[HDU3045] Picnic Cows_picnic cows hdu

本文链接：https://blog.youkuaiyun.com/shiyukun1998/article/details/41832869

本文探讨了排序问题中如何应用动态规划优化算法，通过引入0元素并调整队列顺序，简化状态转移方程，提高了算法效率。文章详细介绍了算法实现步骤及关键点，包括代码实现和实例分析。

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排序过后搞DP 状态转移方程好写化简也不难就不多说了注意要把0加入队列

#include<cstdio>
#include<algorithm>
#include<cstring>
#include<iostream>
using namespace std;
const int MAXN = 400000;
typedef long long LL;
int Q[MAXN+10];
LL S[MAXN+10], d[MAXN+10], A[MAXN+10];
int F, R, n, K;
inline void GET(LL &x)
{
    LL s = 0, f = 1;
    char c;
    while(c = getchar(), c != ' ' && c != '\n')
        if(c == '-') f = -1;
        else s = s * 10 + c - '0';
    x = s * f;
}
LL Slope_U(int i, int j)
{
    return d[i] - S[i] + A[i+1] * i - (d[j] - S[j] + A[j+1] * j);
}
LL Slope_D(int i, int j)
{
    return A[i+1] - A[j+1];
}
int main()
{
    while(scanf("%d %d\n", &n, &K) == 2)
    {
        F = R = Q[0] = d[0] = S[0] = 0;
        Q[R++] = 0;
        for(int i = 1; i <= n; i++) scanf("%I64d", &A[i]);
        sort(A+1, A+1+n);
        for(int i = 1; i <= n; i++) S[i] = S[i-1] + A[i];
        for(int i = 1; i <= n; i++)
        {
            int Now = i - K + 1;
            while(F < R - 1 && Slope_U(Q[F+1], Q[F]) <= i * Slope_D(Q[F+1], Q[F]))
                F++;
            LL tmp = d[Q[F]] + S[i] - S[Q[F]] - A[Q[F]+1] * (i - Q[F]);
            d[i] = tmp;
            if(Now < K) continue;
            while(F < R - 1 && Slope_U(Q[R-1], Q[R-2]) * Slope_D(Now, Q[R-1]) >= Slope_U(Now, Q[R-1]) * Slope_D(Q[R-1], Q[R-2]) )
                R--;
            Q[R++] = Now;
        }
        cout << d[n] << '\n';
    }
}