oj.uz

Submission #697841

# Submission time Handle Problem Language Result Execution time Memory
697841 2023-02-11T08:00:05 Z hadi Catfish Farm (IOI22_fish) C++17
100 / 100
 955 ms 38964 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;

		vector<pair<int,int64>> max_2_discrete;
		max_2_discrete.reserve(dp_iminus1_up.size());
		// 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
3.0 / 3.0

# Verdict Execution time Memory Grader output
1 Correct 198 ms 27660 KB Output is correct
2 Correct 264 ms 33180 KB Output is correct
3 Correct 31 ms 2516 KB Output is correct
4 Correct 32 ms 2644 KB Output is correct
5 Correct 955 ms 38964 KB Output is correct
6 Correct 449 ms 19040 KB Output is correct

Subtask #2
6.0 / 6.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 2644 KB Output is correct
2 Correct 372 ms 34076 KB Output is correct
3 Correct 432 ms 38400 KB Output is correct
4 Correct 194 ms 27712 KB Output is correct
5 Correct 245 ms 33188 KB Output is correct
6 Correct 2 ms 2644 KB Output is correct
7 Correct 1 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 31 ms 2516 KB Output is correct
11 Correct 30 ms 2516 KB Output is correct
12 Correct 291 ms 27984 KB Output is correct
13 Correct 344 ms 33284 KB Output is correct
14 Correct 256 ms 27132 KB Output is correct
15 Correct 218 ms 19796 KB Output is correct
16 Correct 238 ms 27196 KB Output is correct
17 Correct 275 ms 29764 KB Output is correct

Subtask #3
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 31 ms 2636 KB Output is correct
2 Correct 30 ms 2644 KB Output is correct
3 Correct 67 ms 5592 KB Output is correct
4 Correct 65 ms 4628 KB Output is correct
5 Correct 99 ms 8016 KB Output is correct
6 Correct 102 ms 8124 KB Output is correct
7 Correct 105 ms 8140 KB Output is correct
8 Correct 105 ms 8120 KB Output is correct

Subtask #4
14.0 / 14.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2644 KB Output is correct
2 Correct 1 ms 2644 KB Output is correct
3 Correct 2 ms 2644 KB Output is correct
4 Correct 1 ms 2644 KB Output is correct
5 Correct 2 ms 2552 KB Output is correct
6 Correct 1 ms 2516 KB Output is correct
7 Correct 1 ms 2644 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 2644 KB Output is correct
11 Correct 3 ms 2644 KB Output is correct
12 Correct 4 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 1 ms 2644 KB Output is correct
2 Correct 1 ms 2644 KB Output is correct
3 Correct 2 ms 2644 KB Output is correct
4 Correct 1 ms 2644 KB Output is correct
5 Correct 2 ms 2552 KB Output is correct
6 Correct 1 ms 2516 KB Output is correct
7 Correct 1 ms 2644 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 2644 KB Output is correct
11 Correct 3 ms 2644 KB Output is correct
12 Correct 4 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 2644 KB Output is correct
16 Correct 4 ms 2644 KB Output is correct
17 Correct 64 ms 3996 KB Output is correct
18 Correct 57 ms 4180 KB Output is correct
19 Correct 52 ms 4036 KB Output is correct
20 Correct 52 ms 4108 KB Output is correct
21 Correct 45 ms 4080 KB Output is correct
22 Correct 95 ms 5456 KB Output is correct
23 Correct 19 ms 2952 KB Output is correct
24 Correct 58 ms 3588 KB Output is correct
25 Correct 3 ms 2644 KB Output is correct
26 Correct 17 ms 2940 KB Output is correct

Subtask #6
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2644 KB Output is correct
2 Correct 1 ms 2644 KB Output is correct
3 Correct 2 ms 2644 KB Output is correct
4 Correct 1 ms 2644 KB Output is correct
5 Correct 2 ms 2552 KB Output is correct
6 Correct 1 ms 2516 KB Output is correct
7 Correct 1 ms 2644 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 2644 KB Output is correct
11 Correct 3 ms 2644 KB Output is correct
12 Correct 4 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 2644 KB Output is correct
16 Correct 4 ms 2644 KB Output is correct
17 Correct 64 ms 3996 KB Output is correct
18 Correct 57 ms 4180 KB Output is correct
19 Correct 52 ms 4036 KB Output is correct
20 Correct 52 ms 4108 KB Output is correct
21 Correct 45 ms 4080 KB Output is correct
22 Correct 95 ms 5456 KB Output is correct
23 Correct 19 ms 2952 KB Output is correct
24 Correct 58 ms 3588 KB Output is correct
25 Correct 3 ms 2644 KB Output is correct
26 Correct 17 ms 2940 KB Output is correct
27 Correct 6 ms 2772 KB Output is correct
28 Correct 305 ms 9492 KB Output is correct
29 Correct 486 ms 12428 KB Output is correct
30 Correct 692 ms 11456 KB Output is correct
31 Correct 690 ms 11468 KB Output is correct
32 Correct 328 ms 12256 KB Output is correct
33 Correct 708 ms 11500 KB Output is correct
34 Correct 723 ms 11460 KB Output is correct
35 Correct 198 ms 6260 KB Output is correct
36 Correct 660 ms 12016 KB Output is correct

Subtask #7
14.0 / 14.0

# Verdict Execution time Memory Grader output
1 Correct 31 ms 2636 KB Output is correct
2 Correct 30 ms 2644 KB Output is correct
3 Correct 67 ms 5592 KB Output is correct
4 Correct 65 ms 4628 KB Output is correct
5 Correct 99 ms 8016 KB Output is correct
6 Correct 102 ms 8124 KB Output is correct
7 Correct 105 ms 8140 KB Output is correct
8 Correct 105 ms 8120 KB Output is correct
9 Correct 133 ms 8124 KB Output is correct
10 Correct 83 ms 6556 KB Output is correct
11 Correct 169 ms 10460 KB Output is correct
12 Correct 1 ms 2644 KB Output is correct
13 Correct 2 ms 2644 KB Output is correct
14 Correct 1 ms 2644 KB Output is correct
15 Correct 2 ms 2644 KB Output is correct
16 Correct 2 ms 2644 KB Output is correct
17 Correct 1 ms 2644 KB Output is correct
18 Correct 39 ms 2620 KB Output is correct
19 Correct 31 ms 2644 KB Output is correct
20 Correct 30 ms 2644 KB Output is correct
21 Correct 32 ms 2516 KB Output is correct
22 Correct 169 ms 7076 KB Output is correct
23 Correct 282 ms 10460 KB Output is correct
24 Correct 220 ms 10476 KB Output is correct

Subtask #8
16.0 / 16.0

# Verdict Execution time Memory Grader output
1 Correct 198 ms 27660 KB Output is correct
2 Correct 264 ms 33180 KB Output is correct
3 Correct 31 ms 2516 KB Output is correct
4 Correct 32 ms 2644 KB Output is correct
5 Correct 955 ms 38964 KB Output is correct
6 Correct 449 ms 19040 KB Output is correct
7 Correct 2 ms 2644 KB Output is correct
8 Correct 372 ms 34076 KB Output is correct
9 Correct 432 ms 38400 KB Output is correct
10 Correct 194 ms 27712 KB Output is correct
11 Correct 245 ms 33188 KB Output is correct
12 Correct 2 ms 2644 KB Output is correct
13 Correct 1 ms 2644 KB Output is correct
14 Correct 1 ms 2644 KB Output is correct
15 Correct 2 ms 2644 KB Output is correct
16 Correct 31 ms 2516 KB Output is correct
17 Correct 30 ms 2516 KB Output is correct
18 Correct 291 ms 27984 KB Output is correct
19 Correct 344 ms 33284 KB Output is correct
20 Correct 256 ms 27132 KB Output is correct
21 Correct 218 ms 19796 KB Output is correct
22 Correct 238 ms 27196 KB Output is correct
23 Correct 275 ms 29764 KB Output is correct
24 Correct 31 ms 2636 KB Output is correct
25 Correct 30 ms 2644 KB Output is correct
26 Correct 67 ms 5592 KB Output is correct
27 Correct 65 ms 4628 KB Output is correct
28 Correct 99 ms 8016 KB Output is correct
29 Correct 102 ms 8124 KB Output is correct
30 Correct 105 ms 8140 KB Output is correct
31 Correct 105 ms 8120 KB Output is correct
32 Correct 1 ms 2644 KB Output is correct
33 Correct 1 ms 2644 KB Output is correct
34 Correct 2 ms 2644 KB Output is correct
35 Correct 1 ms 2644 KB Output is correct
36 Correct 2 ms 2552 KB Output is correct
37 Correct 1 ms 2516 KB Output is correct
38 Correct 1 ms 2644 KB Output is correct
39 Correct 2 ms 2644 KB Output is correct
40 Correct 2 ms 2644 KB Output is correct
41 Correct 3 ms 2644 KB Output is correct
42 Correct 3 ms 2644 KB Output is correct
43 Correct 4 ms 2644 KB Output is correct
44 Correct 2 ms 2644 KB Output is correct
45 Correct 3 ms 2644 KB Output is correct
46 Correct 2 ms 2644 KB Output is correct
47 Correct 4 ms 2644 KB Output is correct
48 Correct 64 ms 3996 KB Output is correct
49 Correct 57 ms 4180 KB Output is correct
50 Correct 52 ms 4036 KB Output is correct
51 Correct 52 ms 4108 KB Output is correct
52 Correct 45 ms 4080 KB Output is correct
53 Correct 95 ms 5456 KB Output is correct
54 Correct 19 ms 2952 KB Output is correct
55 Correct 58 ms 3588 KB Output is correct
56 Correct 3 ms 2644 KB Output is correct
57 Correct 17 ms 2940 KB Output is correct
58 Correct 6 ms 2772 KB Output is correct
59 Correct 305 ms 9492 KB Output is correct
60 Correct 486 ms 12428 KB Output is correct
61 Correct 692 ms 11456 KB Output is correct
62 Correct 690 ms 11468 KB Output is correct
63 Correct 328 ms 12256 KB Output is correct
64 Correct 708 ms 11500 KB Output is correct
65 Correct 723 ms 11460 KB Output is correct
66 Correct 198 ms 6260 KB Output is correct
67 Correct 660 ms 12016 KB Output is correct
68 Correct 133 ms 8124 KB Output is correct
69 Correct 83 ms 6556 KB Output is correct
70 Correct 169 ms 10460 KB Output is correct
71 Correct 1 ms 2644 KB Output is correct
72 Correct 2 ms 2644 KB Output is correct
73 Correct 1 ms 2644 KB Output is correct
74 Correct 2 ms 2644 KB Output is correct
75 Correct 2 ms 2644 KB Output is correct
76 Correct 1 ms 2644 KB Output is correct
77 Correct 39 ms 2620 KB Output is correct
78 Correct 31 ms 2644 KB Output is correct
79 Correct 30 ms 2644 KB Output is correct
80 Correct 32 ms 2516 KB Output is correct
81 Correct 169 ms 7076 KB Output is correct
82 Correct 282 ms 10460 KB Output is correct
83 Correct 220 ms 10476 KB Output is correct
84 Correct 917 ms 30472 KB Output is correct
85 Correct 929 ms 30904 KB Output is correct
86 Correct 488 ms 19148 KB Output is correct
87 Correct 530 ms 19432 KB Output is correct
88 Correct 2 ms 2644 KB Output is correct
89 Correct 510 ms 19488 KB Output is correct
90 Correct 457 ms 17912 KB Output is correct
91 Correct 348 ms 17356 KB Output is correct