Submission #46308

#	Time	Username	Problem	Language	Result	Execution time	Memory
46308		RayaBurong25_1	Split the sequence (APIO14_sequence)	C++14	71 / 100	2067 ms	86268 KiB

sequence

#include <stdio.h>
#include <vector>
#include <algorithm>
#include <cassert>
#define INF 1e18
long long Sum[100005];
long long SumSq[100005];
long long DP[100005];
int Last[100005][205];
typedef struct line line;
struct line
{
    long long m, c;
    double s;
    int i;
};
line Lines[100005];
int L;
long long max(long long a, long long b)
{
    return (a > b)?a:b;
}
int compare(long long x, line l)
{
    return x < l.s;
}
int I, J;
long long getLine(long long x)
{
    int i;
    for (i = 17; i >= 0; i--)
    {
        if (J + (1 << i) < L && Lines[J + (1 << i)].s <= x)
            J += (1 << i);
    }
    // while (J + 1 < L && Lines[J + 1].s <= x)
    //     J++;
    // int j = std::upper_bound(&Lines[0], &Lines[L], x, compare) - &Lines[0] - 1;
    I = Lines[J].i;
    return Lines[J].m*x + Lines[J].c;
}
double intersect(long long m, long long c, long long m2, long long c2)
{
    if (m == m2)
    {
        if (c2 >= c)
            return -INF;
        else
            return INF;
    }
    else
        return (double) (c2 - c)/(m - m2);
}
void insertLine(int i, long long m, long long c)
{
    double s;
    while (L > 0 && (s = intersect(Lines[L - 1].m, Lines[L - 1].c, m, c)) <= Lines[L - 1].s)
        L--;
    if (s != INF)
    {
        Lines[L] = {m, c, s, i};
        L++;
    }
}
int main()
{
    int N, K;
    scanf("%d %d", &N, &K);
    int n, k, i;
    for (i = 0; i < N; i++)
    {
        scanf("%lld", &Sum[i]);
        if (i > 0)
            Sum[i] += Sum[i - 1];
        SumSq[i] = Sum[i]*Sum[i];
    }
    // Lines.push_back({0, 0, 0});
    long long r;
    for (k = 0; k <= K; k++)
    {
        L = 1;
        J = 0;
        if (k == 0)
            Lines[0] = {0, 0, -INF, -1};
        for (n = 0; n < N; n++)
        {
            r = getLine(Sum[n]);
            Last[n][k] = I;
            // for (i = 0; i < n; i++)
            // {
            //     if (DP[i][k - 1] + Sum[i]*(Sum[n] - Sum[i]) > DP[n][k])
            //     {
            //         DP[n][k] = max(DP[n][k], DP[i][k - 1] + Sum[i]*(Sum[n] - Sum[i]));
            //         Last[n][k] = i;
            //     }
            // }
            if (k > 0 && n < N - 1)
                insertLine(n, Sum[n], DP[n] - SumSq[n]);
            DP[n] = r;
            // printf("DP[%d][%d] = %lld\n", n, k, DP[n]);
        }
        // printf("k%d\n", k);
    }
    printf("%lld\n", DP[N - 1]);
    i = Last[N - 1][K];
    k = K - 1;
    std::vector<int> V;
    while (k >= 0 && i != -1)
    {
        V.push_back(i + 1);
        i = Last[i][k];
        k--;
    }
    for (i = V.size() - 1; i >= 0; i--)
        printf("%d ", V[i]);
}

Compilation message (stderr)

sequence.cpp: In function 'int main()':
sequence.cpp:68:10: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
     scanf("%d %d", &N, &K);
     ~~~~~^~~~~~~~~~~~~~~~~
sequence.cpp:72:14: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
         scanf("%lld", &Sum[i]);
         ~~~~~^~~~~~~~~~~~~~~~~
sequence.cpp: In function 'void insertLine(int, long long int, long long int)':
sequence.cpp:61:18: warning: 's' may be used uninitialized in this function [-Wmaybe-uninitialized]
         Lines[L] = {m, c, s, i};
         ~~~~~~~~~^~~~~~~~~~~~~~

• Subtask 1: 11 / 11
• Subtask 2: 11 / 11
• Subtask 3: 11 / 11
• Subtask 4: 17 / 17
• Subtask 5: 21 / 21
• Subtask 6: 0 / 29