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Submission #851726

# Submission time Handle Problem Language Result Execution time Memory
851726 2023-09-20T13:07:04 Z iah Split the sequence (APIO14_sequence) C++14
100 / 100
 882 ms 84700 KB 
#include<bits/stdc++.h>
using namespace std;

#define ll long long
#define fi first
#define se second
#define sz(x) (int32_t) (x.size())

constexpr int Nmax = 1e5;
ll a[Nmax + 5], dp[Nmax + 5], pre[Nmax + 5];
int trace[Nmax + 5][205];

struct line{
	ll a, b;
	ll calc (ll x) {
		return a * x + b;
	}
	double intersect(line x) {
		return (double) (x.b - b) / (double) (a - x.a);
	}
	
	bool equal(line x) {
		return (a == x.a);
	}
};
signed main() {
    if (fopen("sequence.in","r")) {
        freopen("sequence.in","r",stdin);
        freopen("sequence.out","w",stdout);
    }
    cin.tie(0)->sync_with_stdio(0);
    int n, lim;
    cin >> n >> lim;
    // vector < ll > a(n + 1, 0);
    // vector < vector < ll > > dp(n + 1, vector < ll > (lim + 2, 0));
    // vector < vector < int > > trace(n + 1, vector < int > (lim + 2, 0));
    // dp[i][j] = max(dp[k][j - 1] - a[k] * a[k] + a[i] * a[k]);
    for (int i = 1; i <= n; i ++) {
    	cin >> a[i];
    	a[i] += a[i - 1];
    }
    
    for (int j = 1; j <= lim + 1; j ++) {	
		deque < pair < line , int > > dq;
    	dq.push_back({line{a[j - 1], pre[j - 1] - a[j - 1] * a[j - 1]}, j - 1});
    	for (int i = j; i <= n; i ++) {
    		while (sz(dq) >= 2 && dq[0].fi.intersect(dq[1].fi) <= a[i]) {
    			dq.pop_front();
    		}
    		
    		dp[i] = dq[0].fi.calc(a[i]);
    		trace[i][j] = dq[0].se;
    		// cout << i << " " << j << " " << dp[i][j] << " " << dq[0].fi.a << " " << dq[0].fi.b << " " << dq[0].se << "\n";
    		
    		line cur_line = {a[i], pre[i] - a[i] * a[i]};
    		pre[i] = dp[i];
    		if (j == 1) continue;
    		while (sz(dq) >= 1 && dq[sz(dq) - 1].fi.equal(cur_line)) {
    			dq.pop_back();
    		}
    		while (sz(dq) >= 2 && dq[sz(dq) - 2].fi.intersect(cur_line) <= dq[sz(dq) - 2].fi.intersect(dq[sz(dq) - 1].fi)) {
    			dq.pop_back();
    		}
    		dq.push_back({cur_line, i});
    	}
    }
    cout << dp[n] << "\n";
    int cur_pos = trace[n][lim + 1], cur_k = lim;
    while (cur_k > 0) {
    	cout << cur_pos << " ";
    	cur_pos = trace[cur_pos][cur_k];
    	cur_k --;
    }
    return 0;
}

Compilation message

sequence.cpp: In function 'int main()':
sequence.cpp:28:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
   28 |         freopen("sequence.in","r",stdin);
      |         ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~
sequence.cpp:29:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
   29 |         freopen("sequence.out","w",stdout);
      |         ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~

Subtask #1
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2396 KB contestant found the optimal answer: 108 == 108
2 Correct 1 ms 2396 KB contestant found the optimal answer: 999 == 999
3 Correct 1 ms 2396 KB contestant found the optimal answer: 0 == 0
4 Correct 0 ms 2396 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 0 ms 2396 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 0 ms 2396 KB contestant found the optimal answer: 1 == 1
7 Correct 0 ms 2396 KB contestant found the optimal answer: 1 == 1
8 Correct 1 ms 2392 KB contestant found the optimal answer: 1 == 1
9 Correct 1 ms 2396 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 1 ms 2396 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 0 ms 2396 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 0 ms 2396 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 1 ms 2396 KB contestant found the optimal answer: 140072 == 140072
14 Correct 1 ms 2396 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 0 ms 2396 KB contestant found the optimal answer: 805 == 805
16 Correct 1 ms 2396 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 1 ms 2396 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2396 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 1 ms 2396 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 1 ms 2396 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 1 ms 2396 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 0 ms 2396 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 1 ms 2396 KB contestant found the optimal answer: 933702 == 933702
7 Correct 1 ms 2396 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 1 ms 2396 KB contestant found the optimal answer: 687136 == 687136
9 Correct 1 ms 2396 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 1 ms 2396 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2652 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 1 ms 2652 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 1 ms 2652 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 1 ms 2652 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 1 ms 2652 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 1 ms 2652 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 1 ms 2652 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 1 ms 2652 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 1 ms 2652 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 1 ms 2648 KB contestant found the optimal answer: 490686959791 == 490686959791

Subtask #4
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 4700 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 1 ms 4700 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 7 ms 4896 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 1 ms 4700 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 8 ms 4700 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 7 ms 4700 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 8 ms 4760 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 6 ms 4700 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 2 ms 4700 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 4 ms 4700 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 10840 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 3 ms 11040 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 70 ms 10844 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 3 ms 10840 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 54 ms 11096 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 61 ms 11088 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 65 ms 10844 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 48 ms 10844 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 57 ms 10996 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 73 ms 11016 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
29.0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 25 ms 83804 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 25 ms 84060 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Correct 728 ms 84572 KB contestant found the optimal answer: 497313449256899208 == 497313449256899208
4 Correct 25 ms 84564 KB contestant found the optimal answer: 374850090734572421 == 374850090734572421
5 Correct 882 ms 84316 KB contestant found the optimal answer: 36183271951 == 36183271951
6 Correct 620 ms 83980 KB contestant found the optimal answer: 51629847150471 == 51629847150471
7 Correct 638 ms 84700 KB contestant found the optimal answer: 124074747024496432 == 124074747024496432
8 Correct 530 ms 84572 KB contestant found the optimal answer: 309959349080800 == 309959349080800
9 Correct 565 ms 84276 KB contestant found the optimal answer: 124113525649823701 == 124113525649823701
10 Correct 679 ms 84308 KB contestant found the optimal answer: 124309619349406845 == 124309619349406845