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Submission #1027029

# Submission time Handle Problem Language Result Execution time Memory
1027029 2024-07-18T19:00:41 Z misteg168 Fibonacci representations (CEOI18_fib) C++17
100 / 100
 261 ms 33460 KB 
/*
 * Kamil Debowski
 * O(n log(n)), the intended solution.
 * Finds all changes of intervals offline and then builds a segment tree over them.
 * No BST.
 */

#include <bits/stdc++.h>
using namespace std;
const int INF = 1e9 + 1000; // must be bigger than max(A[i]) + log(n)
const int mod = 1e9 + 7;

set<pair<int,int>> intervals; // pairs of indices (A, B) such that A,A+2,A+4,...,B are all 1's
vector<vector<pair<int,int>>> events;
int current_time;

void add_if_not_empty(int a, int b) {
	assert((b - a) % 2 == 0);
	if(a <= b) {
		assert(0 <= a && b < INF);
		events[current_time].push_back({a, b});
		intervals.insert({a, b});
	}
}

void erase(set<pair<int,int>> :: iterator it) {
	events[current_time].push_back({it -> first, it -> second});
	intervals.erase(it);
}

void add_outside(const int x) {
	auto R = intervals.upper_bound({x, INF});
	if(x + 1 == R -> first) { // just before the interval R
		// the whole interval is compressed to R->second+1
		const int new_value = R -> second + 1;
		erase(R);
		add_outside(new_value);
		return;
	}
	auto L = prev(R);
	if(L -> second + 1 == x) { // just after the interval L
		// erase the last element of L
		add_if_not_empty(L -> first, L -> second - 2);
		erase(L);
		add_outside(x + 1);
		return;
	}
	pair<int,int> new_interval{x, x};
	if(x + 2 == R -> first) {
		new_interval.second = R -> second;
		erase(R);
	}
	if(L -> second + 2 == x) {
		new_interval.first = L -> first;
		erase(L);
	}
	add_if_not_empty(new_interval.first, new_interval.second);
}

void add_possibly_inside(const int x) {
	auto it = intervals.upper_bound({x, INF});
	it--;
	if(!(it -> first <= x && x <= it -> second)) {
		add_outside(x);
		return;
	}
	// now we know that 'x' is inside the interval
	assert(0 <= it -> first && it -> second < INF);
	if(it -> first % 2 != x % 2) {
		/*
		 *   ...0001010101010100...
		 * +            1
		 * = ...0001010100000010...
		 */
		add_if_not_empty(it -> first, x - 1);
		const int new_value = it -> second + 1;
		erase(it);
		add_outside(new_value);
		return;
	}
	/*
	 *   ...0001010101010100...
	 * +           1
	 * = ...0100101011010100...
	 * = ...0100101000000010...
	 */
	const vector<int> new_values{it -> first - 2, it -> second + 1};
	add_if_not_empty(it -> first + 1, x - 1);
	erase(it);
	for(int a : new_values) {
		if(a == -2) continue; // Fib[-2] = 0
		if(a == -1) a = 0; // Fib[-1] = Fib[0]
		add_outside(a);
	}
}

struct M {
	#define REP(i) for(int i = 0; i < 2; ++i)
	int m[2][2]; // m[A][B] = m[rightmost bit can be not-changed][leftmost bit...]
	int * operator [] (int i) { return m[i]; }
	const int * operator [] (int i) const { return m[i]; }
	M() { REP(i) REP(j) m[i][j] = 0; }
	M operator * (const M & b) const {
		M r;
		REP(i) REP(j) REP(k)
			r[i][k] = (r[i][k] + (long long) m[i][j] * b[j][k]) % mod;
		return r;
	}
	#undef REP
};

struct S {
	bool exists = false;
	M m;
	int low, high;
	void init(pair<int,int> p) {
		low = p.first, high = p.second;
		int size = (high - low) / 2 + 1;
		m[0][0] = 1;
		m[0][1] = 0;
		m[1][0] = size - 1;
		m[1][1] = 1;
	}
	void merge(const S & A, const S & B) {
		exists = A.exists || B.exists;
		if(!A.exists) {
			*this = B;
			return;
		}
		if(!B.exists) {
			*this = A;
			return;
		}
		low = A.low;
		high = B.high;
		const int dist = B.low - A.high;
		//~ assert(dist >= 3);
		M mid;
		if(dist % 2 == 0) {
			mid[0][0] = 1;
			mid[1][0] = 1;
		}
		mid[0][1] = mid[1][1] = max(0, (dist - 1) / 2);
		mid[1][1] = (mid[1][1] + 1) % mod;
		m = (B.m * mid) * A.m;
	}
};

int main() {
	int n;
	scanf("%d", &n);
	events.resize(n);
	intervals.insert({-4, -4});
	intervals.insert({INF, INF}); // to simplify the implementation
	for(current_time = 0; current_time < n; ++current_time) {
		int ai;
		scanf("%d", &ai);
		--ai;
		add_possibly_inside(ai);
	}
	
	vector<pair<int,int>> all;
	for(const vector<pair<int,int>> & vec : events)
		for(const pair<int,int> & p : vec)
			all.push_back(p);
	sort(all.begin(), all.end());
	all.resize(unique(all.begin(),all.end()) - all.begin());
	
	int pot = 1;
	while(pot < (int) all.size()) pot *= 2;
	vector<S> tr(2 * pot);
	for(int i = 0; i < (int) all.size(); ++i)
		tr[pot+i].init(all[i]);
	S START;
	START.init({-1, -1});
	START.exists = true;
	for(current_time = 0; current_time < n; ++current_time) {
		for(pair<int,int> p : events[current_time]) {
			int i = lower_bound(all.begin(), all.end(), p) - all.begin();
			tr[pot+i].exists = !tr[pot+i].exists;
			for(int x = (pot + i) / 2; x >= 1; x /= 2)
				tr[x].merge(tr[2*x], tr[2*x+1]);
		}
		S total;
		total.merge(START, tr[1]);
		printf("%d\n", total.m[1][1]);
	}
}

Compilation message

fib.cpp: In function 'int main()':
fib.cpp:151:7: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
  151 |  scanf("%d", &n);
      |  ~~~~~^~~~~~~~~~
fib.cpp:157:8: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
  157 |   scanf("%d", &ai);
      |   ~~~~~^~~~~~~~~~~

Subtask #1
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 600 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 348 KB Output is correct

Subtask #2
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 600 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 348 KB Output is correct
7 Correct 1 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 0 ms 436 KB Output is correct
12 Correct 1 ms 348 KB Output is correct

Subtask #3
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct

Subtask #4
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 600 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 348 KB Output is correct
7 Correct 1 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 0 ms 436 KB Output is correct
12 Correct 1 ms 348 KB Output is correct
13 Correct 0 ms 348 KB Output is correct
14 Correct 0 ms 348 KB Output is correct
15 Correct 1 ms 348 KB Output is correct
16 Correct 0 ms 348 KB Output is correct
17 Correct 0 ms 348 KB Output is correct
18 Correct 0 ms 348 KB Output is correct
19 Correct 0 ms 348 KB Output is correct
20 Correct 0 ms 348 KB Output is correct
21 Correct 1 ms 348 KB Output is correct
22 Correct 0 ms 348 KB Output is correct
23 Correct 1 ms 348 KB Output is correct

Subtask #5
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 604 KB Output is correct
2 Correct 136 ms 20524 KB Output is correct
3 Correct 141 ms 19400 KB Output is correct

Subtask #6
35.0 / 35.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 600 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 348 KB Output is correct
7 Correct 1 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 0 ms 436 KB Output is correct
12 Correct 1 ms 348 KB Output is correct
13 Correct 0 ms 348 KB Output is correct
14 Correct 0 ms 348 KB Output is correct
15 Correct 1 ms 348 KB Output is correct
16 Correct 0 ms 348 KB Output is correct
17 Correct 0 ms 348 KB Output is correct
18 Correct 0 ms 348 KB Output is correct
19 Correct 0 ms 348 KB Output is correct
20 Correct 0 ms 348 KB Output is correct
21 Correct 1 ms 348 KB Output is correct
22 Correct 0 ms 348 KB Output is correct
23 Correct 1 ms 348 KB Output is correct
24 Correct 0 ms 604 KB Output is correct
25 Correct 136 ms 20524 KB Output is correct
26 Correct 141 ms 19400 KB Output is correct
27 Correct 38 ms 6080 KB Output is correct
28 Correct 79 ms 10448 KB Output is correct
29 Correct 36 ms 5944 KB Output is correct
30 Correct 70 ms 10068 KB Output is correct
31 Correct 80 ms 17344 KB Output is correct
32 Correct 79 ms 11208 KB Output is correct
33 Correct 111 ms 16080 KB Output is correct
34 Correct 110 ms 17344 KB Output is correct
35 Correct 139 ms 15676 KB Output is correct
36 Correct 179 ms 16060 KB Output is correct
37 Correct 146 ms 9672 KB Output is correct
38 Correct 141 ms 20468 KB Output is correct
39 Correct 48 ms 8660 KB Output is correct
40 Correct 88 ms 13172 KB Output is correct
41 Correct 221 ms 13180 KB Output is correct
42 Correct 124 ms 20424 KB Output is correct
43 Correct 93 ms 13752 KB Output is correct
44 Correct 156 ms 32136 KB Output is correct
45 Correct 195 ms 32608 KB Output is correct
46 Correct 187 ms 31620 KB Output is correct
47 Correct 189 ms 22204 KB Output is correct
48 Correct 201 ms 33460 KB Output is correct
49 Correct 261 ms 31804 KB Output is correct
50 Correct 181 ms 20804 KB Output is correct