Submission #6978

#	Time	Username	Problem	Language	Result	Execution time	Memory
6978		woqja125	Split the sequence (APIO14_sequence)	C++98	100 / 100	844 ms	85852 KiB

sequence

#include<stdio.h>
int dat[100001], s[100001];
long long dp[2][100001];
int p[210][100001];
int stk[100001], b;
inline long long getY(long long *D, int x)
{
    return D[x] - 1ll*s[x]*s[x];
}
inline bool cmp(long long *D, int z)
{
    int x, y;
    x = stk[b-1];
    y = stk[b];
 
    return (getY(D, y)-getY(D, x))*(s[y]-s[z]) >= (getY(D, z)-getY(D, y)) *(s[x]-s[y]);
}
int main()
{
    int n, k;
    int i, j, l;
    scanf("%d%d", &n, &k); k++;
    for(i=1; i<=n; i++)
    {
        scanf("%d", &dat[i]);
        s[i] = s[i-1] + dat[i];
    }
    for(i=0; i<=1; i++)for(j=0; j<=n; j++) dp[i][j]=-1;
    for(j=0; j<=n; j++)
    {
        dp[1][j] = 0;
    }
    for(i=2; i<=k; i++)
    {
        long long *D = dp[(i-1)%2];
        b = -1;
        int x=1;
        stk[++b] = 0; stk[++b] = 1;
        for(l=2; l<=n; l++)
        {
            if(x>b) x = b;
            while(x < b && (getY(D, stk[x]) -getY(D, stk[x+1])) <= 1ll*(s[stk[x+1]] - s[stk[x]])*s[l] ) x++;
            dp[i%2][l] = D[stk[x]] - 1ll*s[stk[x]]*s[stk[x]] + 1ll*s[stk[x]]*s[l];
            p[i][l] = stk[x];
            while( b>x && cmp(D, l) ) b--;
            stk[++b] = l;
        }
    }
    printf("%lld\n", dp[k%2][n]);
    int x = n;
    for(int i=k; i>1; i--)
    {
        x = p[i][x];
        printf("%d ", x);
    }
    return 0;
}

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