oj.uz

Submission #71055

# Submission time Handle Problem Language Result Execution time Memory
71055 2018-08-24T04:50:11 Z qkxwsm Fibonacci representations (CEOI18_fib) C++17
100 / 100
 2020 ms 25688 KB 
/*
PROG: source
LANG: C++11
_____
.'     '.
/  0   0  \
|     ^     |
|  \     /  |
\  '---'  /
'._____.'
*/
#include <bits/stdc++.h>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/assoc_container.hpp>

using namespace std;
using namespace __gnu_pbds;

struct chash
{
	int operator()(int x) const
	{
		x ^= (x >> 20) ^ (x >> 12);
		return x ^ (x >> 7) ^ (x >> 4);
	}
	int operator()(long long x) const
	{
		return x ^ (x >> 32);
	}
};

template<typename T> using orderedset = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
template<typename T, typename U> using hashtable = gp_hash_table<T, U, chash>;

template<class T>
void readi(T &x)
{
	T input = 0;
	bool negative = false;
	char c = ' ';
	while (c < '-')
	{
		c = getchar();
	}
	if (c == '-')
	{
		negative = true;
		c = getchar();
	}
	while (c >= '0')
	{
		input = input * 10 + (c - '0');
		c = getchar();
	}
	if (negative)
	{
		input = -input;
	}
	x = input;
}
template<class T>
void printi(T output)
{
	if (output == 0)
	{
		putchar('0');
		return;
	}
	if (output < 0)
	{
		putchar('-');
		output = -output;
	}
	int aout[20];
	int ilen = 0;
	while(output)
	{
		aout[ilen] = ((output % 10));
		output /= 10;
		ilen++;
	}
	for (int i = ilen - 1; i >= 0; i--)
	{
		putchar(aout[i] + '0');
	}
	return;
}
template<class T>
void ckmin(T &a, T b)
{
	a = min(a, b);
}
template<class T>
void ckmax(T &a, T b)
{
	a = max(a, b);
}
template<class T, class U>
T normalize(T x, U mod = 1000000007)
{
	return (((x % mod) + mod) % mod);
}
long long randomizell(long long mod)
{
	return ((1ll << 45) * rand() + (1ll << 30) * rand() + (1ll << 15) * rand() + rand()) % mod;
}
int randomize(int mod)
{
	return ((1ll << 15) * rand() + rand()) % mod;
}

#define y0 ___y0
#define y1 ___y1
#define MP make_pair
#define MT make_tuple
#define PB push_back
#define PF push_front
#define LB lower_bound
#define UB upper_bound
#define fi first
#define se second
#define debug(x) cerr << #x << " = " << x << endl;

const long double PI = 4.0 * atan(1.0);
const long double EPS = 1e-10;

#define MAGIC 347
#define SINF 10007
#define CO 1000007
#define INF 1000000007
#define BIG 1000000931
#define LARGE 1696969696967ll
#define GIANT 2564008813937411ll
#define LLINF 2696969696969696969ll
#define MAXN 100013

typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef pair<pii, pii> ppp;
typedef pair<ld, ld> pdd;

int N;
int arr[MAXN];
ppp matpow[40];
set<pii> rep;

ppp get(int dif)
{
	int D = dif / 2;
	ppp res;
	if (dif % 2)
	{
		return {{D + 1, 1}, {0, 0}};
	}
	else
	{
		return {{D + 1, 1}, {INF - 1, 0}};
	}
}
ppp mul(ppp a, ppp b)
{
	ppp res;
	res.fi.fi = ((1ll * a.fi.fi * b.fi.fi + 1ll * a.fi.se * b.se.fi) % INF);
	res.fi.se = ((1ll * a.fi.fi * b.fi.se + 1ll * a.fi.se * b.se.se) % INF);
	res.se.fi = ((1ll * a.se.fi * b.fi.fi + 1ll * a.se.se * b.se.fi) % INF);
	res.se.se = ((1ll * a.se.fi * b.fi.se + 1ll * a.se.se * b.se.se) % INF);
	return res;
}
ppp mat_expo(int e)
{
	e /= 2;
	ppp res = {{1, 0}, {0, 1}};
	if (e == 0) return res;
	for (int i = 0; i <= (31 - __builtin_clz(e)); i++)
	{
		if (e & (1 << i))
		{
			res = mul(res, matpow[i]);
		}
	}
	return res;
}
struct node
{
	node* ch[2];
	pii stor;
	ppp trans, subtrans;
	int pri;
	int subt;
	node(pii p)
	{
		pri = randomize(INF);
		ch[0] = ch[1] = nullptr;
		stor = p;
		subt = 1;
	}
	void recalc()
	{
		if (ch[0] && ch[1])
		{
			subt = ch[0] -> subt + 1 + ch[1] -> subt;
			subtrans = mul(mul(ch[0] -> subtrans, trans), ch[1] -> subtrans);
		}
		else if (ch[0])
		{
			subt = ch[0] -> subt + 1;
			subtrans = mul(ch[0] -> subtrans, trans);
		}
		else if (ch[1])
		{
			subt = 1 + ch[1] -> subt;
			subtrans = mul(trans, ch[1] -> subtrans);
		}
		else
		{
			subt = 1;
			subtrans = trans;
		}
	}
};

node *root;
ll occ;

typedef pair<node*, node*> pnn;

pnn split(node* t, int v)
{
	if (!t) return {t, t};
	t -> recalc();
	int cur = t -> stor.fi;
	if (v < cur)
	{
		pnn p = split(t -> ch[0], v);
		t -> ch[0] = p.se; t -> recalc();
		return {p.fi, t};
	}
	else
	{
		pnn p = split(t -> ch[1], v);
		t -> ch[1] = p.fi; t -> recalc();
		return {t, p.se};
	}
}
node* merge(node *l, node *r)
{
	if (!l) return r;
	if (!r) return l;
	if (l -> pri > r -> pri)
	{
		l -> ch[1] = merge(l -> ch[1], r);
		l -> recalc();
		return l;
	}
	else
	{
		r -> ch[0] = merge(l, r -> ch[0]);
		r -> recalc();
		return r;
	}
}
int lower_bound(node* t, pii p)
{
	if (!t)
	{
		return 0;
	}
	if (t -> stor >= p)
	{
		return lower_bound(t -> ch[0], p);
	}
	return (t -> ch[0] ? t -> ch[0] -> subt : 0) + 1 + lower_bound(t -> ch[1], p);
}
void terase(pii p)
{
	auto it = rep.UB(p);
	int was = prev(prev(it)) -> se;
	pnn t = split(root, p.fi - 1), t1 = split(t.se, p.fi);
	if (it == rep.end())
	{
		root = t.fi;
	}
	else
	{
		pnn t2 = split(t1.se, it -> fi);
		t2.fi -> trans = mul(get((t2.fi -> stor).fi - was), mat_expo(t2.fi -> stor.se - t2.fi -> stor.fi));
		t2.fi -> recalc();
		root = merge(t.fi, merge(t2.fi, t2.se));
	}
	return;
}
void tinsert(pii p)
{
	node* cur = new node(p);
	auto it = rep.UB(p);
	int was = prev(it) -> se;
	pnn t = split(root, p.fi);
	if (it == rep.end())
	{
		cur -> trans = mul(get(p.fi - was), mat_expo(p.se - p.fi));
		cur -> recalc();
		root = merge(t.fi, cur);
	}
	else
	{
		pnn t1 = split(t.se, it -> fi);
		t1.fi -> trans = mul(get(t1.fi -> stor.fi - p.se), mat_expo((t1.fi -> stor.se) - (t1.fi -> stor.fi)));
		t1.fi -> recalc();
		cur -> trans = mul(get(p.fi - was), mat_expo(p.se - p.fi));
		cur -> recalc();
		root = merge(merge(t.fi, cur), merge(t1.fi, t1.se));
	}
}
void smartinsert(int L, int R)
{
	if (L > R) return;
	int lt = L, rt = R;
	auto it = rep.LB({R + 2, -INF});
	if (it != rep.end() && it -> fi == R + 2)
	{
		rt = it -> se;
		rep.erase(it);
		terase({R + 2, rt});
	}
	it = prev(rep.LB({L - 1, -INF}));
	if (it -> se != 0 && it -> se == L - 2)
	{
		lt = it -> fi;
		rep.erase(it);
		terase({lt, L - 2});
	}
	tinsert({lt, rt});
	rep.insert({lt, rt});
	return;
}
void smartdelete(int L, int R)
{
	if (L > R) return;
	auto it = prev(rep.LB({L + 1, -INF}));
	int lt = it -> fi, rt = it -> se;
	rep.erase(it);
	terase({lt, rt});
	if (lt <= L - 2)
	{
		tinsert({lt, L - 2});
		rep.insert({lt, L - 2});
	}
	if (R + 2 <= rt)
	{
		tinsert({R + 2, rt});
		rep.insert({R + 2, rt});
	}
	return;
}
bool chk(int x)
{
	if (x == 0) return false;
	auto it = prev(rep.LB({x + 1, -INF}));
	return ((it -> se != 0) && (it -> fi <= x) && (it -> se >= x) && ((x + it -> fi) % 2 == 0));
}
void ins(int x)
{
	if (x < 0)
	{
		return;
	}
	if (x == 0)
	{
		x = 1;
	}
	if (chk(x + 1))
	{
		int rt = (prev(rep.LB({x + 2, -INF}))) -> se;
		smartdelete(x + 1, rt);
		smartinsert(rt + 1, rt + 1);
	}
	else if (chk(x - 1))
	{
		smartdelete(x - 1, x - 1);
		ins(x + 1);
	}
	else if (chk(x))
	{
		if (x == 1)
		{
			smartdelete(x, x);
			ins(2);
		}
		else if (x == 2)
		{
			smartdelete(x, x);
			ins(3);
			ins(1);
		}
		else
		{
			int lt = (prev(rep.LB({x + 1, -INF}))) -> fi;
			smartdelete(lt, x);
			smartinsert(lt + 1, x - 1);
			ins(lt - 2);
			ins(x + 1);
		}
	}
	else
	{
		smartinsert(x, x);
	}
	return;
}

int32_t main()
{
	// ios_base::sync_with_stdio(0);
	srand(time(0));
	//     cout << fixed << setprecision(10);
	//     cerr << fixed << setprecision(10);
	if (fopen("input.in", "r"))
	{
		freopen ("input.in", "r", stdin);
		freopen ("output.out", "w", stdout);
	}
	rep.insert({0, 0});
	root = new node({0, 0});
	root -> trans = {{1, 0}, {0, 1}};
	root -> recalc();
	matpow[0] = {{2, 1}, {INF - 1, 0}};
	for (int i = 1; i <= 40; i++)
	{
		matpow[i] = mul(matpow[i - 1], matpow[i - 1]);
	}
	readi(N);
	for (int i = 0; i < N; i++)
	{
		readi(arr[i]);
	}
	for (int i = 0; i < N; i++)
	{
		ins(arr[i]);
		ppp cup = root -> subtrans;
		int ans = (cup.fi.fi + cup.se.fi) % INF;
		printi(ans); putchar('\n');
	}
	// cerr << "time elapsed = " << (clock() / (CLOCKS_PER_SEC / 1000)) << " ms" << endl;
	return 0;
}

Compilation message

fib.cpp: In function 'int32_t main()':
fib.cpp:421:11: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)', declared with attribute warn_unused_result [-Wunused-result]
   freopen ("input.in", "r", stdin);
   ~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~
fib.cpp:422:11: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)', declared with attribute warn_unused_result [-Wunused-result]
   freopen ("output.out", "w", stdout);
   ~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~

Subtask #1
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 248 KB Output is correct
2 Correct 3 ms 356 KB Output is correct
3 Correct 3 ms 432 KB Output is correct
4 Correct 3 ms 508 KB Output is correct
5 Correct 3 ms 544 KB Output is correct
6 Correct 3 ms 544 KB Output is correct

Subtask #2
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 248 KB Output is correct
2 Correct 3 ms 356 KB Output is correct
3 Correct 3 ms 432 KB Output is correct
4 Correct 3 ms 508 KB Output is correct
5 Correct 3 ms 544 KB Output is correct
6 Correct 3 ms 544 KB Output is correct
7 Correct 2 ms 544 KB Output is correct
8 Correct 3 ms 544 KB Output is correct
9 Correct 4 ms 672 KB Output is correct
10 Correct 3 ms 672 KB Output is correct
11 Correct 4 ms 672 KB Output is correct
12 Correct 2 ms 672 KB Output is correct

Subtask #3
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 672 KB Output is correct
2 Correct 3 ms 672 KB Output is correct

Subtask #4
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 248 KB Output is correct
2 Correct 3 ms 356 KB Output is correct
3 Correct 3 ms 432 KB Output is correct
4 Correct 3 ms 508 KB Output is correct
5 Correct 3 ms 544 KB Output is correct
6 Correct 3 ms 544 KB Output is correct
7 Correct 2 ms 544 KB Output is correct
8 Correct 3 ms 544 KB Output is correct
9 Correct 4 ms 672 KB Output is correct
10 Correct 3 ms 672 KB Output is correct
11 Correct 4 ms 672 KB Output is correct
12 Correct 2 ms 672 KB Output is correct
13 Correct 3 ms 672 KB Output is correct
14 Correct 3 ms 672 KB Output is correct
15 Correct 3 ms 672 KB Output is correct
16 Correct 3 ms 672 KB Output is correct
17 Correct 3 ms 672 KB Output is correct
18 Correct 3 ms 672 KB Output is correct
19 Correct 4 ms 672 KB Output is correct
20 Correct 3 ms 732 KB Output is correct
21 Correct 3 ms 732 KB Output is correct
22 Correct 3 ms 732 KB Output is correct
23 Correct 3 ms 732 KB Output is correct

Subtask #5
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 732 KB Output is correct
2 Correct 806 ms 14496 KB Output is correct
3 Correct 1004 ms 14496 KB Output is correct

Subtask #6
35.0 / 35.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 248 KB Output is correct
2 Correct 3 ms 356 KB Output is correct
3 Correct 3 ms 432 KB Output is correct
4 Correct 3 ms 508 KB Output is correct
5 Correct 3 ms 544 KB Output is correct
6 Correct 3 ms 544 KB Output is correct
7 Correct 2 ms 544 KB Output is correct
8 Correct 3 ms 544 KB Output is correct
9 Correct 4 ms 672 KB Output is correct
10 Correct 3 ms 672 KB Output is correct
11 Correct 4 ms 672 KB Output is correct
12 Correct 2 ms 672 KB Output is correct
13 Correct 3 ms 672 KB Output is correct
14 Correct 3 ms 672 KB Output is correct
15 Correct 3 ms 672 KB Output is correct
16 Correct 3 ms 672 KB Output is correct
17 Correct 3 ms 672 KB Output is correct
18 Correct 3 ms 672 KB Output is correct
19 Correct 4 ms 672 KB Output is correct
20 Correct 3 ms 732 KB Output is correct
21 Correct 3 ms 732 KB Output is correct
22 Correct 3 ms 732 KB Output is correct
23 Correct 3 ms 732 KB Output is correct
24 Correct 3 ms 732 KB Output is correct
25 Correct 806 ms 14496 KB Output is correct
26 Correct 1004 ms 14496 KB Output is correct
27 Correct 199 ms 14496 KB Output is correct
28 Correct 352 ms 14496 KB Output is correct
29 Correct 96 ms 14496 KB Output is correct
30 Correct 371 ms 14496 KB Output is correct
31 Correct 679 ms 14496 KB Output is correct
32 Correct 512 ms 14496 KB Output is correct
33 Correct 811 ms 14496 KB Output is correct
34 Correct 339 ms 14496 KB Output is correct
35 Correct 991 ms 14496 KB Output is correct
36 Correct 942 ms 14496 KB Output is correct
37 Correct 593 ms 14496 KB Output is correct
38 Correct 858 ms 14624 KB Output is correct
39 Correct 161 ms 14624 KB Output is correct
40 Correct 294 ms 14624 KB Output is correct
41 Correct 959 ms 15280 KB Output is correct
42 Correct 879 ms 15280 KB Output is correct
43 Correct 357 ms 15468 KB Output is correct
44 Correct 489 ms 25596 KB Output is correct
45 Correct 1592 ms 25596 KB Output is correct
46 Correct 564 ms 25596 KB Output is correct
47 Correct 1422 ms 25596 KB Output is correct
48 Correct 1268 ms 25688 KB Output is correct
49 Correct 2020 ms 25688 KB Output is correct
50 Correct 945 ms 25688 KB Output is correct