HDU 3507 PrintArticle (单调队列优化)

题意：给出一个数列C，一个数字M，将数列分成若干段，每段的代价为（设这段的数字为k个）：

dp[i]=min(dp[j]+(sum[i]-sum[j])*(sum[i]-sum[j])+M)

若j1<j2且j2比j1优

dp[j1]+sum[i]^2+sum[j1]^2-2*sum[i]*sum[j1]+M>dp[j2]+sum[i]^2+sum[j2]^2-2*sum[i]*sum[j2]

dp[j1]-dp[j2]+sum[j1]^2-sum[j2]^2>2*sum[i]*(sum[j1]-sum[j2])

 #include<iostream>
 #include<cstdio>
 #include<cstring>
 #include<cmath>
 #include<string>
 #include<algorithm>
 int dp[],sum[],n,m,q[];
 int getup(int j,int k){
     return dp[j]+sum[j]*sum[j]-dp[k]-sum[k]*sum[k];
 }
 int getdown(int x,int y){
     return *(sum[x]-sum[y]);
 }
 int getdp(int i,int j){
     return dp[j]+m+(sum[i]-sum[j])*(sum[i]-sum[j]);
 }
 int main(){
     while (scanf("%d%d",&n,&m)==){
     for (int i=;i<=n;i++){
         scanf("%d",&sum[i]);
     }
     dp[]=sum[]=;
     for (int i=;i<=n;i++)
         sum[i]+=sum[i-];
     int h=,t=;
     q[t++]=;
     for (int i=;i<=n;i++){
         while (h+<t&&getup(q[h+],q[h])<=sum[i]*getdown(q[h+],q[h])) h++;
         dp[i]=getdp(i,q[h]);
         while (h+<t&&getup(i,q[t-])*getdown(q[t-],q[t-])<=getup(q[t-],q[t-])*getdown(i,q[t-])) t--;
         q[t++]=i;
     }
     printf("%d\n",dp[n]);}
     return ;
 }