E29 区间DP 环形石子合并

E29 区间DP 环形石子合并_哔哩哔哩_bilibili

 

P1880 [NOI1995] 石子合并 - 洛谷

// 区间DP O(n^3)
#include <bits/stdc++.h>
using namespace std;

const int N=210;
int n,a[N],s[N];
int f[N][N];  //f[i][j]表示把从i到j合并成一堆的得分最小值 
int g[N][N];  //g[i][j]表示把从i到j合并成一堆的得分最大值 

int main(){
  memset(f,0x3f,sizeof f); memset(g,-0x3f,sizeof g);
  scanf("%d",&n);
  for(int i=1; i<=n; i++) scanf("%d",&a[i]),a[i+n]=a[i];
  for(int i=1; i<=2*n; i++) s[i]=s[i-1]+a[i],g[i][i]=0,f[i][i]=0;
  
  int minv=1e9,maxv=-1e9;
  for(int len=2; len<=n; len++){
    for(int i=1,j=len; j<=2*n; i++,j++){
      for(int k=i; k<j; k++){
        f[i][j]=min(f[i][j],f[i][k]+f[k+1][j]+s[j]-s[i-1]);
        g[i][j]=max(g[i][j],g[i][k]+g[k+1][j]+s[j]-s[i-1]);
      }
      minv=min(minv,f[i][i+n-1]); //f[1,n]...f[n,2n-1]
      maxv=max(maxv,g[i][i+n-1]); //g[1,n]...g[n,2n-1]
    }
  }
  printf("%d\n%d\n",minv,maxv);
}

 

// 区间DP 四边形不等式优化 O(n^2)
#include <bits/stdc++.h>
using namespace std;

const int N=210;
int n,a[N],s[N];
int f[N][N]; //f[i][j]表示把从i到j合并成一堆的得分最小值
int g[N][N]; //g[i][j]表示把从i到j合并成一堆的得分最大值
int p[N][N];

int main(){
  memset(f,0x3f,sizeof f); memset(g,-0x3f,sizeof g);
  scanf("%d",&n);
  for(int i=1;i<=n;i++) scanf("%d",&a[i]),a[i+n]=a[i];
  for(int i=1;i<=2*n;i++) s[i]=s[i-1]+a[i],g[i][i]=0,f[i][i]=0,p[i][i]=i;
  
  int minv=1e9, maxv=-1e9;
  for(int len=2; len<=n; len++){
    for(int i=1,j=len; j<=2*n; i++,j++){
      for(int k=p[i][j-1]; k<=p[i+1][j]; k++){
        if(f[i][k]+f[k+1][j]+s[j]-s[i-1]<f[i][j])
          f[i][j]=f[i][k]+f[k+1][j]+s[j]-s[i-1], p[i][j]=k;
      }
      g[i][j]=max(g[i][j-1],g[i+1][j])+s[j]-s[i-1];
      minv=min(minv,f[i][i+n-1]); //f[1,n]...f[n,2n-1]
      maxv=max(maxv,g[i][i+n-1]); //g[1,n]...g[n,2n-1]
    }
  }
  printf("%d\n%d\n",minv,maxv);
}