_bzoj1096 [ZJOI2007]仓库建设【斜率优化dp】

传送门：http://www.lydsy.com/JudgeOnline/problem.php?id=1096

又是一道经典斜率优化。

#include <cstdio>

const int maxn = 1000005;

int n, c[maxn], head, tail, x[maxn];

long long sp[maxn], sxp[maxn], f[maxn];

char ch;

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 void readll(long long & rt) {

	while ((ch = getchar()) < 48);

	rt = ch - 48;

	while ((ch = getchar()) > 47) {

		rt = rt * 10 + ch - 48;

	}

}

int main(void) {

	//freopen("in.txt", "r", stdin);

	readint(n);

	for (int i = 1; i <= n; ++i) {

		readint(x[i]);  readll(sp[i]);  readint(c[i]);

		sxp[i] = (long long)x[i] * sp[i] + sxp[i - 1];

		sp[i] += sp[i - 1];

	}

	que[tail++] = (point){0, 0, 0};

	int j;

	for (int i = 1; i <= n; ++i) {

		while (tail - head > 1 && que[head].y - que[head + 1].y > x[i] * (que[head].x - que[head + 1].x)) {

			++head;

		}

		j = que[head].id;

		f[i] = f[j] + (long long)x[i] * (sp[i] - sp[j]) - (sxp[i] - sxp[j]) + (long long)c[i];

		tem = (point){sp[i], f[i] + sxp[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;

}