1096: [ZJOI2007]仓库建设

1096: [ZJOI2007]仓库建设

思路

　　斜率优化。

代码

 #include<cstdio>
 #include<iostream>

 using namespace std;
 typedef long long LL;

 const int N = ;
 LL f[N],s[N],x[N],p[N],c[N];
 int q[N],L,R;

 inline int read() {
     int x = ,f = ;char ch = getchar();
     for (; !isdigit(ch); ch=getchar()) if(ch=='-') f=-;
     for (; isdigit(ch); ch=getchar()) x = x*+ch-'';
     return x * f;
 }
 double Slope(int i,int j) {
     return 1.0*(f[i]+s[i]-f[j]-s[j])/(1.0*(p[i]-p[j]));
 }
 int main() {
     int n = read();
     for (int i=; i<=n; ++i)
         x[i] = read(),p[i] = read(),c[i] = read();
     for (int i=; i<=n; ++i) {
         s[i] = s[i-] + 1ll * x[i] * p[i];
         p[i] += p[i-];
     }
     int L = ,R = ;
     q[] = ;
     for (int i=; i<=n; ++i) {
         while (L<R && Slope(q[L],q[L+]) < (double)x[i]) L++;
         int j = q[L];
         f[i] = f[j] + x[i] * (p[i-] - p[j]) - (s[i-] - s[j]) + c[i];
         while (L<R && Slope(q[R-],q[R]) > Slope(q[R],i)) R--;
         q[++R] = i;
     }
     cout << f[n];
     return ;
 }