Submission #420460

#	Submission time	Handle	Problem	Language	Result	Execution time	Memory
420460	2021-06-08T11:30:45 Z	MetalPower	Cigle (COI21_cigle)	C++14	100 / 100	268 ms	67428 KB

cigle

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

const int MX = 5005;

void chmax(int& a, int b){
	if(b > a) a = b;
}

int N, arr[MX], dp[MX][MX];

// Observation #1 : We can easily solve this in O(N^3)
	// dp(i, j) is the largest beauty of the wall if the highest row includes [i, j]
	// the transition is we add another row [j + 1, k] for every j + 1 <= k <= N
	// calculating is easy by two pointer

// Observation #2 : Now we can optimize the first solution so that it becomes O(N^2)
	// if we place j at a certain position
	// and have two pointers (i, k) 
	// we will see that the beauty will increase a total of O(N) times

	// So we can find the positions where the value changes in O(N) for each j
		// update those positions
		// and after we update max the current value with the previous value

// Note : To make finding range query faster use prefix sum (because l = 0)

struct prefix{
	int v[MX];

	void build(int p){
		for(int i = 0; i <= p; i++) v[i] = i == 0 ? dp[i][p] : max(dp[i][p], v[i - 1]);
	}
} ps;

int main(){
	ios_base::sync_with_stdio(0); cin.tie(NULL); cout.tie(NULL);

	cin >> N;

	for(int i = 0; i < N; i++) cin >> arr[i];

	for(int p = 0; p < N; p++){
		int i = p, k = p + 1, cnt = -1, bot = 0, top = 0;

		ps.build(p);

		while(i >= 0 && k < N){
			if(bot == top){
				cnt++; chmax(dp[p + 1][k], ps.v[i] + cnt);
				bot += arr[i--]; top += arr[k++];
			}else if(bot < top){
				bot += arr[i--];
			}else if(top < bot){
				top += arr[k++];
			}
		}

		for(int j = p + 1; j < N; j++) chmax(dp[p + 1][j], dp[p + 1][j - 1]);
	}

	int ans = 0;

	for(int p = 0; p < N; p++) chmax(ans, dp[p][N - 1]);

	cout << ans << '\n';
}

Subtask #1
9.0 / 9.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	1 ms	332 KB	Output is correct
2	Correct	1 ms	332 KB	Output is correct
3	Correct	1 ms	332 KB	Output is correct
4	Correct	1 ms	332 KB	Output is correct
5	Correct	1 ms	332 KB	Output is correct
6	Correct	1 ms	332 KB	Output is correct
7	Correct	0 ms	204 KB	Output is correct
8	Correct	0 ms	332 KB	Output is correct
9	Correct	1 ms	332 KB	Output is correct

Subtask #2
11.0 / 11.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	1 ms	332 KB	Output is correct
2	Correct	1 ms	332 KB	Output is correct
3	Correct	1 ms	332 KB	Output is correct
4	Correct	1 ms	332 KB	Output is correct
5	Correct	1 ms	332 KB	Output is correct
6	Correct	1 ms	332 KB	Output is correct
7	Correct	0 ms	204 KB	Output is correct
8	Correct	0 ms	332 KB	Output is correct
9	Correct	1 ms	332 KB	Output is correct
10	Correct	1 ms	588 KB	Output is correct
11	Correct	1 ms	588 KB	Output is correct
12	Correct	1 ms	588 KB	Output is correct
13	Correct	1 ms	588 KB	Output is correct
14	Correct	1 ms	588 KB	Output is correct
15	Correct	1 ms	588 KB	Output is correct
16	Correct	1 ms	332 KB	Output is correct
17	Correct	1 ms	588 KB	Output is correct
18	Correct	1 ms	588 KB	Output is correct
19	Correct	1 ms	460 KB	Output is correct
20	Correct	1 ms	588 KB	Output is correct

Subtask #3
13.0 / 13.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	3 ms	2764 KB	Output is correct
2	Correct	3 ms	2764 KB	Output is correct
3	Correct	3 ms	2764 KB	Output is correct
4	Correct	4 ms	2764 KB	Output is correct
5	Correct	4 ms	2764 KB	Output is correct
6	Correct	4 ms	2764 KB	Output is correct
7	Correct	4 ms	2764 KB	Output is correct
8	Correct	4 ms	2764 KB	Output is correct
9	Correct	4 ms	2764 KB	Output is correct
10	Correct	3 ms	2764 KB	Output is correct
11	Correct	4 ms	2764 KB	Output is correct
12	Correct	3 ms	2764 KB	Output is correct

Subtask #4
15.0 / 15.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	1 ms	332 KB	Output is correct
2	Correct	1 ms	332 KB	Output is correct
3	Correct	1 ms	332 KB	Output is correct
4	Correct	1 ms	332 KB	Output is correct
5	Correct	1 ms	332 KB	Output is correct
6	Correct	1 ms	332 KB	Output is correct
7	Correct	0 ms	204 KB	Output is correct
8	Correct	0 ms	332 KB	Output is correct
9	Correct	1 ms	332 KB	Output is correct
10	Correct	1 ms	588 KB	Output is correct
11	Correct	1 ms	588 KB	Output is correct
12	Correct	1 ms	588 KB	Output is correct
13	Correct	1 ms	588 KB	Output is correct
14	Correct	1 ms	588 KB	Output is correct
15	Correct	1 ms	588 KB	Output is correct
16	Correct	1 ms	332 KB	Output is correct
17	Correct	1 ms	588 KB	Output is correct
18	Correct	1 ms	588 KB	Output is correct
19	Correct	1 ms	460 KB	Output is correct
20	Correct	1 ms	588 KB	Output is correct
21	Correct	3 ms	2764 KB	Output is correct
22	Correct	3 ms	2764 KB	Output is correct
23	Correct	3 ms	2764 KB	Output is correct
24	Correct	4 ms	2764 KB	Output is correct
25	Correct	4 ms	2764 KB	Output is correct
26	Correct	4 ms	2764 KB	Output is correct
27	Correct	4 ms	2764 KB	Output is correct
28	Correct	4 ms	2764 KB	Output is correct
29	Correct	4 ms	2764 KB	Output is correct
30	Correct	3 ms	2764 KB	Output is correct
31	Correct	4 ms	2764 KB	Output is correct
32	Correct	3 ms	2764 KB	Output is correct
33	Correct	3 ms	2764 KB	Output is correct
34	Correct	3 ms	2764 KB	Output is correct
35	Correct	3 ms	2764 KB	Output is correct
36	Correct	3 ms	2764 KB	Output is correct
37	Correct	4 ms	2764 KB	Output is correct
38	Correct	4 ms	2764 KB	Output is correct
39	Correct	4 ms	2764 KB	Output is correct
40	Correct	3 ms	2028 KB	Output is correct
41	Correct	3 ms	2764 KB	Output is correct
42	Correct	3 ms	2764 KB	Output is correct
43	Correct	3 ms	2636 KB	Output is correct
44	Correct	3 ms	2252 KB	Output is correct
45	Correct	3 ms	2636 KB	Output is correct
46	Correct	3 ms	2636 KB	Output is correct
47	Correct	3 ms	2636 KB	Output is correct
48	Correct	3 ms	2636 KB	Output is correct
49	Correct	3 ms	2636 KB	Output is correct

Subtask #5
52.0 / 52.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	1 ms	332 KB	Output is correct
2	Correct	1 ms	332 KB	Output is correct
3	Correct	1 ms	332 KB	Output is correct
4	Correct	1 ms	332 KB	Output is correct
5	Correct	1 ms	332 KB	Output is correct
6	Correct	1 ms	332 KB	Output is correct
7	Correct	0 ms	204 KB	Output is correct
8	Correct	0 ms	332 KB	Output is correct
9	Correct	1 ms	332 KB	Output is correct
10	Correct	1 ms	588 KB	Output is correct
11	Correct	1 ms	588 KB	Output is correct
12	Correct	1 ms	588 KB	Output is correct
13	Correct	1 ms	588 KB	Output is correct
14	Correct	1 ms	588 KB	Output is correct
15	Correct	1 ms	588 KB	Output is correct
16	Correct	1 ms	332 KB	Output is correct
17	Correct	1 ms	588 KB	Output is correct
18	Correct	1 ms	588 KB	Output is correct
19	Correct	1 ms	460 KB	Output is correct
20	Correct	1 ms	588 KB	Output is correct
21	Correct	3 ms	2764 KB	Output is correct
22	Correct	3 ms	2764 KB	Output is correct
23	Correct	3 ms	2764 KB	Output is correct
24	Correct	4 ms	2764 KB	Output is correct
25	Correct	4 ms	2764 KB	Output is correct
26	Correct	4 ms	2764 KB	Output is correct
27	Correct	4 ms	2764 KB	Output is correct
28	Correct	4 ms	2764 KB	Output is correct
29	Correct	4 ms	2764 KB	Output is correct
30	Correct	3 ms	2764 KB	Output is correct
31	Correct	4 ms	2764 KB	Output is correct
32	Correct	3 ms	2764 KB	Output is correct
33	Correct	3 ms	2764 KB	Output is correct
34	Correct	3 ms	2764 KB	Output is correct
35	Correct	3 ms	2764 KB	Output is correct
36	Correct	3 ms	2764 KB	Output is correct
37	Correct	4 ms	2764 KB	Output is correct
38	Correct	4 ms	2764 KB	Output is correct
39	Correct	4 ms	2764 KB	Output is correct
40	Correct	3 ms	2028 KB	Output is correct
41	Correct	3 ms	2764 KB	Output is correct
42	Correct	3 ms	2764 KB	Output is correct
43	Correct	3 ms	2636 KB	Output is correct
44	Correct	3 ms	2252 KB	Output is correct
45	Correct	3 ms	2636 KB	Output is correct
46	Correct	3 ms	2636 KB	Output is correct
47	Correct	3 ms	2636 KB	Output is correct
48	Correct	3 ms	2636 KB	Output is correct
49	Correct	3 ms	2636 KB	Output is correct
50	Correct	221 ms	67240 KB	Output is correct
51	Correct	197 ms	67152 KB	Output is correct
52	Correct	206 ms	67428 KB	Output is correct
53	Correct	230 ms	67204 KB	Output is correct
54	Correct	204 ms	67152 KB	Output is correct
55	Correct	211 ms	67260 KB	Output is correct
56	Correct	257 ms	67396 KB	Output is correct
57	Correct	264 ms	67212 KB	Output is correct
58	Correct	248 ms	67128 KB	Output is correct
59	Correct	257 ms	67012 KB	Output is correct
60	Correct	251 ms	66216 KB	Output is correct
61	Correct	229 ms	67304 KB	Output is correct
62	Correct	224 ms	67188 KB	Output is correct
63	Correct	219 ms	67072 KB	Output is correct
64	Correct	249 ms	66984 KB	Output is correct
65	Correct	222 ms	66888 KB	Output is correct
66	Correct	232 ms	67008 KB	Output is correct
67	Correct	231 ms	66500 KB	Output is correct
68	Correct	213 ms	66356 KB	Output is correct
69	Correct	217 ms	66460 KB	Output is correct
70	Correct	246 ms	66632 KB	Output is correct
71	Correct	268 ms	67084 KB	Output is correct
72	Correct	234 ms	67044 KB	Output is correct

Submission #420460

Compilation message

Subtask #1 9.0 / 9.0

Subtask #2 11.0 / 11.0

Subtask #3 13.0 / 13.0

Subtask #4 15.0 / 15.0

Subtask #5 52.0 / 52.0

Subtask #1
9.0 / 9.0

Subtask #2
11.0 / 11.0

Subtask #3
13.0 / 13.0

Subtask #4
15.0 / 15.0

Subtask #5
52.0 / 52.0