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Submission #70201

# Submission time Handle Problem Language Result Execution time Memory
70201 2018-08-22T13:24:25 Z model_code Fibonacci representations (CEOI18_fib) C++17
100 / 100
 1267 ms 31120 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]
  scanf("%d", &n);
  ~~~~~^~~~~~~~~~
fib.cpp:157:8: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
   scanf("%d", &ai);
   ~~~~~^~~~~~~~~~~

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 2 ms 356 KB Output is correct
4 Correct 3 ms 432 KB Output is correct
5 Correct 2 ms 508 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 2 ms 356 KB Output is correct
4 Correct 3 ms 432 KB Output is correct
5 Correct 2 ms 508 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 592 KB Output is correct
9 Correct 2 ms 592 KB Output is correct
10 Correct 3 ms 592 KB Output is correct
11 Correct 2 ms 620 KB Output is correct
12 Correct 2 ms 620 KB Output is correct

Subtask #3
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 620 KB Output is correct
2 Correct 2 ms 620 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 2 ms 356 KB Output is correct
4 Correct 3 ms 432 KB Output is correct
5 Correct 2 ms 508 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 592 KB Output is correct
9 Correct 2 ms 592 KB Output is correct
10 Correct 3 ms 592 KB Output is correct
11 Correct 2 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 2 ms 620 KB Output is correct
15 Correct 2 ms 620 KB Output is correct
16 Correct 3 ms 620 KB Output is correct
17 Correct 3 ms 620 KB Output is correct
18 Correct 2 ms 620 KB Output is correct
19 Correct 3 ms 620 KB Output is correct
20 Correct 3 ms 620 KB Output is correct
21 Correct 3 ms 620 KB Output is correct
22 Correct 3 ms 620 KB Output is correct
23 Correct 3 ms 620 KB Output is correct

Subtask #5
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 620 KB Output is correct
2 Correct 731 ms 19908 KB Output is correct
3 Correct 831 ms 19908 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 2 ms 356 KB Output is correct
4 Correct 3 ms 432 KB Output is correct
5 Correct 2 ms 508 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 592 KB Output is correct
9 Correct 2 ms 592 KB Output is correct
10 Correct 3 ms 592 KB Output is correct
11 Correct 2 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 2 ms 620 KB Output is correct
15 Correct 2 ms 620 KB Output is correct
16 Correct 3 ms 620 KB Output is correct
17 Correct 3 ms 620 KB Output is correct
18 Correct 2 ms 620 KB Output is correct
19 Correct 3 ms 620 KB Output is correct
20 Correct 3 ms 620 KB Output is correct
21 Correct 3 ms 620 KB Output is correct
22 Correct 3 ms 620 KB Output is correct
23 Correct 3 ms 620 KB Output is correct
24 Correct 3 ms 620 KB Output is correct
25 Correct 731 ms 19908 KB Output is correct
26 Correct 831 ms 19908 KB Output is correct
27 Correct 173 ms 19908 KB Output is correct
28 Correct 290 ms 19908 KB Output is correct
29 Correct 135 ms 19908 KB Output is correct
30 Correct 362 ms 19908 KB Output is correct
31 Correct 307 ms 19908 KB Output is correct
32 Correct 334 ms 19908 KB Output is correct
33 Correct 439 ms 19908 KB Output is correct
34 Correct 457 ms 19908 KB Output is correct
35 Correct 786 ms 19908 KB Output is correct
36 Correct 970 ms 19908 KB Output is correct
37 Correct 707 ms 19908 KB Output is correct
38 Correct 762 ms 20004 KB Output is correct
39 Correct 213 ms 20004 KB Output is correct
40 Correct 326 ms 20004 KB Output is correct
41 Correct 1006 ms 20004 KB Output is correct
42 Correct 800 ms 20096 KB Output is correct
43 Correct 370 ms 20096 KB Output is correct
44 Correct 463 ms 31072 KB Output is correct
45 Correct 800 ms 31072 KB Output is correct
46 Correct 719 ms 31072 KB Output is correct
47 Correct 852 ms 31072 KB Output is correct
48 Correct 1032 ms 31120 KB Output is correct
49 Correct 1267 ms 31120 KB Output is correct
50 Correct 808 ms 31120 KB Output is correct