【BZOJ1096】[ZJOI2007]仓库建设【斜率优化】

斜率优化咯。

一开始不知道怎么O(1)转移，看了别人blog才发现可以这么玩。

/* Footprints In The Blood Soaked Snow */
#include <cstdio>
#include <algorithm>

using namespace std;

typedef long long LL;

const int maxn = 1000005, maxq = maxn;

int n, q[maxq];
LL dp[maxn], sum[maxn], dif[maxn], x[maxn], p[maxn], c[maxn];

inline int iread() {
	int f = 1, x = 0; char ch = getchar();
	for(; ch < '0' || ch > '9'; ch = getchar()) f = ch == '-' ? -1 : 1;
	for(; ch >= '0' && ch <= '9'; ch = getchar()) x = x * 10 + ch - '0';
	return f * x;
}

inline LL dy(int a, int b) {
	return (dp[a] + dif[a]) - (dp[b] + dif[b]);
}

inline LL dx(int a, int b) {
	return sum[a] - sum[b];
}

int main() {
	n = iread();
	for(int i = 1; i <= n; i++) x[i] = iread(), p[i] = iread(), c[i] = iread();
	for(int i = 1; i <= n; i++) sum[i] = sum[i - 1] + p[i], dif[i] = dif[i - 1] + x[i] * p[i];

	int h = 1, t = 0; q[++t] = 0;
	for(int i = 1; i <= n; i++) {
		for(; h < t && dy(q[h + 1], q[h]) < dx(q[h + 1], q[h]) * x[i]; h++);
		dp[i] = dp[q[h]] + (sum[i] - sum[q[h]]) * x[i] - (dif[i] - dif[q[h]]) + c[i] ;
		for(; h < t && dy(q[t], q[t - 1]) * dx(i, q[t]) >= dy(i, q[t]) * dx(q[t], q[t - 1]); t--);
		q[++t] = i;
	}

	printf("%lld\n", dp[n]);
	return 0;
}