HDU3507(斜率优化)

#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
#include <cmath>
using namespace std;
#define maxn 511111

long long sum[maxn];
long long dp[maxn];
int n, m;
long long a[maxn];
int que[maxn], head, tail;

long long up (int i, int j) {
    return dp[i]+sum[i]*sum[i] - dp[j]-sum[j]*sum[j];
}

long long down (int i, int j) {
    return 2*(sum[i]-sum[j]);
}

int main () {
    while (cin >> n >> m) {
        for (int i = 1; i <= n; i++)
            cin >> a[i];
        sum[0] = 0;
        for (int i = 1; i <= n; i++)
            sum[i] = sum[i-1]+a[i];
        head = tail = 0;
        que[tail++] = 0;
        for (int i = 1; i <= n; i++) {
            while (head+1<tail && up (que[head+1], que[head]) <= sum[i]*down (que[head+1], que[head]))
                head++;
            int j = que[head];
            dp[i] = dp[j] + (sum[i]-sum[j])*(sum[i]-sum[j]) + m;
            while (head+1<tail && up (i, que[tail-1])*down (que[tail-1], que[tail-2]) <= up (que[tail-1], que[tail-2])*down (i, que[tail-1]))
                tail--;
            que[tail++] = i;
        }
        printf ("%lld\n", dp[n]);
    }
    return 0;
}