oj.uz

Submission #84154

# Submission time Handle Problem Language Result Execution time Memory
84154 2018-11-13T19:42:14 Z radoslav11 New Home (APIO18_new_home) C++14
47 / 100
 5000 ms 151820 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.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) 
	{
		int ret;
		pnode l, r;

		split(root, l, r, {x + 1, -(int)2e9});
		ret = query(l, x);
		merge(root, l, r);

		return ret;
	}

	
} 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) 
			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) 
	{
		int ret;
		pnode l, r;

		split(root, l, r, {x - 1, (int)2e9});
		ret = query(r, x);
		merge(root, l, r);

		return ret;
	}

} 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:493:70: 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 46 ms 49656 KB Output is correct
2 Correct 46 ms 49656 KB Output is correct
3 Correct 48 ms 49688 KB Output is correct
4 Correct 46 ms 49688 KB Output is correct
5 Correct 47 ms 49816 KB Output is correct
6 Correct 48 ms 49864 KB Output is correct
7 Correct 48 ms 49940 KB Output is correct
8 Correct 49 ms 50036 KB Output is correct
9 Correct 49 ms 50036 KB Output is correct
10 Correct 48 ms 50036 KB Output is correct
11 Correct 47 ms 50036 KB Output is correct
12 Correct 48 ms 50036 KB Output is correct
13 Correct 51 ms 50036 KB Output is correct
14 Correct 49 ms 50036 KB Output is correct
15 Correct 49 ms 50084 KB Output is correct
16 Correct 50 ms 50084 KB Output is correct
17 Correct 48 ms 50084 KB Output is correct
18 Correct 56 ms 50084 KB Output is correct
19 Correct 50 ms 50084 KB Output is correct
20 Correct 47 ms 50084 KB Output is correct
21 Correct 47 ms 50084 KB Output is correct
22 Correct 53 ms 50084 KB Output is correct
23 Correct 51 ms 50084 KB Output is correct
24 Correct 48 ms 50084 KB Output is correct
25 Correct 49 ms 50084 KB Output is correct
26 Correct 48 ms 50084 KB Output is correct
27 Correct 52 ms 50084 KB Output is correct
28 Correct 51 ms 50084 KB Output is correct
29 Correct 48 ms 50084 KB Output is correct
30 Correct 47 ms 50084 KB Output is correct

Subtask #2
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 46 ms 49656 KB Output is correct
2 Correct 46 ms 49656 KB Output is correct
3 Correct 48 ms 49688 KB Output is correct
4 Correct 46 ms 49688 KB Output is correct
5 Correct 47 ms 49816 KB Output is correct
6 Correct 48 ms 49864 KB Output is correct
7 Correct 48 ms 49940 KB Output is correct
8 Correct 49 ms 50036 KB Output is correct
9 Correct 49 ms 50036 KB Output is correct
10 Correct 48 ms 50036 KB Output is correct
11 Correct 47 ms 50036 KB Output is correct
12 Correct 48 ms 50036 KB Output is correct
13 Correct 51 ms 50036 KB Output is correct
14 Correct 49 ms 50036 KB Output is correct
15 Correct 49 ms 50084 KB Output is correct
16 Correct 50 ms 50084 KB Output is correct
17 Correct 48 ms 50084 KB Output is correct
18 Correct 56 ms 50084 KB Output is correct
19 Correct 50 ms 50084 KB Output is correct
20 Correct 47 ms 50084 KB Output is correct
21 Correct 47 ms 50084 KB Output is correct
22 Correct 53 ms 50084 KB Output is correct
23 Correct 51 ms 50084 KB Output is correct
24 Correct 48 ms 50084 KB Output is correct
25 Correct 49 ms 50084 KB Output is correct
26 Correct 48 ms 50084 KB Output is correct
27 Correct 52 ms 50084 KB Output is correct
28 Correct 51 ms 50084 KB Output is correct
29 Correct 48 ms 50084 KB Output is correct
30 Correct 47 ms 50084 KB Output is correct
31 Correct 997 ms 71232 KB Output is correct
32 Correct 321 ms 71232 KB Output is correct
33 Correct 752 ms 71232 KB Output is correct
34 Correct 839 ms 71336 KB Output is correct
35 Correct 963 ms 71336 KB Output is correct
36 Correct 868 ms 71336 KB Output is correct
37 Correct 574 ms 71336 KB Output is correct
38 Correct 529 ms 71336 KB Output is correct
39 Correct 382 ms 71336 KB Output is correct
40 Correct 406 ms 71336 KB Output is correct
41 Correct 431 ms 71336 KB Output is correct
42 Correct 464 ms 71336 KB Output is correct
43 Correct 211 ms 71336 KB Output is correct
44 Correct 431 ms 71360 KB Output is correct
45 Correct 368 ms 71360 KB Output is correct
46 Correct 279 ms 71360 KB Output is correct
47 Correct 267 ms 71360 KB Output is correct
48 Correct 249 ms 71360 KB Output is correct
49 Correct 315 ms 71360 KB Output is correct
50 Correct 414 ms 71360 KB Output is correct
51 Correct 285 ms 71360 KB Output is correct

Subtask #3
0 / 10.0

# Verdict Execution time Memory Grader output
1 Execution timed out 5088 ms 151820 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 5033 ms 151820 KB Time limit exceeded
2 Halted 0 ms 0 KB -

Subtask #5
35.0 / 35.0

# Verdict Execution time Memory Grader output
1 Correct 46 ms 49656 KB Output is correct
2 Correct 46 ms 49656 KB Output is correct
3 Correct 48 ms 49688 KB Output is correct
4 Correct 46 ms 49688 KB Output is correct
5 Correct 47 ms 49816 KB Output is correct
6 Correct 48 ms 49864 KB Output is correct
7 Correct 48 ms 49940 KB Output is correct
8 Correct 49 ms 50036 KB Output is correct
9 Correct 49 ms 50036 KB Output is correct
10 Correct 48 ms 50036 KB Output is correct
11 Correct 47 ms 50036 KB Output is correct
12 Correct 48 ms 50036 KB Output is correct
13 Correct 51 ms 50036 KB Output is correct
14 Correct 49 ms 50036 KB Output is correct
15 Correct 49 ms 50084 KB Output is correct
16 Correct 50 ms 50084 KB Output is correct
17 Correct 48 ms 50084 KB Output is correct
18 Correct 56 ms 50084 KB Output is correct
19 Correct 50 ms 50084 KB Output is correct
20 Correct 47 ms 50084 KB Output is correct
21 Correct 47 ms 50084 KB Output is correct
22 Correct 53 ms 50084 KB Output is correct
23 Correct 51 ms 50084 KB Output is correct
24 Correct 48 ms 50084 KB Output is correct
25 Correct 49 ms 50084 KB Output is correct
26 Correct 48 ms 50084 KB Output is correct
27 Correct 52 ms 50084 KB Output is correct
28 Correct 51 ms 50084 KB Output is correct
29 Correct 48 ms 50084 KB Output is correct
30 Correct 47 ms 50084 KB Output is correct
31 Correct 997 ms 71232 KB Output is correct
32 Correct 321 ms 71232 KB Output is correct
33 Correct 752 ms 71232 KB Output is correct
34 Correct 839 ms 71336 KB Output is correct
35 Correct 963 ms 71336 KB Output is correct
36 Correct 868 ms 71336 KB Output is correct
37 Correct 574 ms 71336 KB Output is correct
38 Correct 529 ms 71336 KB Output is correct
39 Correct 382 ms 71336 KB Output is correct
40 Correct 406 ms 71336 KB Output is correct
41 Correct 431 ms 71336 KB Output is correct
42 Correct 464 ms 71336 KB Output is correct
43 Correct 211 ms 71336 KB Output is correct
44 Correct 431 ms 71360 KB Output is correct
45 Correct 368 ms 71360 KB Output is correct
46 Correct 279 ms 71360 KB Output is correct
47 Correct 267 ms 71360 KB Output is correct
48 Correct 249 ms 71360 KB Output is correct
49 Correct 315 ms 71360 KB Output is correct
50 Correct 414 ms 71360 KB Output is correct
51 Correct 285 ms 71360 KB Output is correct
52 Correct 1006 ms 151820 KB Output is correct
53 Correct 887 ms 151820 KB Output is correct
54 Correct 1048 ms 151820 KB Output is correct
55 Correct 690 ms 151820 KB Output is correct
56 Correct 765 ms 151820 KB Output is correct
57 Correct 597 ms 151820 KB Output is correct
58 Correct 722 ms 151820 KB Output is correct
59 Correct 821 ms 151820 KB Output is correct
60 Correct 624 ms 151820 KB Output is correct
61 Correct 631 ms 151820 KB Output is correct
62 Correct 1026 ms 151820 KB Output is correct
63 Correct 1014 ms 151820 KB Output is correct
64 Correct 1044 ms 151820 KB Output is correct
65 Correct 789 ms 151820 KB Output is correct
66 Correct 543 ms 151820 KB Output is correct
67 Correct 798 ms 151820 KB Output is correct

Subtask #6
0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 46 ms 49656 KB Output is correct
2 Correct 46 ms 49656 KB Output is correct
3 Correct 48 ms 49688 KB Output is correct
4 Correct 46 ms 49688 KB Output is correct
5 Correct 47 ms 49816 KB Output is correct
6 Correct 48 ms 49864 KB Output is correct
7 Correct 48 ms 49940 KB Output is correct
8 Correct 49 ms 50036 KB Output is correct
9 Correct 49 ms 50036 KB Output is correct
10 Correct 48 ms 50036 KB Output is correct
11 Correct 47 ms 50036 KB Output is correct
12 Correct 48 ms 50036 KB Output is correct
13 Correct 51 ms 50036 KB Output is correct
14 Correct 49 ms 50036 KB Output is correct
15 Correct 49 ms 50084 KB Output is correct
16 Correct 50 ms 50084 KB Output is correct
17 Correct 48 ms 50084 KB Output is correct
18 Correct 56 ms 50084 KB Output is correct
19 Correct 50 ms 50084 KB Output is correct
20 Correct 47 ms 50084 KB Output is correct
21 Correct 47 ms 50084 KB Output is correct
22 Correct 53 ms 50084 KB Output is correct
23 Correct 51 ms 50084 KB Output is correct
24 Correct 48 ms 50084 KB Output is correct
25 Correct 49 ms 50084 KB Output is correct
26 Correct 48 ms 50084 KB Output is correct
27 Correct 52 ms 50084 KB Output is correct
28 Correct 51 ms 50084 KB Output is correct
29 Correct 48 ms 50084 KB Output is correct
30 Correct 47 ms 50084 KB Output is correct
31 Correct 997 ms 71232 KB Output is correct
32 Correct 321 ms 71232 KB Output is correct
33 Correct 752 ms 71232 KB Output is correct
34 Correct 839 ms 71336 KB Output is correct
35 Correct 963 ms 71336 KB Output is correct
36 Correct 868 ms 71336 KB Output is correct
37 Correct 574 ms 71336 KB Output is correct
38 Correct 529 ms 71336 KB Output is correct
39 Correct 382 ms 71336 KB Output is correct
40 Correct 406 ms 71336 KB Output is correct
41 Correct 431 ms 71336 KB Output is correct
42 Correct 464 ms 71336 KB Output is correct
43 Correct 211 ms 71336 KB Output is correct
44 Correct 431 ms 71360 KB Output is correct
45 Correct 368 ms 71360 KB Output is correct
46 Correct 279 ms 71360 KB Output is correct
47 Correct 267 ms 71360 KB Output is correct
48 Correct 249 ms 71360 KB Output is correct
49 Correct 315 ms 71360 KB Output is correct
50 Correct 414 ms 71360 KB Output is correct
51 Correct 285 ms 71360 KB Output is correct
52 Execution timed out 5088 ms 151820 KB Time limit exceeded
53 Halted 0 ms 0 KB -