_bzoj1096 [ZJOI2007]仓库建设斜率优化dp

Posted 2020-08-30 ciao_sora

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;
}