bzoj 3675 [Apio2014]序列分割（斜率DP）

 1 #include<set>
 2 #include<cmath>
 3 #include<queue>
 4 #include<vector>
 5 #include<cstdio>
 6 #include<cstring>
 7 #include<iostream>
 8 #include<algorithm>
 9 #define trav(u,i) for(int i=front[u];i;i=e[i].nxt)
10 #define FOR(a,b,c) for(int a=(b);a<=(c);a++)
11 using namespace std;
12 
13 typedef long long ll;
14 const int N = 2e5+10;
15 
16 ll read() {
17     char c=getchar();
18     ll f=1,x=0;
19     while(!isdigit(c)) {
20         if(c==‘-‘) f=-1; c=getchar();
21     }
22     while(isdigit(c))
23         x=x*10+c-‘0‘,c=getchar();
24     return x*f;
25 }
26 
27 int n,K,tot;
28 ll f[N][2],cur,q[N],qh,qt,a[N],S[N];
29 /*
30 double slop(ll a,ll b) {
31     return (double)(S[b]*S[b]-S[a]*S[a]+f[a][cur^1]-f[b][cur^1])/(double)(S[b]-S[a]);
32 }
33 */
34 ll up(ll a,ll b) 
35 {
36     return (S[b]*S[b]-S[a]*S[a]+f[a][cur^1]-f[b][cur^1]);
37 }
38 ll down(ll a,ll b) 
39 {
40     return (S[b]-S[a]);
41 }
42 
43 int main()
44 {
45     n=read(),K=read();
46     FOR(i,1,n) {
47         a[++tot]=read();
48         if(!a[tot]) --tot;
49     }
50     n=tot;
51     FOR(i,1,n) S[i]=S[i-1]+a[i];
52     FOR(round,1,K) {
53         cur^=1;
54         qh=1; qt=0;
55         FOR(i,round,n) {
56             while(qh<qt&&up(q[qt-1],q[qt])*down(q[qt-1],i-1)>up(q[qt-1],i-1)*down(q[qt-1],q[qt])) qt--;
57             q[++qt]=i-1;
58             while(qh<qt&up(q[qh],q[qh+1])<S[i]*down(q[qh],q[qh+1])) qh++;
59             int t=q[qh];
60             f[i][cur]=f[t][cur^1]+(S[i]-S[t])*S[t];
61         }
62     }
63     printf("%lld\n",f[n][cur]);
64     return 0;
65 }