POJ3612Telephone Wire題解動态規劃DP

Telephone Wire

Time Limit: 1000MS	Memory Limit: 65536K
Total Submissions: 1735	Accepted: 596

Description

Farmer John's cows are getting restless about their poor telephone service; they want FJ to replace the old telephone wire with new, more efficient wire. The new wiring will utilize N (2 ≤ N ≤ 100,000) already-installed telephone poles, each with some heighti meters (1 ≤ heighti ≤ 100). The new wire will connect the tops of each pair of adjacent poles and will incur a penalty cost C × the two poles' height difference for each section of wire where the poles are of different heights (1 ≤ C ≤ 100). The poles, of course, are in a certain sequence and can not be moved.

Farmer John figures that if he makes some poles taller he can reduce his penalties, though with some other additional cost. He can add an integer X number of meters to a pole at a cost of X2.

Help Farmer John determine the cheapest combination of growing pole heights and connecting wire so that the cows can get their new and improved service.

Input

* Line 1: Two space-separated integers: N and C

* Lines 2..N+1: Line i+1 contains a single integer: heighti

Output

* Line 1: The minimum total amount of money that it will cost Farmer John to attach the new telephone wire.

Sample Input

5 2
2
3
5
1
4      

Sample Output

15      

Source

USACO 2007 November Gold 狀态： d[i][j]表示第i個高度為j時最小花費 狀态轉移方程： d[i][j]=min(d[i][j],d[i-1][k]+abs(j-k)*m+(a[i]-j)*(a[i]-j)); 這樣肯定逾時，不知道怎麼優化 看了别人的解題報告:

代碼：

#include<cstdio>

#define min(a,b) ((a)<(b)?(a):(b))

#define inf 1<<30

int main()

{

int n,m,i,j,t,ans,a,low[105],high[105],d[105];

while(scanf("%d%d",&n,&m)==2)

{

scanf("%d",&a);

for(i=1;i<=100;i++)

d[i]=i<a?inf:(a-i)*(a-i);

for(i=1;i<n;i++)

{

scanf("%d",&a);

for(t=inf,j=100;j>0;j--)

low[j]=t=min(t,d[j]+j*m);

for(t=inf,j=1;j<=100;j++)

{

high[j]=t=min(t,d[j]-j*m);

d[j]=inf;

}

for(j=a;j<=100;j++)

d[j]=(j-a)*(j-a)+min(low[j]-j*m,high[j]+j*m);

}

for(ans=inf,i=1;i<=100;i++)

ans=min(ans,d[i]);

printf("%d/n",ans);

}

}