HDU 3507 斜率优化 DP Print Article

在kuangbin巨巨博客上学的。

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>

using namespace std;

const int maxn = 500000 + 10;
int d[maxn], Q[maxn], sum[maxn];

int head, tail;
int n, M;

int inline dx(int i, int j)
{
    return sum[j] - sum[i];
}

int inline dy(int i, int j)
{
    return d[j] + (sum[j]*sum[j]) - d[i] - (sum[i]*sum[i]);
}

int inline DP(int i, int j)
{
    return d[i] + (sum[j]-sum[i])*(sum[j]-sum[i]) + M;
}

int main()
{
    while(scanf("%d%d", &n, &M) == 2 && n)
    {
        for(int i = 1; i <= n; i++) scanf("%d", sum + i);
        for(int i = 2; i <= n; i++) sum[i] += sum[i - 1];

        head = tail = 0;
        Q[tail++] = 0;
        for(int i = 1; i <= n; i++)
        {
            while(head + 1 < tail && dy(Q[head], Q[head + 1]) <= 2 * sum[i] * dx(Q[head], Q[head + 1])) head++;
            d[i] = DP(Q[head], i);
            while(head + 1 < tail && dy(Q[tail-1], i) * dx(Q[tail-2], Q[tail-1]) <= dy(Q[tail-2], Q[tail-1]) * dx(Q[tail-1], i)) tail--;
            Q[tail++] = i;
        }

        printf("%d
", d[n]);
    }

    return 0;
}