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Submission #268126

# Submission time Handle Problem Language Result Execution time Memory
268126 2020-08-16T09:04:42 Z andreiomd Split the sequence (APIO14_sequence) C++11
100 / 100
 1726 ms 83240 KB 
#include <iostream>
#include <cstdio>

using namespace std;

const int NMAX = 1e5 + 5, KMAX = 2e2 + 5;
const long long INF = 1LL * 1e18;

int N, K;

int sp[NMAX];

long long ans, dp[NMAX][2];

int Keep[NMAX][KMAX];
int V[KMAX];

namespace InParser
{
static const int BSIZE = (1 << 16);

static int pos = BSIZE - 1;
static char buff[BSIZE];

static inline char Char ()
{
    ++pos;

    if(pos == BSIZE)
    {
        pos = 0;

        int n = fread(buff, 1, BSIZE, stdin);

        if(n != BSIZE)
            for(int i = n; i < BSIZE; ++i)
                buff[i] = 0;
    }

    return buff[pos];
}

inline int Int ()
{
    int ans = 0;

    for( ; ; )
    {
        char Ch = Char();

        if(Ch >= '0' && Ch <= '9')
        {
            ans = (int)(Ch - '0');

            break;
        }
    }

    for( ; ; )
    {
        char Ch = Char();

        if(Ch >= '0' && Ch <= '9')
            ans = ans * 10 + (int)(Ch - '0');
        else
            break;
    }

    return ans;
}
};

static inline void Read ()
{
    ios_base :: sync_with_stdio(false);
    cin.tie(nullptr);

    /// freopen("sequence.in", "r", stdin);
    /// freopen("sequence.out", "w", stdout);

    N = InParser :: Int(), K = InParser :: Int();

    for(int i = 1; i <= N; ++i)
    {
        int A = InParser :: Int();

        sp[i] = sp[i - 1] + A;
    }

    return;
}

static inline int Query (int Left, int Right)
{
    if(Left > Right)
        return 0;

    return sp[Right] - sp[(Left - 1)];
}

static inline long long Cost (int Left, int Right)
{
    if(Left > Right)
        return 0;

    int s = Query(Left, Right);
    return (1LL * s * s);
}

static inline void Load ()
{
    ans = Cost(1, N);

    return;
}

static inline int MIN (int a, int b)
{
    return ((a < b) ? a : b);
}

static inline void Go (int Left, int Right, int Chosen_Left, int Chosen_Right, int Level)
{
    if(Left > Right)
        return;

    int Mid = ((Left + Right) >> 1);
    int Chosen = Mid;

    for(int k = Chosen_Left; k <= MIN(Mid, Chosen_Right); ++k)
    {
        long long Now = dp[k - 1][((Level - 1) & 1)] + Cost(k, Mid);

        if(Now < dp[Mid][(Level & 1)])
            dp[Mid][(Level & 1)] = Now, Chosen = k;
    }

    Keep[Mid][Level] = Chosen;

    Go(Left, Mid - 1, Chosen_Left, Chosen, Level);
    Go(Mid + 1, Right, Chosen, Chosen_Right, Level);

    return;
}

static inline void Initialize ()
{
    for(int i = 0; i <= N; ++i)
        for(int j = 0; j < (2 - (K == 1)); ++j)
            dp[i][j] = INF;

    for(int i = 1; i <= N; ++i)
        dp[i][1] = Cost(1, i);

    for(int i = 1; i <= N; ++i)
        Keep[i][1] = i;

    return;
}

static inline void Write ()
{
    int pos = N;

    for(int i = (K + 1); i > 1; --i)
        pos = V[i - 1] = Keep[pos][i] - 1;

    for(int i = 1; i <= K; ++i)
    {
        printf("%d", V[i]);

        if(i != K)
            printf(" ");
    }

    printf("\n");

    return;
}

static inline void Solve ()
{
    Initialize();

    for(int j = 2; j <= (K + 1); ++j)
        Go(j, N, j, N, j);

    ans -= 1LL * dp[N][((K + 1) & 1)];
    ans >>= 1LL;

    printf("%lld\n", ans);

    Write();

    return;
}

int main()
{
    Read();

    Load();

    Solve();

    return 0;
}

Subtask #1
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 384 KB contestant found the optimal answer: 108 == 108
2 Correct 1 ms 384 KB contestant found the optimal answer: 999 == 999
3 Correct 1 ms 384 KB contestant found the optimal answer: 0 == 0
4 Correct 1 ms 384 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 1 ms 384 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 1 ms 384 KB contestant found the optimal answer: 1 == 1
7 Correct 1 ms 512 KB contestant found the optimal answer: 1 == 1
8 Correct 1 ms 512 KB contestant found the optimal answer: 1 == 1
9 Correct 1 ms 384 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 1 ms 384 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 1 ms 384 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 1 ms 384 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 1 ms 384 KB contestant found the optimal answer: 140072 == 140072
14 Correct 1 ms 384 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 1 ms 384 KB contestant found the optimal answer: 805 == 805
16 Correct 1 ms 384 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 1 ms 384 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 512 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 1 ms 512 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 1 ms 512 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 1 ms 512 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 1 ms 512 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 1 ms 512 KB contestant found the optimal answer: 933702 == 933702
7 Correct 1 ms 512 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 1 ms 512 KB contestant found the optimal answer: 687136 == 687136
9 Correct 1 ms 512 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 1 ms 512 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 640 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 1 ms 640 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 1 ms 640 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 1 ms 640 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 2 ms 640 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 1 ms 640 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 1 ms 640 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 1 ms 640 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 1 ms 640 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 1 ms 640 KB contestant found the optimal answer: 490686959791 == 490686959791

Subtask #4
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 1280 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 2 ms 1280 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 6 ms 1280 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 1 ms 1280 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 10 ms 1280 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 8 ms 1280 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 8 ms 1280 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 6 ms 1300 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 3 ms 1280 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 5 ms 1280 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 8 ms 8704 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 7 ms 8704 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 81 ms 8740 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 6 ms 8704 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 81 ms 8704 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 79 ms 8704 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 79 ms 8704 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 58 ms 8824 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 73 ms 8704 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 91 ms 8704 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
29.0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 67 ms 82808 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 65 ms 82936 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Correct 1277 ms 82936 KB contestant found the optimal answer: 497313449256899208 == 497313449256899208
4 Correct 59 ms 82808 KB contestant found the optimal answer: 374850090734572421 == 374850090734572421
5 Correct 1726 ms 82824 KB contestant found the optimal answer: 36183271951 == 36183271951
6 Correct 1132 ms 82936 KB contestant found the optimal answer: 51629847150471 == 51629847150471
7 Correct 1096 ms 83240 KB contestant found the optimal answer: 124074747024496432 == 124074747024496432
8 Correct 887 ms 83064 KB contestant found the optimal answer: 309959349080800 == 309959349080800
9 Correct 1041 ms 82992 KB contestant found the optimal answer: 124113525649823701 == 124113525649823701
10 Correct 1284 ms 82680 KB contestant found the optimal answer: 124309619349406845 == 124309619349406845