P1120 关路灯(区间dp，前缀和)

 

 

#include <iostream>
#include <algorithm>
#include <cstring>
using namespace std;
const int N=55;
typedef long long ll;
ll p[N],w[N];
ll dp[N][N][2];
int main()
{
	int  n,c;
	cin>>n>>c;
	for(int i=1;i<=n;i++)
		cin>>p[i],cin>>w[i];
	for(int i=1;i<=n;i++)
		w[i]+=w[i-1];
	
	memset(dp,0x3f,sizeof dp);

	for(int len=1;len<=n;len++)
		for(int i=1;i+len-1<=n;i++)
		{
			int j=i+len-1;
			if(len==1) dp[c][c][0]=dp[c][c][1]=0;
			else
			{
				ll x=w[n]-(w[j]-w[i]);
				ll y=w[n]-(w[j-1]-w[i-1]);
				
				dp[i][j][0]=min(dp[i+1][j][0]+x*(p[i+1]-p[i]),dp[i+1][j][1]+x*(p[j]-p[i]));
				dp[i][j][1]=min(dp[i][j-1][0]+y*(p[j]-p[i]),dp[i][j-1][1]+y*(p[j]-p[j-1]));
				
			}
	
		}
	cout<<min(dp[1][n][0],dp[1][n][1]);
	return 0;

}