模板斜率优化dp

Posted 2020-11-25 xiaobuxie

题目链接：https://codeforces.com/problemset/problem/1083/E

本来是想写计几的，结果发现是到斜率优化dp，正好也没怎么做过斜率dp，整理一下板子。

感觉斜率优化dp就和凸包差不多，维护一个上（下）凸包的亚子。

 1 // f[j] = yi * xj + wi - xi * yi + fi;
 2 //维护上凸包,斜率递减
 3 #include<bits/stdc++.h>
 4 using namespace std;
 5 typedef long long ll;
 6 const int N = 1e6 + 9;
 7 struct Point{
 8     ll x,y,w;
 9     bool operator < (const Point& b)const{
10         return x < b.x;
11     }
12 }a[N];
13 ll q[N],f[N];
14 double cal(int i,int j){
15     return 1.0 * (f[j] - f[i]) / (a[j].x - a[i].x);
16 }
17 int main(){
18     int n; scanf("%d",&n);
19     for(int i =1;i<=n;++i) scanf("%lld %lld %lld",&a[i].x,&a[i].y,&a[i].w);
20     sort(a+1,a+1+n);
21     int l = 1, r = 1;
22     ll ans = -1000000000000000;
23     for(int i = 1;i<=n;++i){
24         while( l < r && cal(q[l],q[l+1]) >= a[i].y ) ++l;
25         int j = q[l];
26         f[i] = f[j] - a[i].y * a[j].x - a[i].w + a[i].x * a[i].y;
27         ans = max(ans,f[i]);
28         while( l < r && cal(q[r-1],q[r]) <= cal(q[r],i) ) --r;
29         q[++r] = i;
30     }
31     printf("%lld",ans);
32 }

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