oj.uz

Submission #84168

# Submission time Handle Problem Language Result Execution time Memory
84168 2018-11-13T20:32:20 Z radoslav11 New Home (APIO18_new_home) C++14
47 / 100
 5000 ms 155948 KB 
/*
   We will use sweep line to solve the problem. We split the stores into 2 queries: 
   1) Add store i at time a[i]
   2) Remove store i at time b[i] + 1
   We will also have queries in the sweep line. Everything will be sorted by time in increasing order.

   Now to handle queries we will maintain K sets - the available positions of j-type stores. Then if A and B are two consecutive stores, the closest elements to all positions in [A; B] are A or B.
   Then let's have a two segment trees wtih sets - one for closest elements to the left and one for closest elements to the right. Now addition of store with type X will be done like that:

   1) Let A <= X <= B and A and B are the closest stores of the same type. 
   2) We remove the interval [A; B] from the DS.
   3) We add the intervals [A; X] and [X; B].

   Adding or removing an interval is done by finding the middle position and then concidering the two ranges - [L; Mid] and [Mid + 1; R].

   The complexity will be O(N * log N * log N).

   As sets are slow, we will compress the input in each segment tree node beforehand and then use priority queue instead of sets.

   Unfortunately the above data structure was too slow. So my second idea is to change the data structure to two simple treaps and do binary search on them. 
   The complexity will be O(N log N) this way. 
   */

#include <bits/stdc++.h>
#define endl '\n'

//#pragma GCC optimize ("O3")
//#pragma GCC target ("sse4")

#define SZ(x) ((int)x.size())
#define ALL(V) V.begin(), V.end()
#define L_B lower_bound
#define U_B upper_bound

using namespace std;
template<class T, class T2> inline int chkmax(T &x, const T2 &y) { return x < y ? x = y, 1 : 0; }
template<class T, class T2> inline int chkmin(T &x, const T2 &y) { return x > y ? x = y, 1 : 0; }
const int MAXN = (1 << 20);
const int inf = (int)1e9 + 42;

int read_int();

random_device rd;
mt19937 mt(rd() ^ 231231);

struct treap_l
{
	struct node
	{
		pair<int, int> v;
		int mx;
		int prior;

		node *l, *r;

		node() { v = {0, 0}; prior = mx = 0; l = r = nullptr; }
		node(int L, int R) 
		{ 
			v = {L, R};
			mx = R;
			prior = mt();
			l = r = nullptr; 
		}
	};

	using pnode = node*;

	void pull(pnode &t)
	{
		if(!t) return;

		t->mx = t->v.second;
		if(t->l) chkmax(t->mx, t->l->mx);
		if(t->r) chkmax(t->mx, t->r->mx);
	}

	void merge(pnode &t, pnode l, pnode r)
	{
		if(!l) { t = r; return; }
		if(!r) { t = l; return; }

		if(l->prior > r->prior)
			merge(l->r, l->r, r), t = l;
		else
			merge(r->l, l, r->l), t = r;

		pull(t);
	}

	void split(pnode t, pnode &l, pnode &r, pair<int, int> k)
	{
		if(!t) { l = r = nullptr; return; }	

		if(t->v <= k)
			split(t->r, t->r, r, k), l = t;
		else
			split(t->l, l, t->l, k), r = t;

		pull(t);
	}

	pnode root;
	treap_l() { root = nullptr; }

	pnode rotate_left(pnode x)
	{
		pnode y = x->r, T2 = y->l;
		x->r = T2;
		y->l = x;
		return y;
	}

	pnode rotate_right(pnode y)
	{
		pnode x = y->l, T2 = x->r;
		y->l = T2;
		x->r = y;
		return x;
	}

	pnode lazy_add(pnode t, pair<int, int> x)
	{
		if(!t) return new node(x.first, x.second);

		if(x < t->v)
		{
			t->l = lazy_add(t->l, x);
			if(t->l->prior > t->prior)
				t = rotate_right(t);

			pull(t->r);
		}
		else
		{
			t->r = lazy_add(t->r, x);
			if(t->r->prior > t->prior)
				t = rotate_left(t);

			pull(t->l);
		}

		pull(t);
		return t;
	}

	pnode lazy_remove(pnode t, pair<int, int> x)
	{
		if(t->v == x)
		{
			merge(t, t->l, t->r);
			return t;
		}

		if(t->v < x)
			t->r = lazy_remove(t->r, x);
		else
			t->l = lazy_remove(t->l, x);

		pull(t);
		return t;
	}
	
	void add_interval(int l, int r)
	{	
		root = lazy_add(root, {l, r});
	}

	void rem_interval(int l, int r)
	{
		root = lazy_remove(root, {l, r});
	}

	int query(pnode t, int x)
	{
		if(!t) return 0;

		int ret = 0;
		if(t->v.first <= x && t->v.second >= x) 
			chkmax(ret, x - t->v.first);

		if(t->l && t->l->mx >= x)
			chkmax(ret, query(t->l, x));
		else
			chkmax(ret, query(t->r, x));

		return ret;
	}

	int query(int x) 
	{
		return query(root, x);
	}

	
} L;

struct treap_r
{
	struct node
	{
		pair<int, int> v;
		int mn;
		int prior;

		node *l, *r;

		node() { v = {0, 0}; prior = mn = 0; l = r = nullptr; }
		node(int R, int L) 
		{ 
			v = {R, L};
			mn = L;
			prior = mt();
			l = r = nullptr; 
		}
	};

	using pnode = node*;

	void pull(pnode &t)
	{
		if(!t) return;

		t->mn = t->v.second;
		if(t->l) chkmin(t->mn, t->l->mn);
		if(t->r) chkmin(t->mn, t->r->mn);
	}

	void merge(pnode &t, pnode l, pnode r)
	{
		if(!l) { t = r; return; }
		if(!r) { t = l; return; }

		if(l->prior > r->prior)
			merge(l->r, l->r, r), t = l;
		else
			merge(r->l, l, r->l), t = r;

		pull(t);
	}

	void split(pnode t, pnode &l, pnode &r, pair<int, int> k)
	{
		if(!t) { l = r = nullptr; return; }	

		if(t->v <= k)
			split(t->r, t->r, r, k), l = t;
		else
			split(t->l, l, t->l, k), r = t;

		pull(t);
	}
	
	pnode root;
	treap_r() { root = nullptr; }

	pnode rotate_left(pnode x)
	{
		pnode y = x->r, T2 = y->l;
		x->r = T2;
		y->l = x;
		return y;
	}

	pnode rotate_right(pnode y)
	{
		pnode x = y->l, T2 = x->r;
		y->l = T2;
		x->r = y;
		return x;
	}

	pnode lazy_add(pnode t, pair<int, int> x)
	{
		if(!t) return new node(x.first, x.second);

		if(x < t->v)
		{
			t->l = lazy_add(t->l, x);
			if(t->l->prior > t->prior)
				t = rotate_right(t);

			pull(t->r);
		}
		else
		{
			t->r = lazy_add(t->r, x);
			if(t->r->prior > t->prior)
				t = rotate_left(t);

			pull(t->l);
		}

		pull(t);
		return t;
	}

	pnode lazy_remove(pnode t, pair<int, int> x)
	{
		if(t->v == x)
		{
			merge(t, t->l, t->r);
			return t;
		}

		if(t->v < x)
			t->r = lazy_remove(t->r, x);
		else
			t->l = lazy_remove(t->l, x);

		pull(t);
		return t;
	}
	
	void add_interval(int l, int r)
	{	
		root = lazy_add(root, {r, l});
	}

	void rem_interval(int l, int r)
	{
		root = lazy_remove(root, {r, l});
	}

	int query(pnode t, int x)
	{
		if(!t) return 0;

		int ret = 0;
		if(t->v.second <= x && x <= t->v.first) 
			chkmax(ret, t->v.first - x);

		if(t->r && t->r->mn <= x)
			chkmax(ret, query(t->r, x));
		else
			chkmax(ret, query(t->l, x));

		return ret;
	}

	int query(int x) 
	{
		return query(root, x);
	}

} R;

int n, k, q;

struct event
{
	int type;
	int T, x, tp, idx;

	event() { type = tp = T = x = 0; idx = -1; }
	event(int t, int Tm, int X, int i, int pp = -1)
	{
		type = t;
		T = Tm;
		x = X;
		idx = i;
		tp = pp;
	}
};

bool cmp(event a, event b) 
{ 
	if(a.T != b.T) return a.T < b.T; 
	return a.type < b.type;
}

vector<event> Ev;
int answer[MAXN];

void read()
{
	n = read_int();
	k = read_int();
	q = read_int();

	for(int i = 0; i < n; i++)
	{
		int x, t, a, b;
		x = read_int();
		t = read_int();
		a = read_int();
		b = read_int();

		Ev.push_back(event(0, a, x, i, t));
		Ev.push_back(event(1, b + 1, x, i, t));
	}

	for(int i = 0; i < q; i++)
	{
		int x, t;
		x = read_int();
		t = read_int();
		Ev.push_back(event(2, t, x, i));
	}
}

set<pair<int, int> > ST[MAXN];

void add_interval(int l, int r)
{
	int mid = (l + r) / 2;
	if(l <= mid) L.add_interval(l, mid);
	if(mid + 1 <= r) R.add_interval(mid + 1, r);
}

void rem_interval(int l, int r)
{
	int mid = (l + r) / 2;
	if(l <= mid) L.rem_interval(l, mid);
	if(mid + 1 <= r) R.rem_interval(mid + 1, r);
}

int query(int x) { return max(L.query(x), R.query(x)); }

void add(int y, int x, int i)
{
	auto aft = ST[y].L_B({x, i});
	auto bef = prev(aft);

	ST[y].insert({x, i});

	rem_interval(bef->first, aft->first);
	add_interval(bef->first, x);
	add_interval(x, aft->first);
}

void rem(int y, int x, int i)
{
	ST[y].erase({x, i});

	auto aft = ST[y].L_B({x, i});
	auto bef = prev(aft);

	rem_interval(bef->first, x);
	rem_interval(x, aft->first);
	add_interval(bef->first, aft->first);
}

void solve()
{
	for(int i = 1; i <= k; i++)
	{
		ST[i].insert({-inf, -1}), ST[i].insert({inf, -1});
		add_interval(-inf, inf);
	}

	sort(ALL(Ev), cmp);
	for(auto it: Ev)
		if(it.type == 0)
			add(it.tp, it.x, it.idx);
		else if(it.type == 1)
			rem(it.tp, it.x, it.idx);
		else 
			answer[it.idx] = query(it.x);

	for(int i = 0; i < q; i++)
		if(answer[i] < (int)2e8) cout << answer[i] << endl;
		else cout << -1 << endl;
}

int main()
{
	ios_base::sync_with_stdio(false);
	cin.tie(NULL);

	read();
	solve();
	return 0;
}

const int maxl = 100000;
char buff[maxl];
int ret_int, pos_buff = 0;

void next_char() { if(++pos_buff == maxl) fread(buff, 1, maxl, stdin), pos_buff = 0; }

int read_int()
{
	ret_int = 0;
	for(; buff[pos_buff] < '0' || buff[pos_buff] > '9'; next_char());
	for(; buff[pos_buff] >= '0' && buff[pos_buff] <= '9'; next_char())
		ret_int = ret_int * 10 + buff[pos_buff] - '0';
	return ret_int;
}

Compilation message

new_home.cpp: In function 'void next_char()':
new_home.cpp:479:70: warning: ignoring return value of 'size_t fread(void*, size_t, size_t, FILE*)', declared with attribute warn_unused_result [-Wunused-result]
 void next_char() { if(++pos_buff == maxl) fread(buff, 1, maxl, stdin), pos_buff = 0; }
                                           ~~~~~~~~~~~~~~~~~~~~~~~~~~~^~~~~~~~~~~~~~

Subtask #1
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 52 ms 49528 KB Output is correct
2 Correct 47 ms 49672 KB Output is correct
3 Correct 46 ms 49720 KB Output is correct
4 Correct 46 ms 49780 KB Output is correct
5 Correct 46 ms 50008 KB Output is correct
6 Correct 47 ms 50012 KB Output is correct
7 Correct 48 ms 50028 KB Output is correct
8 Correct 48 ms 50028 KB Output is correct
9 Correct 53 ms 50284 KB Output is correct
10 Correct 48 ms 50284 KB Output is correct
11 Correct 47 ms 50284 KB Output is correct
12 Correct 48 ms 50284 KB Output is correct
13 Correct 47 ms 50284 KB Output is correct
14 Correct 47 ms 50284 KB Output is correct
15 Correct 48 ms 50284 KB Output is correct
16 Correct 47 ms 50284 KB Output is correct
17 Correct 47 ms 50284 KB Output is correct
18 Correct 48 ms 50284 KB Output is correct
19 Correct 49 ms 50284 KB Output is correct
20 Correct 48 ms 50284 KB Output is correct
21 Correct 48 ms 50284 KB Output is correct
22 Correct 56 ms 50284 KB Output is correct
23 Correct 48 ms 50284 KB Output is correct
24 Correct 48 ms 50284 KB Output is correct
25 Correct 48 ms 50284 KB Output is correct
26 Correct 48 ms 50284 KB Output is correct
27 Correct 48 ms 50284 KB Output is correct
28 Correct 47 ms 50284 KB Output is correct
29 Correct 51 ms 50284 KB Output is correct
30 Correct 50 ms 50284 KB Output is correct

Subtask #2
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 52 ms 49528 KB Output is correct
2 Correct 47 ms 49672 KB Output is correct
3 Correct 46 ms 49720 KB Output is correct
4 Correct 46 ms 49780 KB Output is correct
5 Correct 46 ms 50008 KB Output is correct
6 Correct 47 ms 50012 KB Output is correct
7 Correct 48 ms 50028 KB Output is correct
8 Correct 48 ms 50028 KB Output is correct
9 Correct 53 ms 50284 KB Output is correct
10 Correct 48 ms 50284 KB Output is correct
11 Correct 47 ms 50284 KB Output is correct
12 Correct 48 ms 50284 KB Output is correct
13 Correct 47 ms 50284 KB Output is correct
14 Correct 47 ms 50284 KB Output is correct
15 Correct 48 ms 50284 KB Output is correct
16 Correct 47 ms 50284 KB Output is correct
17 Correct 47 ms 50284 KB Output is correct
18 Correct 48 ms 50284 KB Output is correct
19 Correct 49 ms 50284 KB Output is correct
20 Correct 48 ms 50284 KB Output is correct
21 Correct 48 ms 50284 KB Output is correct
22 Correct 56 ms 50284 KB Output is correct
23 Correct 48 ms 50284 KB Output is correct
24 Correct 48 ms 50284 KB Output is correct
25 Correct 48 ms 50284 KB Output is correct
26 Correct 48 ms 50284 KB Output is correct
27 Correct 48 ms 50284 KB Output is correct
28 Correct 47 ms 50284 KB Output is correct
29 Correct 51 ms 50284 KB Output is correct
30 Correct 50 ms 50284 KB Output is correct
31 Correct 892 ms 71316 KB Output is correct
32 Correct 325 ms 71316 KB Output is correct
33 Correct 736 ms 71316 KB Output is correct
34 Correct 764 ms 71360 KB Output is correct
35 Correct 892 ms 71360 KB Output is correct
36 Correct 834 ms 71360 KB Output is correct
37 Correct 511 ms 71360 KB Output is correct
38 Correct 478 ms 71360 KB Output is correct
39 Correct 341 ms 71360 KB Output is correct
40 Correct 360 ms 71360 KB Output is correct
41 Correct 368 ms 71360 KB Output is correct
42 Correct 395 ms 71360 KB Output is correct
43 Correct 217 ms 71360 KB Output is correct
44 Correct 356 ms 71424 KB Output is correct
45 Correct 314 ms 71424 KB Output is correct
46 Correct 247 ms 71424 KB Output is correct
47 Correct 240 ms 71424 KB Output is correct
48 Correct 220 ms 71424 KB Output is correct
49 Correct 268 ms 71424 KB Output is correct
50 Correct 339 ms 71424 KB Output is correct
51 Correct 252 ms 71424 KB Output is correct

Subtask #3
0 / 10.0

# Verdict Execution time Memory Grader output
1 Execution timed out 5104 ms 155948 KB Time limit exceeded
2 Halted 0 ms 0 KB -

Subtask #4
0 / 23.0

# Verdict Execution time Memory Grader output
1 Execution timed out 5016 ms 155948 KB Time limit exceeded
2 Halted 0 ms 0 KB -

Subtask #5
35.0 / 35.0

# Verdict Execution time Memory Grader output
1 Correct 52 ms 49528 KB Output is correct
2 Correct 47 ms 49672 KB Output is correct
3 Correct 46 ms 49720 KB Output is correct
4 Correct 46 ms 49780 KB Output is correct
5 Correct 46 ms 50008 KB Output is correct
6 Correct 47 ms 50012 KB Output is correct
7 Correct 48 ms 50028 KB Output is correct
8 Correct 48 ms 50028 KB Output is correct
9 Correct 53 ms 50284 KB Output is correct
10 Correct 48 ms 50284 KB Output is correct
11 Correct 47 ms 50284 KB Output is correct
12 Correct 48 ms 50284 KB Output is correct
13 Correct 47 ms 50284 KB Output is correct
14 Correct 47 ms 50284 KB Output is correct
15 Correct 48 ms 50284 KB Output is correct
16 Correct 47 ms 50284 KB Output is correct
17 Correct 47 ms 50284 KB Output is correct
18 Correct 48 ms 50284 KB Output is correct
19 Correct 49 ms 50284 KB Output is correct
20 Correct 48 ms 50284 KB Output is correct
21 Correct 48 ms 50284 KB Output is correct
22 Correct 56 ms 50284 KB Output is correct
23 Correct 48 ms 50284 KB Output is correct
24 Correct 48 ms 50284 KB Output is correct
25 Correct 48 ms 50284 KB Output is correct
26 Correct 48 ms 50284 KB Output is correct
27 Correct 48 ms 50284 KB Output is correct
28 Correct 47 ms 50284 KB Output is correct
29 Correct 51 ms 50284 KB Output is correct
30 Correct 50 ms 50284 KB Output is correct
31 Correct 892 ms 71316 KB Output is correct
32 Correct 325 ms 71316 KB Output is correct
33 Correct 736 ms 71316 KB Output is correct
34 Correct 764 ms 71360 KB Output is correct
35 Correct 892 ms 71360 KB Output is correct
36 Correct 834 ms 71360 KB Output is correct
37 Correct 511 ms 71360 KB Output is correct
38 Correct 478 ms 71360 KB Output is correct
39 Correct 341 ms 71360 KB Output is correct
40 Correct 360 ms 71360 KB Output is correct
41 Correct 368 ms 71360 KB Output is correct
42 Correct 395 ms 71360 KB Output is correct
43 Correct 217 ms 71360 KB Output is correct
44 Correct 356 ms 71424 KB Output is correct
45 Correct 314 ms 71424 KB Output is correct
46 Correct 247 ms 71424 KB Output is correct
47 Correct 240 ms 71424 KB Output is correct
48 Correct 220 ms 71424 KB Output is correct
49 Correct 268 ms 71424 KB Output is correct
50 Correct 339 ms 71424 KB Output is correct
51 Correct 252 ms 71424 KB Output is correct
52 Correct 883 ms 155948 KB Output is correct
53 Correct 783 ms 155948 KB Output is correct
54 Correct 957 ms 155948 KB Output is correct
55 Correct 619 ms 155948 KB Output is correct
56 Correct 720 ms 155948 KB Output is correct
57 Correct 520 ms 155948 KB Output is correct
58 Correct 632 ms 155948 KB Output is correct
59 Correct 725 ms 155948 KB Output is correct
60 Correct 534 ms 155948 KB Output is correct
61 Correct 626 ms 155948 KB Output is correct
62 Correct 903 ms 155948 KB Output is correct
63 Correct 920 ms 155948 KB Output is correct
64 Correct 896 ms 155948 KB Output is correct
65 Correct 687 ms 155948 KB Output is correct
66 Correct 432 ms 155948 KB Output is correct
67 Correct 698 ms 155948 KB Output is correct

Subtask #6
0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 52 ms 49528 KB Output is correct
2 Correct 47 ms 49672 KB Output is correct
3 Correct 46 ms 49720 KB Output is correct
4 Correct 46 ms 49780 KB Output is correct
5 Correct 46 ms 50008 KB Output is correct
6 Correct 47 ms 50012 KB Output is correct
7 Correct 48 ms 50028 KB Output is correct
8 Correct 48 ms 50028 KB Output is correct
9 Correct 53 ms 50284 KB Output is correct
10 Correct 48 ms 50284 KB Output is correct
11 Correct 47 ms 50284 KB Output is correct
12 Correct 48 ms 50284 KB Output is correct
13 Correct 47 ms 50284 KB Output is correct
14 Correct 47 ms 50284 KB Output is correct
15 Correct 48 ms 50284 KB Output is correct
16 Correct 47 ms 50284 KB Output is correct
17 Correct 47 ms 50284 KB Output is correct
18 Correct 48 ms 50284 KB Output is correct
19 Correct 49 ms 50284 KB Output is correct
20 Correct 48 ms 50284 KB Output is correct
21 Correct 48 ms 50284 KB Output is correct
22 Correct 56 ms 50284 KB Output is correct
23 Correct 48 ms 50284 KB Output is correct
24 Correct 48 ms 50284 KB Output is correct
25 Correct 48 ms 50284 KB Output is correct
26 Correct 48 ms 50284 KB Output is correct
27 Correct 48 ms 50284 KB Output is correct
28 Correct 47 ms 50284 KB Output is correct
29 Correct 51 ms 50284 KB Output is correct
30 Correct 50 ms 50284 KB Output is correct
31 Correct 892 ms 71316 KB Output is correct
32 Correct 325 ms 71316 KB Output is correct
33 Correct 736 ms 71316 KB Output is correct
34 Correct 764 ms 71360 KB Output is correct
35 Correct 892 ms 71360 KB Output is correct
36 Correct 834 ms 71360 KB Output is correct
37 Correct 511 ms 71360 KB Output is correct
38 Correct 478 ms 71360 KB Output is correct
39 Correct 341 ms 71360 KB Output is correct
40 Correct 360 ms 71360 KB Output is correct
41 Correct 368 ms 71360 KB Output is correct
42 Correct 395 ms 71360 KB Output is correct
43 Correct 217 ms 71360 KB Output is correct
44 Correct 356 ms 71424 KB Output is correct
45 Correct 314 ms 71424 KB Output is correct
46 Correct 247 ms 71424 KB Output is correct
47 Correct 240 ms 71424 KB Output is correct
48 Correct 220 ms 71424 KB Output is correct
49 Correct 268 ms 71424 KB Output is correct
50 Correct 339 ms 71424 KB Output is correct
51 Correct 252 ms 71424 KB Output is correct
52 Execution timed out 5104 ms 155948 KB Time limit exceeded
53 Halted 0 ms 0 KB -