hdu 1158 Employment Planning

Description
A project manager wants to determine the number of the workers needed in every month. He does know the minimal number of the workers needed in each month. When he hires or fires a worker, there will be some extra cost. Once a worker is hired, he will get the salary even if he is not working. The manager knows the costs of hiring a worker, firing a worker, and the salary of a worker. Then the manager will confront such a problem: how many workers he will hire or fire each month in order to keep the lowest total cost of the project.

Input
The input may contain several data sets. Each data set contains three lines. First line contains the months of the project planed to use which is no more than 12. The second line contains the cost of hiring a worker, the amount of the salary, the cost of firing a worker. The third line contains several numbers, which represent the minimal number of the workers needed each month. The input is terminated by line containing a single '0'.

Output
The output contains one line. The minimal total cost of the project.

Sample Input
3
4 5 6
10 9 11
0

Sample Output

199

设dp[i][j]表示前i个月j个人的最小花费，a[ i]表示第i个月至少需要的人数，那么

dp[i][j]=min(dp[i-1][k]+pay*j+fun(k,j));其中a[i]<=j<=max(a),a[i-1]<=k<=max(a),fun(k,j)表示雇佣或者裁掉j-k人所需的花费

#include<iostream>#include<cstdio>#include<cstring>#include<algorithm>using namespace std;const int inf=0x7f7f7f7f;int dp[20][1000005],a[20],hire,pay,fire;int fun(int a,int b){if(a<=b)return hire*(b-a);else return fire*(a-b);}int main(){int i,j,k,n,minn,maxx;while(scanf("%d",&n)!=EOF){if(n==0) break;scanf("%d%d%d",&hire,&pay,&fire);maxx=-1,minn=inf;for(i=1;i<=n;i++){scanf("%d",&a[i]);maxx=max(a[i],maxx);minn=min(a[i],minn);}for(i=0;i<=n;i++){for(j=minn;j<=maxx;j++){if(i==0) dp[i][j]=0;else dp[i][j]=inf;}}for(i=1;i<=n;i++){for(j=a[i];j<=maxx;j++){if(i==1)dp[i][j]=dp[i-1][0]+fun(0,j)+pay*j;else{for(k=a[i-1];k<=maxx;k++)dp[i][j]=min(dp[i][j],dp[i-1][k]+fun(k,j)+pay*j);}}}int ans=inf;for(i=a[n];i<=maxx;i++){ans=min(ans,dp[n][i]);}printf("%d\n",ans);}return 0;}