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Submission #59973

# Submission time Handle Problem Language Result Execution time Memory
59973 2018-07-23T11:52:07 Z Eae02 Circle selection (APIO18_circle_selection) C++14
19 / 100
 3000 ms 21676 KB 
#include <bits/stdc++.h>
#define ALL(x) x.begin(),x.end()

struct Circle
{
	int64_t x;
	int64_t y;
	int64_t r;
	int64_t i;
	int64_t elimBy;
	
	int64_t minX() const { return x - r; }
	int64_t maxX() const { return x + r; }
	int64_t minY() const { return y - r; }
	int64_t maxY() const { return y + r; }
	
	bool intersects(const Circle& other) const
	{
		int64_t dx = x - other.x;
		int64_t dy = y - other.y;
		int64_t rSum = r + other.r;
		return dx * dx + dy * dy <= rSum * rSum;
	}
	
	bool contains(int64_t x, int64_t y) const
	{
		int64_t dx = x - this->x;
		int64_t dy = y - this->y;
		return dx * dx + dy * dy <= r * r;
	}
};

Circle* outerCircle;

struct OctNode
{
	int64_t minX;
	int64_t minY;
	int64_t maxX;
	int64_t maxY;
	std::vector<Circle*> circles;
	OctNode* children = nullptr;
	
	bool intersects(const Circle& c)
	{
		if (c.contains(minX, minY) || c.contains(minX, maxY - 1) || c.contains(maxX - 1, minY) || c.contains(maxX - 1, maxY - 1))
			return true;
		if (c.x >= minX && c.x < maxX && c.y >= minY && c.y < maxY)
			return true;
		return false;
	}
	
	bool contains(int64_t x, int64_t y, int64_t r)
	{
		return x - r >= minX && x + r < maxX && y - r >= minY && y + r < maxY;
	}
	
	void mark()
	{
		if (children)
		{
			for (int i = 0; i < 4; i++)
			{
				if (children[i].intersects(*outerCircle))
					children[i].mark();
			}
		}
		
		for (long i = circles.size() - 1; i >= 0; i--)
		{
			if (circles[i]->elimBy == -1 && circles[i]->intersects(*outerCircle))
			{
				circles[i]->elimBy = outerCircle->i;
				circles[i] = circles.back();
				circles.pop_back();
			}
		}
	}
};

void genOctree(OctNode* node)
{
	int64_t halfSX = (node->maxX - node->minX) / 2;
	int64_t halfSY = (node->maxY - node->minY) / 2;
	int64_t midX = node->minX + halfSX;
	int64_t midY = node->minY + halfSY;
	
	bool subdivide = false;
	for (Circle* circle : node->circles)
	{
		if (circle->maxX() < midX || circle->minX() > midX || circle->maxY() > midY || circle->minY() < midY)
		{
			subdivide = true;
			break;
		}
	}
	
	if (!subdivide)
		return;
	
	node->children = new OctNode[4];
	for (int i = 0; i < 4; i++)
	{
		node->children[i].minX = (i % 2) ? midX : node->minX;
		node->children[i].maxX = (i % 2) ? node->maxX : midX;
		node->children[i].minY = (i / 2) ? midY : node->minY;
		node->children[i].maxY = (i / 2) ? node->maxY : midY;
		
		node->children[i].circles.reserve(node->circles.size());
		
		for (int j = node->circles.size() - 1; j >= 0; j--)
		{
			if (node->contains(node->circles[j]->x, node->circles[j]->y, node->circles[j]->r))
			{
				node->children[i].circles.push_back(node->circles[j]);
				node->circles[j] = node->circles.back();
				node->circles.pop_back();
			}
		}
	}
}

int main()
{
	int num;
	std::cin >> num;
	std::vector<Circle> circles(num);
	std::vector<Circle*> cByMin(num);
	std::vector<Circle*> cByMax(num);
	
	bool allZeroY = true;
	int64_t sameRad = -1;
	
	for (int i = 0; i < num; i++)
	{
		std::cin >> circles[i].x;
		std::cin >> circles[i].y;
		std::cin >> circles[i].r;
		circles[i].i = i;
		circles[i].elimBy = -1;
		cByMin[i] = &circles[i];
		cByMax[i] = &circles[i];
		
		if (i == 0)
			sameRad = circles[i].r;
		else if (sameRad != circles[i].r)
			sameRad = -1;
		
		if (circles[i].y != 0)
			allZeroY = false;
	}
	
	if (sameRad == -1)
	{
		std::sort(ALL(circles), [&] (const Circle& a, const Circle& b)
		{
			if (a.r == b.r)
				return a.i < b.i;
			return a.r > b.r;
		});
	}
	
	if (allZeroY)
	{
		std::sort(ALL(cByMin), [&] (const Circle* a, const Circle* b)
		{
			return a->minX() < b->minX();
		});
		
		std::sort(ALL(cByMax), [&] (const Circle* a, const Circle* b)
		{
			return a->maxX() < b->maxX();
		});
		
		for (Circle& outer : circles)
		{
			if (outer.elimBy != -1)
				continue;
			outer.elimBy = outer.i;
			
			auto minB = std::lower_bound(ALL(cByMin), outer.minX(), [&] (Circle* c, int64_t pos) { return c->minX() < pos; });
			auto minE = std::upper_bound(ALL(cByMin), outer.maxX(), [&] (int64_t pos, Circle* c) { return pos < c->minX(); });
			
			auto maxB = std::lower_bound(ALL(cByMax), outer.minX(), [&] (Circle* c, int64_t pos) { return c->maxX() < pos; });
			auto maxE = std::upper_bound(ALL(cByMax), outer.maxX(), [&] (int64_t pos, Circle* c) { return pos <= c->maxX(); });
			
			std::for_each(minB, minE, [&] (Circle* c)
			{
				if (c->elimBy == -1)
					c->elimBy = outer.i;
			});
			std::for_each(maxB, maxE, [&] (Circle* c)
			{
				if (c->elimBy == -1)
					c->elimBy = outer.i;
			});
		}
	}
	else if (num <= 5000)
	{
		for (Circle& outer : circles)
		{
			if (outer.elimBy != -1)
				continue;
			outer.elimBy = outer.i;
			for (Circle& inner : circles)
			{
				if (inner.elimBy == -1 && inner.intersects(outer))
					inner.elimBy = outer.i;
			}
		}
	}
	else
	{
		int64_t minX;
		int64_t minY;
		int64_t maxX;
		int64_t maxY;
		
		OctNode root;
		root.circles.reserve(circles.size());
		root.minX = INT64_MAX;
		root.minY = INT64_MAX;
		root.maxX = INT64_MIN;
		root.maxY = INT64_MIN;
		
		for (Circle& circle : circles)
		{
			root.circles.push_back(&circle);
			root.minX = std::min(root.minX, circle.minX());
			root.maxX = std::min(root.maxX, circle.maxX());
			root.minY = std::min(root.minY, circle.minY());
			root.maxY = std::min(root.maxY, circle.maxY());
		}
		root.maxX++;
		root.maxY++;
		
		genOctree(&root);
		
		for (Circle& circle : circles)
		{
			if (circle.elimBy == -1)
			{
				circle.elimBy = circle.i;
				outerCircle = &circle;
				root.mark();
			}
		}
	}
	
	std::vector<int64_t> result(num);
	for (int i = 0; i < num; i++)
		result[circles[i].i] = circles[i].elimBy + 1;
	for (int i = 0; i < num; i++)
		std::cout << result[i] << " ";
	std::cout << std::endl;
}

Compilation message

circle_selection.cpp: In function 'int main()':
circle_selection.cpp:215:11: warning: unused variable 'minX' [-Wunused-variable]
   int64_t minX;
           ^~~~
circle_selection.cpp:216:11: warning: unused variable 'minY' [-Wunused-variable]
   int64_t minY;
           ^~~~
circle_selection.cpp:217:11: warning: unused variable 'maxX' [-Wunused-variable]
   int64_t maxX;
           ^~~~
circle_selection.cpp:218:11: warning: unused variable 'maxY' [-Wunused-variable]
   int64_t maxY;
           ^~~~

Subtask #1
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 376 KB Output is correct
2 Correct 3 ms 488 KB Output is correct
3 Correct 2 ms 540 KB Output is correct
4 Correct 3 ms 540 KB Output is correct
5 Correct 3 ms 540 KB Output is correct
6 Correct 3 ms 540 KB Output is correct
7 Correct 3 ms 540 KB Output is correct
8 Correct 4 ms 540 KB Output is correct
9 Correct 2 ms 572 KB Output is correct
10 Correct 4 ms 620 KB Output is correct
11 Correct 4 ms 620 KB Output is correct
12 Correct 2 ms 620 KB Output is correct
13 Correct 3 ms 620 KB Output is correct
14 Correct 3 ms 620 KB Output is correct
15 Correct 3 ms 620 KB Output is correct
16 Correct 5 ms 620 KB Output is correct
17 Correct 6 ms 620 KB Output is correct
18 Correct 7 ms 620 KB Output is correct
19 Correct 19 ms 892 KB Output is correct
20 Correct 18 ms 936 KB Output is correct
21 Correct 14 ms 952 KB Output is correct
22 Correct 63 ms 952 KB Output is correct
23 Correct 67 ms 1052 KB Output is correct
24 Correct 100 ms 1092 KB Output is correct
25 Correct 94 ms 1092 KB Output is correct
26 Correct 65 ms 1092 KB Output is correct

Subtask #2
12.0 / 12.0

# Verdict Execution time Memory Grader output
1 Correct 849 ms 21660 KB Output is correct
2 Correct 681 ms 21676 KB Output is correct
3 Correct 656 ms 21676 KB Output is correct
4 Correct 654 ms 21676 KB Output is correct
5 Correct 843 ms 21676 KB Output is correct
6 Correct 894 ms 21676 KB Output is correct
7 Correct 646 ms 21676 KB Output is correct
8 Correct 699 ms 21676 KB Output is correct

Subtask #3
0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 21676 KB Output is correct
2 Execution timed out 3009 ms 21676 KB Time limit exceeded
3 Halted 0 ms 0 KB -

Subtask #4
0 / 23.0

# Verdict Execution time Memory Grader output
1 Execution timed out 3020 ms 21676 KB Time limit exceeded
2 Halted 0 ms 0 KB -

Subtask #5
0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 376 KB Output is correct
2 Correct 3 ms 488 KB Output is correct
3 Correct 2 ms 540 KB Output is correct
4 Correct 3 ms 540 KB Output is correct
5 Correct 3 ms 540 KB Output is correct
6 Correct 3 ms 540 KB Output is correct
7 Correct 3 ms 540 KB Output is correct
8 Correct 4 ms 540 KB Output is correct
9 Correct 2 ms 572 KB Output is correct
10 Correct 4 ms 620 KB Output is correct
11 Correct 4 ms 620 KB Output is correct
12 Correct 2 ms 620 KB Output is correct
13 Correct 3 ms 620 KB Output is correct
14 Correct 3 ms 620 KB Output is correct
15 Correct 3 ms 620 KB Output is correct
16 Correct 5 ms 620 KB Output is correct
17 Correct 6 ms 620 KB Output is correct
18 Correct 7 ms 620 KB Output is correct
19 Correct 19 ms 892 KB Output is correct
20 Correct 18 ms 936 KB Output is correct
21 Correct 14 ms 952 KB Output is correct
22 Correct 63 ms 952 KB Output is correct
23 Correct 67 ms 1052 KB Output is correct
24 Correct 100 ms 1092 KB Output is correct
25 Correct 94 ms 1092 KB Output is correct
26 Correct 65 ms 1092 KB Output is correct
27 Correct 23 ms 21676 KB Output is correct
28 Correct 22 ms 21676 KB Output is correct
29 Correct 24 ms 21676 KB Output is correct
30 Correct 293 ms 21676 KB Output is correct
31 Correct 401 ms 21676 KB Output is correct
32 Correct 316 ms 21676 KB Output is correct
33 Correct 205 ms 21676 KB Output is correct
34 Correct 200 ms 21676 KB Output is correct
35 Correct 237 ms 21676 KB Output is correct
36 Execution timed out 3010 ms 21676 KB Time limit exceeded
37 Halted 0 ms 0 KB -

Subtask #6
0 / 13.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 376 KB Output is correct
2 Correct 3 ms 488 KB Output is correct
3 Correct 2 ms 540 KB Output is correct
4 Correct 3 ms 540 KB Output is correct
5 Correct 3 ms 540 KB Output is correct
6 Correct 3 ms 540 KB Output is correct
7 Correct 3 ms 540 KB Output is correct
8 Correct 4 ms 540 KB Output is correct
9 Correct 2 ms 572 KB Output is correct
10 Correct 4 ms 620 KB Output is correct
11 Correct 4 ms 620 KB Output is correct
12 Correct 2 ms 620 KB Output is correct
13 Correct 3 ms 620 KB Output is correct
14 Correct 3 ms 620 KB Output is correct
15 Correct 3 ms 620 KB Output is correct
16 Correct 5 ms 620 KB Output is correct
17 Correct 6 ms 620 KB Output is correct
18 Correct 7 ms 620 KB Output is correct
19 Correct 19 ms 892 KB Output is correct
20 Correct 18 ms 936 KB Output is correct
21 Correct 14 ms 952 KB Output is correct
22 Correct 63 ms 952 KB Output is correct
23 Correct 67 ms 1052 KB Output is correct
24 Correct 100 ms 1092 KB Output is correct
25 Correct 94 ms 1092 KB Output is correct
26 Correct 65 ms 1092 KB Output is correct
27 Correct 849 ms 21660 KB Output is correct
28 Correct 681 ms 21676 KB Output is correct
29 Correct 656 ms 21676 KB Output is correct
30 Correct 654 ms 21676 KB Output is correct
31 Correct 843 ms 21676 KB Output is correct
32 Correct 894 ms 21676 KB Output is correct
33 Correct 646 ms 21676 KB Output is correct
34 Correct 699 ms 21676 KB Output is correct
35 Correct 3 ms 21676 KB Output is correct
36 Execution timed out 3009 ms 21676 KB Time limit exceeded
37 Halted 0 ms 0 KB -