oj.uz

Submission #697840

# Submission time Handle Problem Language Result Execution time Memory
697840 2023-02-11T07:58:51 Z hadi Catfish Farm (IOI22_fish) C++17
81 / 100
 1000 ms 41884 KB 
#include <iostream>
#include <vector>
#include <algorithm>
#include <map>
#include <array>
// #include <assert.h>
#include <deque>

using namespace std;
#define assert(X) {}

class NoOutput : public std::basic_ostream<char> {

};

template<class V>
NoOutput& operator<<(NoOutput& os, const V& v) {
	return os;
}
// NoOutput err;
// ostream& err = cerr;

typedef long long int64 ;
const int64 INF = 1e15L;
const int MAXN = 100000+10;

bool is_sorted(const vector<int>& v) {
	for (size_t i=1; i<v.size(); i++) {
		if (v[i-1] > v[i]) return false;
	}
	return true;
}

// return first index i such that k<=v[i], if not returns v.size()
int lowest_geq(const vector<int>& v, int k) {
	auto it = lower_bound(v.begin(), v.end(), k);
	return it == v.end() ? (int) v.size() : it - v.begin();
}

vector<pair<int,int>> transform_container(const vector<int>& c, std::function<pair<int,int> (int)> &&f)
{
    vector<pair<int,int>> ret;
    std::transform(std::begin(c), std::end(c), std::inserter(ret, std::end(ret)), f);
    return ret;
}

template<typename T>
ostream& operator<<(ostream& os, const vector<T>& v) {
	os << "[";
	for (auto const& vv: v) 
		os << vv << " ";
	return os << "]";
}

template<typename T>
ostream& operator<<(ostream& os, const deque<T>& v) {
	os << "[";
	for (auto const& vv: v) 
		os << vv << " ";
	return os << "]";
}


template<typename T, typename C>
ostream& operator<<(ostream& os, const pair<T, C>& v) {
	return os << v.first << ":" << v.second;
}

struct IntervalTree {
	int n;
	vector<int64> t; 
	vector<int> key;

	void build(const vector<pair<int,int>> key_value) {
		n = key_value.size();
		t.resize(2*n);
		key.clear();
		for (size_t i=0; i<key_value.size(); i++) {
			key.push_back(key_value[i].first);
			t[n+i] = key_value[i].second;
		}
		assert(is_sorted(key));
		for (int i = n - 1; i > 0; --i) t[i] = t[i<<1] + t[i<<1|1];
	}

	int get_index(int p) const {
		return t[p+n];
	}

	void set_index(int p, int value) {
		for (t[p += n] = value; p > 1; p >>= 1) t[p>>1] = t[p] + t[p^1];
	}

	int64 query_index(int l, int r) const {  // sum on interval [l, r)
		int64 res = 0;
		for (l += n, r += n; l < r; l >>= 1, r >>= 1) {
			if (l&1) res += t[l++];
			if (r&1) res += t[--r];
		}
		return res;
	}

	int lowest_geq_index(int v) const {
		return lowest_geq(key, v);
	}

	int64 query(int l_v, int r_v) const {
		return query_index(lowest_geq(key, l_v), lowest_geq(key, r_v));
	}

};


// sum of weight of fishes in column i in rows [x-y)
int64 fish(const IntervalTree & tree, int x, int y) {
	return tree.query(x, y);
}

int N;
map<int, int64> dp_iminus1_down, dp_iminus1_up;
// , dp_i_down, dp_i_up;

// max_{N>=y >= x} DP[i-1,y,down] + fish(i,[x-y)), DP[i-1,y,up] + fish(i,[x-y))
int64 max_1(const IntervalTree& tree_i, int x) {
	//naive
	int64 res = 0;
	for (int y = x; y <= N; y++) {
		// err << "max_1(" << x << ") " << (dp_iminus1_down.find(y) != dp_iminus1_down.end() ? dp_iminus1_down[y] : -INF) << " " << (dp_iminus1_up.find(y) != dp_iminus1_up.end() ? dp_iminus1_up[y] : -INF) << " " << fish(tree_i, x, y) << endl;
		res = max(res, max(
			dp_iminus1_down.find(y) != dp_iminus1_down.end() ? dp_iminus1_down[y] : -INF, 
			dp_iminus1_up.find(y) != dp_iminus1_up.end() ? dp_iminus1_up[y] : -INF) + fish(tree_i, x, y));
	}
	return res;
}

// max_{0<=y<= x} DP[i-1,y,up] + fish(i-1,[y-x))
int64 max_2(const IntervalTree& tree_iminus1, int x) {
	//naive
	int64 res = 0;
	for (int y = 0; y <= x; y++) {
		// err << "max_2(" << x << ") " << (dp_iminus1_up.find(y) != dp_iminus1_up.end() ? dp_iminus1_up[y] : -INF) << " " << fish(tree_iminus1, y, x) << endl;
		res = max(res, 
			(dp_iminus1_up.find(y) != dp_iminus1_up.end() ? dp_iminus1_up[y] : -INF) + fish(tree_iminus1, y, x));
	}
	return res;
}

int64 max_weights(int N, int M, vector<int> X, vector<int> Y, vector<int> W) {
	::N = N;
	// err << "Input: X=" << X << " Y=" << Y << " W=" << W << endl;

	array<vector<int>, MAXN> column_fish_index;
	for (size_t f=0; f<(size_t)M; f++) {
		column_fish_index[X[f]].push_back(f);
	}

	for (size_t i=0; i<(size_t)N+1; i++) {
		sort(column_fish_index[i].begin(), column_fish_index[i].end(), [&](int f1, int f2) { return Y[f1] < Y[f2]; });
		// err << "column_fish_index[" << i << "]=" << column_fish_index[i] << endl;
	}

	IntervalTree tree_iminus1;
	tree_iminus1.build(transform_container(column_fish_index[0], [&Y, &W](int f) { return make_pair(Y[f], W[f]); }));

	dp_iminus1_down = dp_iminus1_up = map<int, int64>();
	dp_iminus1_down[0] = dp_iminus1_up[0] = 0;
	for (size_t c=0; c<=1; c++) {
		for (auto f : column_fish_index[c]) {
			dp_iminus1_up[Y[f]+1] = 0;
		}
	}

	for (size_t i=1; i<(size_t)N+1; i++) {
		// err << "Column " << i << endl;
		vector<int> important_rows_i;
		important_rows_i.push_back(0);
		for (size_t c=i-1; c<=i+1; c++) {
			for (auto f : column_fish_index[c]) {
				important_rows_i.push_back(Y[f]+1);
			}
		}
		sort(important_rows_i.begin(), important_rows_i.end());
		// err << "important_rows_i: " << important_rows_i << endl;
		important_rows_i.resize(unique(important_rows_i.begin(), important_rows_i.end()) - important_rows_i.begin());
		// err << "important_rows_i: " << important_rows_i << endl;
		
		//fill fish interval tree
		IntervalTree tree_i;
		tree_i.build(transform_container(column_fish_index[i], [&Y, &W](int f) { return make_pair(Y[f], W[f]); }));

		// max_{N>=y >= x} DP[i-1,y,down] + fish(i,[x-y)), DP[i-1,y,up] + fish(i,[x-y))
		vector<pair<int,int64>> max_1_discrete;
		max_1_discrete.reserve(dp_iminus1_up.size() + 1);
		max_1_discrete.push_back(make_pair(N+1, -INF));
		for (map<int, int64>::reverse_iterator x = dp_iminus1_up.rbegin(); x != dp_iminus1_up.rend(); x++) {
			auto prev = max_1_discrete.back();
			max_1_discrete.push_back(make_pair(x->first, 
				max(fish(tree_i, x->first, prev.first) + prev.second, 
					max(dp_iminus1_down[x->first], dp_iminus1_up[x->first])) 
			));
			// err << "max_1_discrete[" << x->first << "] p=" << prev << " a)" << (fish(tree_i, x->first, prev.first) + prev.second) << " b)" << dp_iminus1_down[x->first] << " c)" << dp_iminus1_up[x->first] << endl;
		}
		reverse(max_1_discrete.begin(), max_1_discrete.end());
		// err << "max_1_discrete: " << max_1_discrete << endl;

		deque<pair<int,int64>> max_2_discrete;
		// max_{0<=y<= x} DP[i-1,y,up] + fish(i-1,[y-x))
		for (auto const& x: dp_iminus1_up) {
			if (max_2_discrete.size() > 0) {
				auto prev = max_2_discrete.back();
				max_2_discrete.push_back(
					make_pair(
						x.first,
						max(
							fish(tree_iminus1, prev.first, x.first) + prev.second,
							dp_iminus1_up[x.first]
						)
					)
				);
			} else {
				max_2_discrete.push_back(
					make_pair(
						x.first,						
						dp_iminus1_up[x.first]
					)
				);
			}
		}
		// err << "max_2_discrete: " << max_2_discrete << endl;

		// dp_i_down = dp_i_up = map<int, int64>();
		vector<pair<int,int64>> dp_i_down, dp_i_up;
		for (auto x : important_rows_i) {
			// dp_i_down[x] = max_1(tree_i, x);
			auto max_1_discrete_it = lower_bound(max_1_discrete.begin(), max_1_discrete.end(), x, [](const pair<int, int64>& max_1_disc, int r) { return max_1_disc.first < r; });
			// err << "max_1_discrete_it: " << *max_1_discrete_it << endl;
			// dp_i_down[x] = 
			dp_i_down.push_back(make_pair(x,
			max_1_discrete_it == max_1_discrete.end() ? -INF : max_1_discrete_it->second + fish(tree_i, x, max_1_discrete_it->first)
			));
			
			// dp_i_up[x] = max(max_2(tree_iminus1, x), dp_iminus1_down[0]);
			auto max_2_discrete_it = lower_bound(max_2_discrete.rbegin(), max_2_discrete.rend(), x, [](const pair<int, int64>& max_2_disc, int r) { return !(max_2_disc.first <= r); } );
			// err << "max_2_discrete_it: " << *max_2_discrete_it << " p=" << (max_2_discrete_it == max_2_discrete.rbegin() ? make_pair<int,int64>(-1,-1) : *prev(max_2_discrete_it)) << endl;
			assert(max_2_discrete_it->first <= x);
			assert(max_2_discrete_it == max_2_discrete.rbegin() || prev(max_2_discrete_it)->first > x);
			// dp_i_up[x] = 
			dp_i_up.push_back(make_pair(
				x, 
				max(max_2_discrete_it->second + fish(tree_iminus1, max_2_discrete_it->first, x), dp_iminus1_down[0])
			));
			// err << "dp[" << i << "," << x << "]=" << dp_i_down[x] << " ^:" << dp_i_up[x] << endl;
		}
		// dp_iminus1_down = dp_i_down;
		// dp_iminus1_up = dp_i_up;
		dp_iminus1_down = map<int,int64>(dp_i_down.begin(), dp_i_down.end());
		dp_iminus1_up = map<int,int64>(dp_i_up.begin(), dp_i_up.end());

		tree_iminus1 = tree_i;
	}
	return dp_iminus1_down[0];
}

Subtask #1
0 / 3.0

# Verdict Execution time Memory Grader output
1 Correct 205 ms 28108 KB Output is correct
2 Correct 257 ms 33680 KB Output is correct
3 Correct 32 ms 2644 KB Output is correct
4 Correct 32 ms 2516 KB Output is correct
5 Execution timed out 1010 ms 39060 KB Time limit exceeded
6 Halted 0 ms 0 KB -

Subtask #2
6.0 / 6.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2644 KB Output is correct
2 Correct 386 ms 36948 KB Output is correct
3 Correct 459 ms 41884 KB Output is correct
4 Correct 206 ms 29192 KB Output is correct
5 Correct 246 ms 35068 KB Output is correct
6 Correct 2 ms 2644 KB Output is correct
7 Correct 2 ms 2644 KB Output is correct
8 Correct 1 ms 2644 KB Output is correct
9 Correct 2 ms 2644 KB Output is correct
10 Correct 33 ms 2600 KB Output is correct
11 Correct 32 ms 2516 KB Output is correct
12 Correct 295 ms 29352 KB Output is correct
13 Correct 375 ms 35204 KB Output is correct
14 Correct 263 ms 28656 KB Output is correct
15 Correct 227 ms 21292 KB Output is correct
16 Correct 261 ms 28600 KB Output is correct
17 Correct 303 ms 31492 KB Output is correct

Subtask #3
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 33 ms 2644 KB Output is correct
2 Correct 33 ms 2516 KB Output is correct
3 Correct 73 ms 5960 KB Output is correct
4 Correct 67 ms 5196 KB Output is correct
5 Correct 109 ms 9648 KB Output is correct
6 Correct 114 ms 8996 KB Output is correct
7 Correct 107 ms 9664 KB Output is correct
8 Correct 107 ms 9692 KB Output is correct

Subtask #4
14.0 / 14.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 2644 KB Output is correct
2 Correct 2 ms 2604 KB Output is correct
3 Correct 2 ms 2644 KB Output is correct
4 Correct 2 ms 2644 KB Output is correct
5 Correct 2 ms 2644 KB Output is correct
6 Correct 2 ms 2644 KB Output is correct
7 Correct 2 ms 2644 KB Output is correct
8 Correct 1 ms 2600 KB Output is correct
9 Correct 2 ms 2644 KB Output is correct
10 Correct 4 ms 2644 KB Output is correct
11 Correct 3 ms 2608 KB Output is correct
12 Correct 3 ms 2644 KB Output is correct
13 Correct 2 ms 2644 KB Output is correct
14 Correct 3 ms 2644 KB Output is correct

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 2644 KB Output is correct
2 Correct 2 ms 2604 KB Output is correct
3 Correct 2 ms 2644 KB Output is correct
4 Correct 2 ms 2644 KB Output is correct
5 Correct 2 ms 2644 KB Output is correct
6 Correct 2 ms 2644 KB Output is correct
7 Correct 2 ms 2644 KB Output is correct
8 Correct 1 ms 2600 KB Output is correct
9 Correct 2 ms 2644 KB Output is correct
10 Correct 4 ms 2644 KB Output is correct
11 Correct 3 ms 2608 KB Output is correct
12 Correct 3 ms 2644 KB Output is correct
13 Correct 2 ms 2644 KB Output is correct
14 Correct 3 ms 2644 KB Output is correct
15 Correct 2 ms 2600 KB Output is correct
16 Correct 5 ms 2772 KB Output is correct
17 Correct 65 ms 4800 KB Output is correct
18 Correct 58 ms 4932 KB Output is correct
19 Correct 53 ms 4820 KB Output is correct
20 Correct 46 ms 4784 KB Output is correct
21 Correct 45 ms 4792 KB Output is correct
22 Correct 102 ms 6992 KB Output is correct
23 Correct 20 ms 3028 KB Output is correct
24 Correct 58 ms 4072 KB Output is correct
25 Correct 3 ms 2640 KB Output is correct
26 Correct 18 ms 3080 KB Output is correct

Subtask #6
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 2644 KB Output is correct
2 Correct 2 ms 2604 KB Output is correct
3 Correct 2 ms 2644 KB Output is correct
4 Correct 2 ms 2644 KB Output is correct
5 Correct 2 ms 2644 KB Output is correct
6 Correct 2 ms 2644 KB Output is correct
7 Correct 2 ms 2644 KB Output is correct
8 Correct 1 ms 2600 KB Output is correct
9 Correct 2 ms 2644 KB Output is correct
10 Correct 4 ms 2644 KB Output is correct
11 Correct 3 ms 2608 KB Output is correct
12 Correct 3 ms 2644 KB Output is correct
13 Correct 2 ms 2644 KB Output is correct
14 Correct 3 ms 2644 KB Output is correct
15 Correct 2 ms 2600 KB Output is correct
16 Correct 5 ms 2772 KB Output is correct
17 Correct 65 ms 4800 KB Output is correct
18 Correct 58 ms 4932 KB Output is correct
19 Correct 53 ms 4820 KB Output is correct
20 Correct 46 ms 4784 KB Output is correct
21 Correct 45 ms 4792 KB Output is correct
22 Correct 102 ms 6992 KB Output is correct
23 Correct 20 ms 3028 KB Output is correct
24 Correct 58 ms 4072 KB Output is correct
25 Correct 3 ms 2640 KB Output is correct
26 Correct 18 ms 3080 KB Output is correct
27 Correct 8 ms 2848 KB Output is correct
28 Correct 315 ms 13172 KB Output is correct
29 Correct 491 ms 16100 KB Output is correct
30 Correct 714 ms 15280 KB Output is correct
31 Correct 714 ms 15204 KB Output is correct
32 Correct 367 ms 15936 KB Output is correct
33 Correct 718 ms 15412 KB Output is correct
34 Correct 722 ms 15152 KB Output is correct
35 Correct 209 ms 8140 KB Output is correct
36 Correct 718 ms 15720 KB Output is correct

Subtask #7
14.0 / 14.0

# Verdict Execution time Memory Grader output
1 Correct 33 ms 2644 KB Output is correct
2 Correct 33 ms 2516 KB Output is correct
3 Correct 73 ms 5960 KB Output is correct
4 Correct 67 ms 5196 KB Output is correct
5 Correct 109 ms 9648 KB Output is correct
6 Correct 114 ms 8996 KB Output is correct
7 Correct 107 ms 9664 KB Output is correct
8 Correct 107 ms 9692 KB Output is correct
9 Correct 162 ms 9476 KB Output is correct
10 Correct 85 ms 8232 KB Output is correct
11 Correct 173 ms 13848 KB Output is correct
12 Correct 2 ms 2692 KB Output is correct
13 Correct 2 ms 2644 KB Output is correct
14 Correct 2 ms 2644 KB Output is correct
15 Correct 2 ms 2644 KB Output is correct
16 Correct 2 ms 2600 KB Output is correct
17 Correct 1 ms 2644 KB Output is correct
18 Correct 32 ms 2516 KB Output is correct
19 Correct 32 ms 2516 KB Output is correct
20 Correct 33 ms 2516 KB Output is correct
21 Correct 39 ms 2624 KB Output is correct
22 Correct 183 ms 9192 KB Output is correct
23 Correct 255 ms 13960 KB Output is correct
24 Correct 221 ms 14100 KB Output is correct

Subtask #8
0 / 16.0

# Verdict Execution time Memory Grader output
1 Correct 205 ms 28108 KB Output is correct
2 Correct 257 ms 33680 KB Output is correct
3 Correct 32 ms 2644 KB Output is correct
4 Correct 32 ms 2516 KB Output is correct
5 Execution timed out 1010 ms 39060 KB Time limit exceeded
6 Halted 0 ms 0 KB -