POJ1160-四边形不等式优化

/*第一个四边形不等式优化题(虽然数据量小，普通的dp即可秒过)写倒是好写，难在四边形不等式的证明上，不会证~待会看证明去~*/#include <cstdio>#include <cstring>#include <iostream>using namespace std;const int NN=310;const int INF=0x7fffffff;int n,m;int s[NN],dp[NN][NN],w[NN][NN],p[NN][NN];void get_w()//求在i~j号村庄间建一个邮局的最小距离和{    for (int i=1; i<n; i++)      for (int j=i+1; j<=n; j++)      {          if ((i+j)%2) w[i][j]=s[j]-s[(i+j)/2]*2+s[i-1];          else         w[i][j]=s[j]-s[(i+j)/2]-s[(i+j)/2-1]+s[i-1];      }}void get_dp(){    for (int i=1; i<=n; i++)    {        dp[1][i]=w[1][i];        p[1][i]=0;    }    for (int c=2; c<=m; c++)    {        p[c][n+1]=n;        for (int i=n; i; i--)        {            int tmp=INF,k;            for (int j=p[c-1][i]; j<=p[c][i+1]; j++)            {                if (dp[c-1][j]+w[j+1][i]<tmp) tmp=dp[c-1][k=j]+w[j+1][i];            }            dp[c][i]=tmp;            p[c][i]=k;        }    }}int main(){    scanf("%d%d",&n,&m);    s[0]=0;    int x;    for (int i=1; i<=n; i++)    {        scanf("%d",&x);        s[i]=s[i-1]+x;    }    get_w();    get_dp();    printf("%d",dp[m][n]);    return 0;}