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Submission #949723

# Submission time Handle Problem Language Result Execution time Memory
949723 2024-03-19T15:26:16 Z VinhLuu Split the sequence (APIO14_sequence) C++17
89 / 100
 1502 ms 89936 KB 
#include <bits/stdc++.h>
//#define int long long
#define ll long long
#define fi first
#define se second
#define pb push_back
#define all(lmao) lmao.begin(), lmao.end()

using namespace std;

typedef pair<int,int> pii;
typedef tuple<int,int,int> tp;
const int N = 2e5 + 5;
const ll oo = -1e12;
const int K = 205;
const int mod = 998244353;
//const int base = 23;

ll n, k, a[N];

namespace sub3{

    ll f[N][205], dp[N][205], s[N];

    int cal(ll i,int j){
        return 1ll * (s[j] - s[i]) * (s[n] - s[j]);
    }

    void solve(int j,int l,int r,int pl,int pr){
        if(l > r) return;
        int mid = (l + r) / 2;
        for(int i = pl; i <= min(mid - 1, pr); i ++){
            ll val = dp[i][j - 1] + cal(i, mid);
            if(val > dp[mid][j]){
                dp[mid][j] = val;
                f[mid][j] = i;
            }
        }
        solve(j, l, mid - 1, pl, f[mid][j]);
        solve(j, mid + 1, r, f[mid][j], pr);
    }

    void sol(){

        for(int i = 1; i <= n; i ++){

            s[i] = s[i - 1] + a[i];
        }
        if(k == 0){
            cout << 0;
            return ;
        }
        for(int j = 0; j <= k; j ++){
            for(int i = 0; i <= n; i ++){
                dp[i][j] = oo;
            }
        }
        for(int i = 1; i <= n; i ++) dp[i][1] = 1ll * s[i] * (s[n] - s[i]), f[i][1] = 0;
        for(int j = 2; j <= k; j ++){
            solve(j, j, n, 1, n);
        }
        ll ans = oo, tmp = 0, cnt = k;
        for(int i = 1; i <= n; i ++){
            if(ans < dp[i][k]){
                ans = dp[i][k];
                tmp = i;
            }
        }
        cout << ans << "\n";

        vector<int> vr;
        vr.pb(tmp);
        while(f[tmp][cnt]){
            vr.pb(f[tmp][cnt]);
            tmp = f[tmp][cnt];
            cnt--;
        }
        reverse(all(vr));
        for(auto j : vr) cout << j << " ";

    }
}
namespace AC{
    ll dp[N][5], s[N], pre, nx;

    int f[N][K];

    ll cal(int i,int j){
        return 1ll * (s[j] - s[i]) * (s[n] - s[j]);
    }

    void solve(int j,int l,int r,int pl,int pr){
        if(l > r) return;
        int mid = (l + r) / 2;
        dp[mid][nx] = oo;
        for(int i = pl; i <= min(mid - 1, pr); i ++){
            ll val = dp[i][pre] + cal(i, mid);
            if(val > dp[mid][nx]){
                dp[mid][nx] = val;
                f[mid][j] = i;
            }
        }
        solve(j, l, mid - 1, pl, f[mid][j]);
        solve(j, mid + 1, r, f[mid][j], pr);
    }

    void sol(){
        for(int i = 1; i <= n; i ++) s[i] = s[i - 1] + a[i];
        if(k == 0){
            cout << 0;
            return ;
        }
        for(int j = 0; j <= 1; j ++){
            for(int i = 0; i <= n; i ++){
                dp[i][j] = oo;
            }
        }

        pre = 0, nx = 1;
        for(int i = 1; i <= n; i ++) dp[i][0] = 1ll * s[i] * (s[n] - s[i]), f[i][0] = 0;
        for(int j = 2; j <= k; j ++){
            solve(j, j, n, 1, n);
            swap(pre, nx);
        }
        ll ans = oo;
        int tmp = 0, cnt = k;
        for(int i = 1; i <= n; i ++){
            if(ans < dp[i][pre]){
                ans = dp[i][pre];
                tmp = i;
            }
        }
        cout << ans << "\n";

        vector<int> vr;
        vr.pb(tmp);
        while(f[tmp][cnt]){
            vr.pb(f[tmp][cnt]);
            tmp = f[tmp][cnt];
            cnt--;
        }
        for(int i = vr.size() - 1; i >= 0; i --) cout << vr[i] << " ";

    }
}

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

    #define task "v"
    if(fopen(task ".inp","r")){
        freopen(task ".inp","r",stdin);
        freopen(task ".out","w",stdout);
    }
    cin >> n >> k;
    for(int i = 1; i <= n; i ++){
        cin >> a[i];
    }
//    if(n <= 200 && k <= 200) sub3 :: sol();
//    else
        AC :: sol();
}

Compilation message

sequence.cpp: In function 'int main()':
sequence.cpp:152:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  152 |         freopen(task ".inp","r",stdin);
      |         ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~
sequence.cpp:153:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  153 |         freopen(task ".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 1 ms 2396 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 1 ms 2396 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 1 ms 2396 KB contestant found the optimal answer: 1 == 1
7 Correct 1 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 1 ms 2396 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 1 ms 2392 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 2392 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 1 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 2392 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 1 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 2392 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 1 ms 2396 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2648 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 2648 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 1 ms 2652 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Incorrect 1 ms 2652 KB Unexpected end of file - int32 expected
7 Halted 0 ms 0 KB -

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 5 ms 4700 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 4792 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 8 ms 4796 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 6 ms 4700 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 4 ms 4800 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 2 ms 4700 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 3 ms 4804 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 13148 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 3 ms 13148 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 61 ms 13148 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 3 ms 13148 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 60 ms 13148 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 57 ms 13392 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 54 ms 13148 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 36 ms 13148 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 52 ms 13260 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 66 ms 13148 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
29.0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 29 ms 89692 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 32 ms 89692 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Correct 1072 ms 89880 KB contestant found the optimal answer: 497313449256899208 == 497313449256899208
4 Correct 29 ms 89692 KB contestant found the optimal answer: 374850090734572421 == 374850090734572421
5 Correct 1502 ms 89880 KB contestant found the optimal answer: 36183271951 == 36183271951
6 Correct 1170 ms 89936 KB contestant found the optimal answer: 51629847150471 == 51629847150471
7 Correct 1089 ms 89880 KB contestant found the optimal answer: 124074747024496432 == 124074747024496432
8 Correct 879 ms 89888 KB contestant found the optimal answer: 309959349080800 == 309959349080800
9 Correct 959 ms 87864 KB contestant found the optimal answer: 124113525649823701 == 124113525649823701
10 Correct 1278 ms 89884 KB contestant found the optimal answer: 124309619349406845 == 124309619349406845