_bzoj1911 [Apio2010]特别行动队【斜率优化dp】

传送门：http://www.lydsy.com/JudgeOnline/problem.php?id=1911

裸的斜率优化dp。

#include <cstdio>

const int maxn = 1000005;

int n, a, b, c, s[maxn], head, tail;
char ch;
long long f[maxn];
struct point {
	long long x, y;
	int id;
} que[maxn], tem;

inline void readint(int & rt) {
	while ((ch = getchar()) < 48);
	rt = ch - 48;
	while ((ch = getchar()) > 47) {
		rt = rt * 10 + ch - 48;
	}
}
inline long long poww(long long aa) {
	return aa * aa;
}

int main(void) {
	//freopen("in.txt", "r", stdin);
	readint(n);
	scanf("%d%d%d", &a, &b, &c);
	for (int i = 1; i <= n; ++i) {
		readint(s[i]);
		s[i] += s[i - 1];
	}
	int j;
	que[tail++] = (point){0, 0, 0};
	for (int i = 1; i <= n; ++i) {
		while (tail - head > 1 && que[head].y - que[head + 1].y < 2 * a * s[i] * (que[head].x - que[head + 1].x)) {
			++head;
		}
		j = que[head].id;
		f[i] = f[j] + a * poww(s[i] - s[j]) + b * (long long)(s[i] - s[j]) + c;
		tem = (point){s[i], f[i] + a * poww(s[i]) - b * (long long)s[i], i};
		while (tail - head > 1 && (tem.y - que[tail - 1].y) * (que[tail - 1].x - que[tail - 2].x) > (que[tail - 1].y - que[tail - 2].y) * (tem.x - que[tail - 1].x)) {
			--tail;
		}
		que[tail++] = tem;
	}
	printf("%lld\n", f[n]);
	return 0;
}