100 / 100
 1670 ms 144312 KB 
#include "keys.h"
#include <set>
#include <iostream>
using namespace std;

const int maxN = 300'000;

int N;
int M;






struct edge
{
	int v;
	int c;
};

bool operator < (edge A, edge B)
{
	return A.c < B.c;
}

set<int> good_edge[maxN]; //over SCCs, does not use labels
multiset<edge> bad_edge[maxN];
set<int> keys[maxN];


vector<int> scc_label(maxN);
vector<int> scc_list[maxN];


vector<int> wcc_label(maxN);
vector<int> wcc_list[maxN];

vector<int> func_parent(maxN); //itself if this is a root.   //access only by label.


void scc_join(int u, int v)
{
	u = scc_label[u];
	v = scc_label[v];

	if(u == v) return;

	if(scc_list[u].size() < scc_list[v].size()) swap(u, v);


	int new_func_parent;
	if(scc_label[ func_parent[u] ] == v)
		new_func_parent = scc_label[ func_parent[v] ];
	else
		new_func_parent = scc_label[ func_parent[u] ];

	//also handle good edges, bad edges, keys



	for(int k: keys[v])
	{
		while(1)
		{
			multiset<edge>::iterator it = bad_edge[u].find(edge{-1, k});
			if(it == bad_edge[u].end()) break;
			good_edge[u].insert(it->v);
			bad_edge[u].erase(it);
		}

		keys[u].insert(k);
	}
	keys[v].clear();



	for(int g: good_edge[v])
	{
		good_edge[u].insert(g);
	}
	good_edge[v].clear();



	for(edge b: bad_edge[v])
	{
		if(keys[u].find(b.c) == keys[u].end())
			bad_edge[u].insert(b);
		else
			good_edge[u].insert(b.v);
	}
	bad_edge[v].clear();



	for(int x: scc_list[v])
	{
		scc_label[x] = u;
		scc_list[u].push_back(x);
	}
	scc_list[v].clear();



	func_parent[u] = new_func_parent;

	// cerr << "after joining " << v << " and  " << u << '\n';
	// for(int i = 0; i < N; i++)
	// 	cerr << i << ' ' << scc_label[i] << ' ' << wcc_label[i] << ' ' << func_parent[ scc_label[i] ] << '\n';
	// cerr << "\n\n\n";
}

void wcc_join(int u, int v)
{
	u = wcc_label[u];
	v = wcc_label[v];

	if(u == v) return;

	if(wcc_list[u].size() < wcc_list[v].size()) swap(u, v);

	for(int x: wcc_list[v])
	{
		wcc_label[x] = u;
		wcc_list[u].push_back(x);
	}
	wcc_list[v].clear();
}



bool in_wcc(int v, int u) //return whether v is in the WCC rooted at u (u and v are both scc labels)
{
	// cerr << "in wcc " << v << ' ' << u << ' ' << ((wcc_label[v] == wcc_label[u]) && (scc_label[func_parent[scc_label[u]]] == scc_label[u])) << '\n';
	// cerr << wcc_label[v] << ' ' << wcc_label[u] << '\n';
	return (wcc_label[v] == wcc_label[u]) && (scc_label[func_parent[u]] == u);
}

void compress(int v) //compress the chain from v to the root (v is a scc label)
{
	// cerr << "compress " << v << '\n';
	v = scc_label[v];
	// cerr << "compressing " << v << '\n';
	if(scc_label[ func_parent[v] ] == v) return;
	while(1)
	{
		// cerr << "? " << v << ' ' << scc_label[ func_parent[v] ] << '\n';
		if(scc_label[ func_parent[v] ] == v) return;
		else
		{
			scc_join(v, scc_label[ func_parent[v] ]);
			v = scc_label[v];
		}
	}
}

void addChild(int u, int v) //add v as a functional graph child of u
{
	u = scc_label[u];
	v = scc_label[v];

	func_parent[v] = u;

	wcc_join(u, v);

	// cerr << "after adding " << v << " as child of " << u << '\n';
	// for(int i = 0; i < N; i++)
	// 	cerr << i << ' ' << scc_label[i] << ' ' << wcc_label[i] << ' ' << func_parent[ scc_label[i] ] << '\n';
	// cerr << "\n\n\n";
}


vector<int> find_reachable(vector<int> r1, vector<int> u1, vector<int> v1, vector<int> c1)
{
	N = r1.size();
	M = u1.size();

	for(int i = 0; i < N; i++)
	{
		keys[i].insert(r1[i]);

		scc_label[i] = i;
		scc_list[i].push_back(i);

		wcc_label[i] = i;
		wcc_list[i].push_back(i);

		func_parent[i] = i;
	}


	for(int j = 0; j < M; j++)
	{
		if(keys[ u1[j] ].find( c1[j] ) == keys[ u1[j] ].end())
		{
			bad_edge[ u1[j] ].insert( edge{v1[j], c1[j]} );
		}
		else
		{
			good_edge[ u1[j] ].insert( v1[j] );
		}

		if(keys[ v1[j] ].find( c1[j] ) == keys[ v1[j] ].end())
		{
			bad_edge[ v1[j] ].insert( edge{u1[j], c1[j]} );
		}
		else
		{
			good_edge[ v1[j] ].insert( u1[j] );
		}
	}



	// cerr << "\n\n\n";
	// cerr << "initial state: \n";
	// for(int i = 0; i < N; i++)
	// 	cerr << i << ' ' << scc_label[i] << ' ' << wcc_label[i] << ' ' << func_parent[ scc_label[i] ] << '\n';
	// cerr << "\n\n\n";



	for(int u_temp = 0; u_temp < N; u_temp++)
	{
		int u = u_temp;

		if(scc_label[u] != u) continue; //u is a scc label
		if(scc_label[ func_parent[u] ] != u) continue; //u is a functional graph root.

		// cerr << "\n\n\n\n\n\n\n";
		// cerr << "new value of u = " << u << '\n';

		while(!good_edge[u].empty())
		{
			int v = *good_edge[u].begin();
			good_edge[u].erase(v);

			v = scc_label[v];

			if(v == u) continue;

			if(in_wcc(v, u))
				compress(v);
			else
			{
				addChild(v, u);
				// cerr << "breaking\n";
				break;
			}

			u = scc_label[u]; //IMPORTANT!
		}
	}


	vector<int> res_list;
	int min_reach = N;
	for(int i = 0; i < N; i++)
	{
		if(scc_label[ func_parent[ scc_label[i] ] ] != scc_label[i]) continue;

		if(scc_list[ scc_label[i] ].size() < min_reach)
		{
			min_reach = scc_list[ scc_label[i] ].size();
			res_list.clear();
			res_list.push_back(i);
		}
		else if(scc_list[ scc_label[i] ].size() == min_reach)
		{
			res_list.push_back(i);
		}
	}

	vector<int> res(N, 0);
	for(int R: res_list)
		res[R] = 1;

	return res;
}

Compilation message

keys.cpp: In function 'std::vector<int> find_reachable(std::vector<int>, std::vector<int>, std::vector<int>, std::vector<int>)':
keys.cpp:263:38: warning: comparison of integer expressions of different signedness: 'std::vector<int>::size_type' {aka 'long unsigned int'} and 'int' [-Wsign-compare]
  263 |   if(scc_list[ scc_label[i] ].size() < min_reach)
      |      ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~^~~~~~~~~~~
keys.cpp:269:43: warning: comparison of integer expressions of different signedness: 'std::vector<int>::size_type' {aka 'long unsigned int'} and 'int' [-Wsign-compare]
  269 |   else if(scc_list[ scc_label[i] ].size() == min_reach)
      |           ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~^~~~~~~~~~~~

Subtask #1
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 32 ms 60100 KB Output is correct
2 Correct 32 ms 60172 KB Output is correct
3 Correct 31 ms 60172 KB Output is correct
4 Correct 34 ms 60204 KB Output is correct
5 Correct 34 ms 60128 KB Output is correct
6 Correct 33 ms 60076 KB Output is correct
7 Correct 32 ms 60172 KB Output is correct
8 Correct 34 ms 60156 KB Output is correct
9 Correct 32 ms 60224 KB Output is correct

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 32 ms 60100 KB Output is correct
2 Correct 32 ms 60172 KB Output is correct
3 Correct 31 ms 60172 KB Output is correct
4 Correct 34 ms 60204 KB Output is correct
5 Correct 34 ms 60128 KB Output is correct
6 Correct 33 ms 60076 KB Output is correct
7 Correct 32 ms 60172 KB Output is correct
8 Correct 34 ms 60156 KB Output is correct
9 Correct 32 ms 60224 KB Output is correct
10 Correct 33 ms 60172 KB Output is correct
11 Correct 32 ms 60164 KB Output is correct
12 Correct 31 ms 60108 KB Output is correct
13 Correct 34 ms 60056 KB Output is correct
14 Correct 33 ms 60064 KB Output is correct
15 Correct 32 ms 60176 KB Output is correct
16 Correct 33 ms 60068 KB Output is correct
17 Correct 33 ms 60196 KB Output is correct
18 Correct 32 ms 60108 KB Output is correct
19 Correct 34 ms 60084 KB Output is correct
20 Correct 33 ms 60192 KB Output is correct
21 Correct 33 ms 60164 KB Output is correct
22 Correct 32 ms 60256 KB Output is correct
23 Correct 33 ms 60224 KB Output is correct
24 Correct 32 ms 60180 KB Output is correct
25 Correct 33 ms 60160 KB Output is correct
26 Correct 33 ms 60164 KB Output is correct

Subtask #3
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 32 ms 60100 KB Output is correct
2 Correct 32 ms 60172 KB Output is correct
3 Correct 31 ms 60172 KB Output is correct
4 Correct 34 ms 60204 KB Output is correct
5 Correct 34 ms 60128 KB Output is correct
6 Correct 33 ms 60076 KB Output is correct
7 Correct 32 ms 60172 KB Output is correct
8 Correct 34 ms 60156 KB Output is correct
9 Correct 32 ms 60224 KB Output is correct
10 Correct 33 ms 60172 KB Output is correct
11 Correct 32 ms 60164 KB Output is correct
12 Correct 31 ms 60108 KB Output is correct
13 Correct 34 ms 60056 KB Output is correct
14 Correct 33 ms 60064 KB Output is correct
15 Correct 32 ms 60176 KB Output is correct
16 Correct 33 ms 60068 KB Output is correct
17 Correct 33 ms 60196 KB Output is correct
18 Correct 32 ms 60108 KB Output is correct
19 Correct 34 ms 60084 KB Output is correct
20 Correct 33 ms 60192 KB Output is correct
21 Correct 33 ms 60164 KB Output is correct
22 Correct 32 ms 60256 KB Output is correct
23 Correct 33 ms 60224 KB Output is correct
24 Correct 32 ms 60180 KB Output is correct
25 Correct 33 ms 60160 KB Output is correct
26 Correct 33 ms 60164 KB Output is correct
27 Correct 34 ms 60648 KB Output is correct
28 Correct 33 ms 60620 KB Output is correct
29 Correct 34 ms 60644 KB Output is correct
30 Correct 34 ms 60328 KB Output is correct
31 Correct 36 ms 60328 KB Output is correct
32 Correct 32 ms 60228 KB Output is correct
33 Correct 33 ms 60312 KB Output is correct
34 Correct 33 ms 60388 KB Output is correct
35 Correct 33 ms 60348 KB Output is correct
36 Correct 36 ms 60584 KB Output is correct
37 Correct 36 ms 60628 KB Output is correct
38 Correct 36 ms 60712 KB Output is correct
39 Correct 36 ms 60656 KB Output is correct
40 Correct 34 ms 60356 KB Output is correct
41 Correct 37 ms 60464 KB Output is correct

Subtask #4
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 32 ms 60100 KB Output is correct
2 Correct 32 ms 60172 KB Output is correct
3 Correct 31 ms 60172 KB Output is correct
4 Correct 34 ms 60204 KB Output is correct
5 Correct 34 ms 60128 KB Output is correct
6 Correct 33 ms 60076 KB Output is correct
7 Correct 32 ms 60172 KB Output is correct
8 Correct 34 ms 60156 KB Output is correct
9 Correct 32 ms 60224 KB Output is correct
10 Correct 672 ms 114712 KB Output is correct
11 Correct 794 ms 140544 KB Output is correct
12 Correct 147 ms 74436 KB Output is correct
13 Correct 703 ms 131928 KB Output is correct
14 Correct 336 ms 140540 KB Output is correct

Subtask #5
33.0 / 33.0

# Verdict Execution time Memory Grader output
1 Correct 32 ms 60100 KB Output is correct
2 Correct 32 ms 60172 KB Output is correct
3 Correct 31 ms 60172 KB Output is correct
4 Correct 34 ms 60204 KB Output is correct
5 Correct 34 ms 60128 KB Output is correct
6 Correct 33 ms 60076 KB Output is correct
7 Correct 32 ms 60172 KB Output is correct
8 Correct 34 ms 60156 KB Output is correct
9 Correct 32 ms 60224 KB Output is correct
10 Correct 33 ms 60172 KB Output is correct
11 Correct 32 ms 60164 KB Output is correct
12 Correct 31 ms 60108 KB Output is correct
13 Correct 34 ms 60056 KB Output is correct
14 Correct 33 ms 60064 KB Output is correct
15 Correct 32 ms 60176 KB Output is correct
16 Correct 33 ms 60068 KB Output is correct
17 Correct 33 ms 60196 KB Output is correct
18 Correct 32 ms 60108 KB Output is correct
19 Correct 34 ms 60084 KB Output is correct
20 Correct 33 ms 60192 KB Output is correct
21 Correct 33 ms 60164 KB Output is correct
22 Correct 32 ms 60256 KB Output is correct
23 Correct 33 ms 60224 KB Output is correct
24 Correct 32 ms 60180 KB Output is correct
25 Correct 33 ms 60160 KB Output is correct
26 Correct 33 ms 60164 KB Output is correct
27 Correct 34 ms 60648 KB Output is correct
28 Correct 33 ms 60620 KB Output is correct
29 Correct 34 ms 60644 KB Output is correct
30 Correct 34 ms 60328 KB Output is correct
31 Correct 36 ms 60328 KB Output is correct
32 Correct 32 ms 60228 KB Output is correct
33 Correct 33 ms 60312 KB Output is correct
34 Correct 33 ms 60388 KB Output is correct
35 Correct 33 ms 60348 KB Output is correct
36 Correct 36 ms 60584 KB Output is correct
37 Correct 36 ms 60628 KB Output is correct
38 Correct 36 ms 60712 KB Output is correct
39 Correct 36 ms 60656 KB Output is correct
40 Correct 34 ms 60356 KB Output is correct
41 Correct 37 ms 60464 KB Output is correct
42 Correct 672 ms 114712 KB Output is correct
43 Correct 794 ms 140544 KB Output is correct
44 Correct 147 ms 74436 KB Output is correct
45 Correct 703 ms 131928 KB Output is correct
46 Correct 336 ms 140540 KB Output is correct
47 Correct 32 ms 60116 KB Output is correct
48 Correct 32 ms 60052 KB Output is correct
49 Correct 33 ms 60156 KB Output is correct
50 Correct 362 ms 140364 KB Output is correct
51 Correct 398 ms 143552 KB Output is correct
52 Correct 425 ms 113476 KB Output is correct
53 Correct 431 ms 113464 KB Output is correct
54 Correct 430 ms 113480 KB Output is correct
55 Correct 827 ms 115820 KB Output is correct
56 Correct 681 ms 144312 KB Output is correct
57 Correct 628 ms 141016 KB Output is correct
58 Correct 661 ms 140908 KB Output is correct
59 Correct 1670 ms 133924 KB Output is correct
60 Correct 1316 ms 133672 KB Output is correct
61 Correct 1411 ms 133916 KB Output is correct
62 Correct 1459 ms 123188 KB Output is correct
63 Correct 338 ms 123072 KB Output is correct
64 Correct 38 ms 61524 KB Output is correct
65 Correct 38 ms 61508 KB Output is correct
66 Correct 1482 ms 123724 KB Output is correct
67 Correct 61 ms 68164 KB Output is correct
68 Correct 79 ms 73648 KB Output is correct
69 Correct 1551 ms 134636 KB Output is correct
70 Correct 130 ms 87272 KB Output is correct
71 Correct 330 ms 142040 KB Output is correct
72 Correct 1579 ms 134280 KB Output is correct
73 Correct 1452 ms 123676 KB Output is correct