oj.uz

Submission #546253

# Submission time Handle Problem Language Result Execution time Memory
546253 2022-04-07T00:37:43 Z theshadow_04 Split the sequence (APIO14_sequence) C++14
100 / 100
 964 ms 85256 KB 
// annotshy

#include <bits/stdc++.h>

#define Task "CF"
#define F first
#define S second

using namespace std;

const int maxn = 100005;

int n, k;
int a[maxn], s[maxn];

bool maximize(long long &x, long long y) {
	if(x < y) {x = y; return 1;}
	return 0;
}

//namespace BF {
//
//	long long dp[205][205];
//	int tr[205][205];
//
//	void Solve() {
//		memset(dp, -0x3f, sizeof dp);
//		dp[0][0] = 0;
//		for(int i = 1; i <= n; ++ i) {
//			for(int j = 0; j < k; ++ j) if(dp[i - 1][j] >= 0) {
//				for(int x = i; x < n; ++ x) {
//					if(maximize(dp[x][j + 1], dp[i - 1][j] + (s[n] - s[x]) * (s[x] - s[i - 1]))) {
//						tr[x][j + 1] = i - 1;
//					}
//				}
//			}
//		}
//		long long ans = -1;
//		int pos = 0;
//		for(int i = 1; i <= n; ++ i) {
//     if(maximize(ans, dp[i][k])) pos = i;
//		}
//		vector<int> id;
//		while(pos) {
//			id.push_back(pos);
//			pos = tr[pos][k];
//			k --;
//		}
//		cout << ans << "\n";
//		reverse(id.begin(), id.end());
//		for(auto x : id) cout << x << " ";
//	}
//} // BF

namespace Full {

  pair<int, long long> line[maxn];
  long long p[maxn], q[maxn];
  double x[maxn];
  long long dp[2][maxn];
  int st[maxn], top = 0, tr[205][maxn];

  bool Check(int i, int j, int k) {
    if(line[i].F == line[j].F || line[i].F == line[k].F) return 0;
    double x1 = 1.0 * (line[i].S - line[j].S) / (line[j].F - line[i].F);
    double x2 = 1.0 * (line[i].S - line[k].S) / (line[k].F - line[i].F);
    return (x1 > x2);
  }

  void Update(int i) {
    while(top > 1 && !Check(i, st[top], st[top - 1])) -- top;
    st[++ top] = i;
    p[top] = line[i].F, q[top] = line[i].S;
    if(top == 1) x[top] = -2e9;
    else {
//      assert(p[top - 1] != p[top]);
      x[top] = 1.0 * (q[top] - q[top - 1]) / (p[top - 1] - p[top]);
    }

  }

  void Solve() {
    for(int i = 0; i < 2; ++ i) {
      for(int j = 0; j < n; ++ j) dp[i][j] = -2e9;
    }
    dp[0][0] = 0;
    for(int t = 1; t <= k; ++ t) {
      top = 0;
      for(int i = 0; i < n; ++ i) {
        if(dp[(t - 1) & 1][i] >= 0) line[i] = {s[i], dp[(t - 1) & 1][i]};
      }
      for(int i = 1; i < n; ++ i) {
        if(dp[(t - 1) & 1][i - 1] >= 0)
          Update(i - 1);
        int pos = upper_bound(x + 1, x + top + 1, s[i] - s[n]) - x - 1;
        if(pos <= 0) continue;
        int id = st[pos];
        dp[t & 1][i] = dp[(t - 1) & 1][id] + 1ll * (s[i] - s[id]) * (s[n] - s[i]);
        tr[t][i] = id;
      }
      for(int i = 0; i < n; ++ i) {
        if(dp[(t - 1) & 1][i] >= 0) dp[(t - 1) & 1][i] = -2e9;
      }
    }
    long long ans = -1;
		int pos = 0;
		for(int i = 1; i <= n; ++ i) {
     if(maximize(ans, dp[k & 1][i])) pos = i;
		}
		vector<int> id;
		while(pos) {
			id.push_back(pos);
			pos = tr[k][pos];
			k --;
		}
		cout << ans << "\n";
		reverse(id.begin(), id.end());
		for(auto x : id) cout << x << " ";
  }
}

void Solve(int Test) {
  cin >> n >> k;
  for(int i = 1; i <= n; ++ i) cin >> a[i], s[i] = s[i - 1] + a[i];
//  if(n <= 200 && k <= 200) {
//  	BF::Solve();
//  	return;
//  }
  Full::Solve();
}

signed main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0), cout.tie(0);
  if(fopen(Task".inp", "r")) {
    freopen(Task".inp", "r", stdin);
    freopen(Task".out", "w", stdout);
  }
  int test = 1;
  // cin >> test;
  for(int i = 1; i <= test; ++ i) {
    Solve(i);
  }
}

/*no pain no gain*/

Compilation message

sequence.cpp: In function 'int main()':
sequence.cpp:136:12: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  136 |     freopen(Task".inp", "r", stdin);
      |     ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~
sequence.cpp:137:12: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  137 |     freopen(Task".out", "w", stdout);
      |     ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~

Subtask #1
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 340 KB contestant found the optimal answer: 108 == 108
2 Correct 0 ms 340 KB contestant found the optimal answer: 999 == 999
3 Correct 0 ms 340 KB contestant found the optimal answer: 0 == 0
4 Correct 0 ms 340 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 1 ms 340 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 0 ms 340 KB contestant found the optimal answer: 1 == 1
7 Correct 0 ms 340 KB contestant found the optimal answer: 1 == 1
8 Correct 0 ms 340 KB contestant found the optimal answer: 1 == 1
9 Correct 1 ms 340 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 1 ms 340 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 1 ms 340 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 0 ms 340 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 0 ms 340 KB contestant found the optimal answer: 140072 == 140072
14 Correct 0 ms 340 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 1 ms 340 KB contestant found the optimal answer: 805 == 805
16 Correct 0 ms 340 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 0 ms 340 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 340 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 0 ms 340 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 1 ms 596 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 0 ms 340 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 0 ms 340 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 0 ms 340 KB contestant found the optimal answer: 933702 == 933702
7 Correct 0 ms 468 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 1 ms 340 KB contestant found the optimal answer: 687136 == 687136
9 Correct 1 ms 340 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 1 ms 340 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 340 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 0 ms 340 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 1 ms 1364 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 0 ms 340 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 1 ms 1108 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 2 ms 1236 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 2 ms 1364 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 1 ms 596 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 1 ms 468 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 1 ms 596 KB contestant found the optimal answer: 490686959791 == 490686959791

Subtask #4
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 340 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 1 ms 340 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 9 ms 2052 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 1 ms 468 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 8 ms 2004 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 7 ms 1808 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 8 ms 1984 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 6 ms 2076 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 2 ms 680 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 4 ms 1108 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 1108 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 2 ms 1108 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 72 ms 9724 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 2 ms 1108 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 54 ms 6152 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 67 ms 7080 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 62 ms 7472 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 54 ms 6244 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 57 ms 7076 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 79 ms 8836 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
29.0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 19 ms 7604 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 17 ms 7616 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Correct 751 ms 85256 KB contestant found the optimal answer: 497313449256899208 == 497313449256899208
4 Correct 18 ms 8164 KB contestant found the optimal answer: 374850090734572421 == 374850090734572421
5 Correct 964 ms 84812 KB contestant found the optimal answer: 36183271951 == 36183271951
6 Correct 770 ms 61508 KB contestant found the optimal answer: 51629847150471 == 51629847150471
7 Correct 687 ms 66280 KB contestant found the optimal answer: 124074747024496432 == 124074747024496432
8 Correct 656 ms 55008 KB contestant found the optimal answer: 309959349080800 == 309959349080800
9 Correct 602 ms 61772 KB contestant found the optimal answer: 124113525649823701 == 124113525649823701
10 Correct 787 ms 77516 KB contestant found the optimal answer: 124309619349406845 == 124309619349406845