답안 #1104612

#	제출 시각	아이디	문제	언어	결과	실행 시간	메모리
1104612	2024-10-24T07:08:42 Z	Shadow1	Mountains (NOI20_mountains)	C++17	100 / 100	685 ms	48228 KB

Mountains

// Programmer: Shadow1

#include <bits/stdc++.h>
using namespace std;

using ll = long long;
using ld = long double;
using ull = unsigned long long;
using str = string; // yay python!

#define i64 int64_t
#define watch(x) cerr << (#x) << " = " << (x) << '\n';
#define output_vector(v) for(auto &x : v){cout << x << " ";}cout << '\n';
#define vt vector
#define st stack
#define pq priority_queue
#define pb push_back
#define eb emplace_back
#define pii pair<int,int>
#define umap unordered_map
#define uset unordered_set
#define fir first
#define sec second
#define sz(x) int(x.size())
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()


// T: O(n log n)
// M : O(n + k log n)

class FenwickTree {
private:
	vector<int64_t> ft;
public:
	FenwickTree(int m) {  // Create empty Fenwick Tree
		ft.assign(m+1,0);
	}

	int LSOne(int x) {    // Return Least significant 1-bit of x
		return ((x) & (-x));
	}
	void build(const vector<int64_t> &f) {  // Build the fenwick tree array from the frequency array
		int m = sz(f) - 1;
		ft.assign(m+1,0);
		for(int i=1; i<=m; ++i) {
			ft[i] += f[i];
			if(i + LSOne(i) <= m)
				ft[i+LSOne(i)] += ft[i];
		}
	}

	FenwickTree(int m, const vector<int64_t> &s) {   // Convert the array to a frequency array with m integer keys
		vector<int64_t> f(m+1,0);						// i.e. the array's maximum value must be m
		for(int i=0; i<sz(s); ++i)
			++f[s[i]];
	}

	int64_t rsq(int i, int j) {  // i <= j   // O(log m)
		int64_t sum = 0;
		while(j > 0) {
			sum += ft[j];
			j -= LSOne(j);
		}
		--i;
		while(i > 0) {
			sum -= ft[i];
			i -= LSOne(i);
		}
		return sum;
	}

	void update(int i, int64_t v) {
		for(; i<sz(ft); i+=LSOne(i))   // O(log m)
			ft[i] += v;
	}

};


void solve() {
	int n;
	cin >> n;
	vector<int64_t> h(n), cnt(n+1), p(n+1); // cnt[i] is the number of ith smallest elements.
	set<int64_t> s;
	map<int64_t, int> rank;

	for(int i=0; i<n; ++i) {  // O(n log n)
		cin >> h[i];
		s.insert(h[i]);
	}
	int k = 1;
	for(auto &S : s) {  // Worse case O(n log n)
		rank[S] = k;     // S is the kth smallest element
		++k;
	}
	--k;
	assert(k <= n);
	for(auto &H : h) 
		cnt[rank[H]]++;   
	
	p[1] = cnt[1];
	for(int i=2; i<=k; ++i)
		p[i] = p[i-1] + cnt[i];

	// Algorithm starts: 
	FenwickTree ft(k);  // ft[i] will contain the number of ith smallest elements
	int64_t ans = 0;
	
	ft.update(rank[h[0]],1);
	for(int i=1; i<n-1; ++i) {
		int64_t x = ft.rsq(1,rank[h[i]]-1);    // O(log n)	
		int64_t y = p[rank[h[i]]-1];
		ans += (x * (y - x));
		ft.update(rank[h[i]],1);  // update
	}
	cout << ans << '\n';
}

int main() {
	// freopen("output.txt", "w", stdout);
	// freopen("input.txt", "r", stdin);
	ios::sync_with_stdio(false);
	cin.tie(NULL); 
	
	solve();
	return 0;
}

/* CHECK :
1. COMPARATOR FUNCTION MUST RETURN FALSE WHEN ARGUMENTS ARE EQUAL!!!
2. Overflow! Typecase int64_t on operations if varaibles are int
3. Check array bounds!!!
4. Check array indexing!!!
5. Edge cases. (N==1)!!!
*/

Subtask #1
2.0 / 2.0

#	결과	실행 시간	메모리	Grader output
1	Correct	1 ms	336 KB	Output is correct
2	Correct	260 ms	48200 KB	Output is correct
3	Correct	263 ms	48200 KB	Output is correct
4	Correct	264 ms	48200 KB	Output is correct
5	Correct	269 ms	48228 KB	Output is correct
6	Correct	262 ms	48200 KB	Output is correct
7	Correct	269 ms	48212 KB	Output is correct
8	Correct	281 ms	48200 KB	Output is correct
9	Correct	203 ms	31304 KB	Output is correct
10	Correct	212 ms	31304 KB	Output is correct

Subtask #2
4.0 / 4.0

#	결과	실행 시간	메모리	Grader output
1	Correct	19 ms	8016 KB	Output is correct
2	Correct	19 ms	8016 KB	Output is correct
3	Correct	20 ms	8016 KB	Output is correct
4	Correct	19 ms	7944 KB	Output is correct
5	Correct	20 ms	8016 KB	Output is correct
6	Correct	19 ms	8016 KB	Output is correct
7	Correct	18 ms	8016 KB	Output is correct
8	Correct	16 ms	8016 KB	Output is correct
9	Correct	17 ms	8016 KB	Output is correct
10	Correct	1 ms	336 KB	Output is correct

Subtask #3
9.0 / 9.0

#	결과	실행 시간	메모리	Grader output
1	Correct	19 ms	8016 KB	Output is correct
2	Correct	19 ms	8016 KB	Output is correct
3	Correct	20 ms	8016 KB	Output is correct
4	Correct	19 ms	7944 KB	Output is correct
5	Correct	20 ms	8016 KB	Output is correct
6	Correct	19 ms	8016 KB	Output is correct
7	Correct	18 ms	8016 KB	Output is correct
8	Correct	16 ms	8016 KB	Output is correct
9	Correct	17 ms	8016 KB	Output is correct
10	Correct	1 ms	336 KB	Output is correct
11	Correct	45 ms	8272 KB	Output is correct
12	Correct	45 ms	8144 KB	Output is correct
13	Correct	47 ms	8272 KB	Output is correct
14	Correct	45 ms	8440 KB	Output is correct
15	Correct	45 ms	8272 KB	Output is correct
16	Correct	45 ms	8272 KB	Output is correct
17	Correct	45 ms	8272 KB	Output is correct
18	Correct	23 ms	8272 KB	Output is correct
19	Correct	23 ms	8272 KB	Output is correct
20	Correct	1 ms	336 KB	Output is correct

Subtask #4
36.0 / 36.0

#	결과	실행 시간	메모리	Grader output
1	Correct	1 ms	336 KB	Output is correct
2	Correct	1 ms	336 KB	Output is correct
3	Correct	1 ms	336 KB	Output is correct
4	Correct	1 ms	336 KB	Output is correct
5	Correct	1 ms	504 KB	Output is correct
6	Correct	1 ms	336 KB	Output is correct
7	Correct	1 ms	336 KB	Output is correct
8	Correct	1 ms	468 KB	Output is correct
9	Correct	1 ms	336 KB	Output is correct
10	Correct	1 ms	336 KB	Output is correct

Subtask #5
28.0 / 28.0

#	결과	실행 시간	메모리	Grader output
1	Correct	1 ms	336 KB	Output is correct
2	Correct	1 ms	336 KB	Output is correct
3	Correct	1 ms	336 KB	Output is correct
4	Correct	1 ms	336 KB	Output is correct
5	Correct	1 ms	504 KB	Output is correct
6	Correct	1 ms	336 KB	Output is correct
7	Correct	1 ms	336 KB	Output is correct
8	Correct	1 ms	468 KB	Output is correct
9	Correct	1 ms	336 KB	Output is correct
10	Correct	1 ms	336 KB	Output is correct
11	Correct	10 ms	1872 KB	Output is correct
12	Correct	11 ms	1872 KB	Output is correct
13	Correct	11 ms	2060 KB	Output is correct
14	Correct	10 ms	1872 KB	Output is correct
15	Correct	11 ms	1872 KB	Output is correct
16	Correct	10 ms	2060 KB	Output is correct
17	Correct	11 ms	1872 KB	Output is correct
18	Correct	8 ms	1360 KB	Output is correct
19	Correct	3 ms	592 KB	Output is correct
20	Correct	1 ms	336 KB	Output is correct

Subtask #6
9.0 / 9.0

#	결과	실행 시간	메모리	Grader output
1	Correct	19 ms	8016 KB	Output is correct
2	Correct	19 ms	8016 KB	Output is correct
3	Correct	20 ms	8016 KB	Output is correct
4	Correct	19 ms	7944 KB	Output is correct
5	Correct	20 ms	8016 KB	Output is correct
6	Correct	19 ms	8016 KB	Output is correct
7	Correct	18 ms	8016 KB	Output is correct
8	Correct	16 ms	8016 KB	Output is correct
9	Correct	17 ms	8016 KB	Output is correct
10	Correct	1 ms	336 KB	Output is correct
11	Correct	45 ms	8272 KB	Output is correct
12	Correct	45 ms	8144 KB	Output is correct
13	Correct	47 ms	8272 KB	Output is correct
14	Correct	45 ms	8440 KB	Output is correct
15	Correct	45 ms	8272 KB	Output is correct
16	Correct	45 ms	8272 KB	Output is correct
17	Correct	45 ms	8272 KB	Output is correct
18	Correct	23 ms	8272 KB	Output is correct
19	Correct	23 ms	8272 KB	Output is correct
20	Correct	1 ms	336 KB	Output is correct
21	Correct	374 ms	20300 KB	Output is correct
22	Correct	333 ms	20296 KB	Output is correct
23	Correct	362 ms	20372 KB	Output is correct
24	Correct	347 ms	20296 KB	Output is correct
25	Correct	326 ms	20312 KB	Output is correct
26	Correct	306 ms	20296 KB	Output is correct
27	Correct	334 ms	20160 KB	Output is correct
28	Correct	132 ms	20296 KB	Output is correct
29	Correct	135 ms	20300 KB	Output is correct
30	Correct	1 ms	336 KB	Output is correct

Subtask #7
12.0 / 12.0

#	결과	실행 시간	메모리	Grader output
1	Correct	1 ms	336 KB	Output is correct
2	Correct	260 ms	48200 KB	Output is correct
3	Correct	263 ms	48200 KB	Output is correct
4	Correct	264 ms	48200 KB	Output is correct
5	Correct	269 ms	48228 KB	Output is correct
6	Correct	262 ms	48200 KB	Output is correct
7	Correct	269 ms	48212 KB	Output is correct
8	Correct	281 ms	48200 KB	Output is correct
9	Correct	203 ms	31304 KB	Output is correct
10	Correct	212 ms	31304 KB	Output is correct
11	Correct	19 ms	8016 KB	Output is correct
12	Correct	19 ms	8016 KB	Output is correct
13	Correct	20 ms	8016 KB	Output is correct
14	Correct	19 ms	7944 KB	Output is correct
15	Correct	20 ms	8016 KB	Output is correct
16	Correct	19 ms	8016 KB	Output is correct
17	Correct	18 ms	8016 KB	Output is correct
18	Correct	16 ms	8016 KB	Output is correct
19	Correct	17 ms	8016 KB	Output is correct
20	Correct	1 ms	336 KB	Output is correct
21	Correct	45 ms	8272 KB	Output is correct
22	Correct	45 ms	8144 KB	Output is correct
23	Correct	47 ms	8272 KB	Output is correct
24	Correct	45 ms	8440 KB	Output is correct
25	Correct	45 ms	8272 KB	Output is correct
26	Correct	45 ms	8272 KB	Output is correct
27	Correct	45 ms	8272 KB	Output is correct
28	Correct	23 ms	8272 KB	Output is correct
29	Correct	23 ms	8272 KB	Output is correct
30	Correct	1 ms	336 KB	Output is correct
31	Correct	1 ms	336 KB	Output is correct
32	Correct	1 ms	336 KB	Output is correct
33	Correct	1 ms	336 KB	Output is correct
34	Correct	1 ms	336 KB	Output is correct
35	Correct	1 ms	504 KB	Output is correct
36	Correct	1 ms	336 KB	Output is correct
37	Correct	1 ms	336 KB	Output is correct
38	Correct	1 ms	468 KB	Output is correct
39	Correct	1 ms	336 KB	Output is correct
40	Correct	1 ms	336 KB	Output is correct
41	Correct	10 ms	1872 KB	Output is correct
42	Correct	11 ms	1872 KB	Output is correct
43	Correct	11 ms	2060 KB	Output is correct
44	Correct	10 ms	1872 KB	Output is correct
45	Correct	11 ms	1872 KB	Output is correct
46	Correct	10 ms	2060 KB	Output is correct
47	Correct	11 ms	1872 KB	Output is correct
48	Correct	8 ms	1360 KB	Output is correct
49	Correct	3 ms	592 KB	Output is correct
50	Correct	1 ms	336 KB	Output is correct
51	Correct	374 ms	20300 KB	Output is correct
52	Correct	333 ms	20296 KB	Output is correct
53	Correct	362 ms	20372 KB	Output is correct
54	Correct	347 ms	20296 KB	Output is correct
55	Correct	326 ms	20312 KB	Output is correct
56	Correct	306 ms	20296 KB	Output is correct
57	Correct	334 ms	20160 KB	Output is correct
58	Correct	132 ms	20296 KB	Output is correct
59	Correct	135 ms	20300 KB	Output is correct
60	Correct	1 ms	336 KB	Output is correct
61	Correct	603 ms	48200 KB	Output is correct
62	Correct	566 ms	48200 KB	Output is correct
63	Correct	522 ms	48088 KB	Output is correct
64	Correct	669 ms	48204 KB	Output is correct
65	Correct	685 ms	48076 KB	Output is correct
66	Correct	606 ms	48128 KB	Output is correct
67	Correct	679 ms	48044 KB	Output is correct
68	Correct	445 ms	31304 KB	Output is correct
69	Correct	424 ms	24392 KB	Output is correct
70	Correct	1 ms	336 KB	Output is correct

답안 #1104612

Compilation message

Subtask #1 2.0 / 2.0

Subtask #2 4.0 / 4.0

Subtask #3 9.0 / 9.0

Subtask #4 36.0 / 36.0

Subtask #5 28.0 / 28.0

Subtask #6 9.0 / 9.0

Subtask #7 12.0 / 12.0

Subtask #1
2.0 / 2.0

Subtask #2
4.0 / 4.0

Subtask #3
9.0 / 9.0

Subtask #4
36.0 / 36.0

Subtask #5
28.0 / 28.0

Subtask #6
9.0 / 9.0

Subtask #7
12.0 / 12.0