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hdu3507Print Article(斜率优化dp)

2024-10-30 22:49:02   208人阅读

Print Article

Time Limit: 9000/3000 MS (Java/Others)    Memory Limit: 131072/65536 K (Java/Others)
Total Submission(s): 12824    Accepted Submission(s): 3967


Problem Description
Zero has an old printer that doesn‘t work well sometimes. As it is antique, he still like to use it to print articles. But it is too old to work for a long time and it will certainly wear and tear, so Zero use a cost to evaluate this degree.
One day Zero want to print an article which has N words, and each word i has a cost Ci to be printed. Also, Zero know that print k words in one line will cost
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M is a const number.
Now Zero want to know the minimum cost in order to arrange the article perfectly.
 

 

Input
There are many test cases. For each test case, There are two numbers N and M in the first line (0 ≤ n ≤ 500000, 0 ≤ M ≤ 1000). Then, there are N numbers in the next 2 to N + 1 lines. Input are terminated by EOF.
 

 

Output
A single number, meaning the mininum cost to print the article.
 

 

Sample Input
5 559575
 

 

Sample Output
230
 

 

Author
Xnozero
 

 

Source
2010 ACM-ICPC Multi-University Training Contest（7）——Host by HIT
 

 

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斜率优化dp学习:http://www.cnblogs.com/ka200812/archive/2012/08/03/2621345.html
 
#include<iostream>#include<cstdio>#include<cstring>#define N 500005using namespace std;int dp[N],q[N],sum[N];int head,tail,n,m;int get_dp(int i,int j){    return dp[j]+m+(sum[i]-sum[j])*(sum[i]-sum[j]);}int get_up(int j,int k){    return dp[j]+sum[j]*sum[j]-(dp[k]+sum[k]*sum[k]);}int get_down(int j,int k){    return 2*(sum[j]-sum[k]);}int main(){    while(scanf("%d%d",&n,&m)==2)    {        for(int i=1;i<=n;i++) scanf("%d",&sum[i]);        sum[0]=dp[0]=0;head=tail=0;        for(int i=1;i<=n;i++) sum[i]+=sum[i-1];        q[tail++]=0;        for(int i=1;i<=n;i++)        {            while(head+1<tail && get_up(q[head+1],q[head])<=sum[i]*get_down(q[head+1],q[head]))              head++;            dp[i]=get_dp(i,q[head]);            while(head+1<tail && get_up(i,q[tail-1])*get_down(q[tail-1],q[tail-2])<=get_up(q[tail-1],q[tail-2])*get_down(i,q[tail-1]))              tail--;            q[tail++]=i;        }        printf("%d\n",dp[n]);    }    return 0;}

 

hdu3507Print Article(斜率优化dp)


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