oj.uz

Submission #697734

# Submission time Handle Problem Language Result Execution time Memory
697734 2023-02-11T00:18:39 Z hadi Catfish Farm (IOI22_fish) C++17
81 / 100
 1000 ms 38712 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))
		deque<pair<int,int64>> max_1_discrete;
		max_1_discrete.push_front(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.front();
			max_1_discrete.push_front(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;
		}
		// 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 207 ms 28104 KB Output is correct
2 Correct 242 ms 33584 KB Output is correct
3 Correct 41 ms 2644 KB Output is correct
4 Correct 44 ms 2644 KB Output is correct
5 Execution timed out 1025 ms 38524 KB Time limit exceeded
6 Halted 0 ms 0 KB -

Subtask #2
6.0 / 6.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 2644 KB Output is correct
2 Correct 383 ms 34628 KB Output is correct
3 Correct 456 ms 38712 KB Output is correct
4 Correct 192 ms 28112 KB Output is correct
5 Correct 244 ms 33488 KB Output is correct
6 Correct 2 ms 2644 KB Output is correct
7 Correct 2 ms 2644 KB Output is correct
8 Correct 2 ms 2600 KB Output is correct
9 Correct 2 ms 2644 KB Output is correct
10 Correct 39 ms 2516 KB Output is correct
11 Correct 37 ms 2644 KB Output is correct
12 Correct 290 ms 28364 KB Output is correct
13 Correct 361 ms 33656 KB Output is correct
14 Correct 267 ms 27396 KB Output is correct
15 Correct 213 ms 19868 KB Output is correct
16 Correct 298 ms 27380 KB Output is correct
17 Correct 281 ms 30092 KB Output is correct

Subtask #3
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 37 ms 2644 KB Output is correct
2 Correct 37 ms 2644 KB Output is correct
3 Correct 78 ms 5712 KB Output is correct
4 Correct 72 ms 4664 KB Output is correct
5 Correct 128 ms 8264 KB Output is correct
6 Correct 106 ms 8252 KB Output is correct
7 Correct 130 ms 8252 KB Output is correct
8 Correct 124 ms 8140 KB Output is correct

Subtask #4
14.0 / 14.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 2644 KB Output is correct
2 Correct 2 ms 2644 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 1 ms 2608 KB Output is correct
8 Correct 2 ms 2644 KB Output is correct
9 Correct 2 ms 2644 KB Output is correct
10 Correct 3 ms 2744 KB Output is correct
11 Correct 3 ms 2644 KB Output is correct
12 Correct 3 ms 2644 KB Output is correct
13 Correct 2 ms 2644 KB Output is correct
14 Correct 2 ms 2644 KB Output is correct

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 2644 KB Output is correct
2 Correct 2 ms 2644 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 1 ms 2608 KB Output is correct
8 Correct 2 ms 2644 KB Output is correct
9 Correct 2 ms 2644 KB Output is correct
10 Correct 3 ms 2744 KB Output is correct
11 Correct 3 ms 2644 KB Output is correct
12 Correct 3 ms 2644 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 4 ms 2784 KB Output is correct
17 Correct 75 ms 4300 KB Output is correct
18 Correct 65 ms 4332 KB Output is correct
19 Correct 52 ms 4180 KB Output is correct
20 Correct 49 ms 4248 KB Output is correct
21 Correct 47 ms 4216 KB Output is correct
22 Correct 99 ms 5588 KB Output is correct
23 Correct 28 ms 3028 KB Output is correct
24 Correct 63 ms 3724 KB Output is correct
25 Correct 3 ms 2644 KB Output is correct
26 Correct 18 ms 2960 KB Output is correct

Subtask #6
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 2644 KB Output is correct
2 Correct 2 ms 2644 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 1 ms 2608 KB Output is correct
8 Correct 2 ms 2644 KB Output is correct
9 Correct 2 ms 2644 KB Output is correct
10 Correct 3 ms 2744 KB Output is correct
11 Correct 3 ms 2644 KB Output is correct
12 Correct 3 ms 2644 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 4 ms 2784 KB Output is correct
17 Correct 75 ms 4300 KB Output is correct
18 Correct 65 ms 4332 KB Output is correct
19 Correct 52 ms 4180 KB Output is correct
20 Correct 49 ms 4248 KB Output is correct
21 Correct 47 ms 4216 KB Output is correct
22 Correct 99 ms 5588 KB Output is correct
23 Correct 28 ms 3028 KB Output is correct
24 Correct 63 ms 3724 KB Output is correct
25 Correct 3 ms 2644 KB Output is correct
26 Correct 18 ms 2960 KB Output is correct
27 Correct 6 ms 2772 KB Output is correct
28 Correct 307 ms 9688 KB Output is correct
29 Correct 517 ms 12672 KB Output is correct
30 Correct 745 ms 11824 KB Output is correct
31 Correct 743 ms 11808 KB Output is correct
32 Correct 361 ms 12428 KB Output is correct
33 Correct 756 ms 11836 KB Output is correct
34 Correct 772 ms 11724 KB Output is correct
35 Correct 216 ms 6536 KB Output is correct
36 Correct 721 ms 12188 KB Output is correct

Subtask #7
14.0 / 14.0

# Verdict Execution time Memory Grader output
1 Correct 37 ms 2644 KB Output is correct
2 Correct 37 ms 2644 KB Output is correct
3 Correct 78 ms 5712 KB Output is correct
4 Correct 72 ms 4664 KB Output is correct
5 Correct 128 ms 8264 KB Output is correct
6 Correct 106 ms 8252 KB Output is correct
7 Correct 130 ms 8252 KB Output is correct
8 Correct 124 ms 8140 KB Output is correct
9 Correct 150 ms 8140 KB Output is correct
10 Correct 100 ms 6600 KB Output is correct
11 Correct 197 ms 10576 KB Output is correct
12 Correct 2 ms 2644 KB Output is correct
13 Correct 3 ms 2736 KB Output is correct
14 Correct 2 ms 2644 KB Output is correct
15 Correct 2 ms 2604 KB Output is correct
16 Correct 2 ms 2644 KB Output is correct
17 Correct 2 ms 2644 KB Output is correct
18 Correct 37 ms 2516 KB Output is correct
19 Correct 48 ms 2644 KB Output is correct
20 Correct 39 ms 2644 KB Output is correct
21 Correct 41 ms 2644 KB Output is correct
22 Correct 183 ms 7256 KB Output is correct
23 Correct 238 ms 10572 KB Output is correct
24 Correct 234 ms 10616 KB Output is correct

Subtask #8
0 / 16.0

# Verdict Execution time Memory Grader output
1 Correct 207 ms 28104 KB Output is correct
2 Correct 242 ms 33584 KB Output is correct
3 Correct 41 ms 2644 KB Output is correct
4 Correct 44 ms 2644 KB Output is correct
5 Execution timed out 1025 ms 38524 KB Time limit exceeded
6 Halted 0 ms 0 KB -