10.19 比赛总结 USACO 、 POJ3189

地址：http://pan.baidu.com/s/1bneZgxp

T1：

经典区间dp，f[i][j]表示取i~j，那么f[i][j]=max{f[i+1][j]+v[i]*k,f[i][j-1]+v[j]*k};

#include<set>
#include<map>
#include<cmath>
#include<queue>
#include<vector>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<iostream>
#include<algorithm>
using namespace std;
const int N = 2010;
#define For(i,n) for(int i=1;i<=n;i++)
#define Rep(i,l,r) for(int i=l;i<=r;i++)
#define Down(i,r,l) for(int i=r;i>=l;i--)
int n,v[N],f[N][N],Time,j;
void init(){
    freopen("trt.in","r",stdin);
    freopen("trt.out","w",stdout);
    scanf("%d",&n);
    For(i,n)  scanf("%d",&v[i]);
}
void dp(){
    For(k,n)
      for(int i=1;i+k-1<=n;i++){
          behind=n-k+1; j=i+k-1;
          f[i][j]=max(f[i][j],max(f[i+1][j]+Time*v[i],f[i][j-1]+Time*v[j]));
      }
    printf("%d
",f[1][n]);
}
int main(){
    init(); 
    dp();
    return 0;
}

T2:

爆搜即可，我加了二项式定理的剪枝

#include<set>
#include<map>
#include<cmath>
#include<queue>
#include<vector>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<iostream>
#include<algorithm>
using namespace std;
const int N = 12;
#define For(i,n) for(int i=1;i<=n;i++)
#define Rep(i,l,r) for(int i=l;i<=r;i++)
#define Down(i,r,l) for(int i=r;i>=l;i--)
bool flag=false,used[N];
int n,sum,A[N],C[N][N];

void DFS(int k,int s){
    if(flag) return;
    if(s>sum) return;
    if(k==n+1){
        if(s==sum) flag=true;
        return;
    }
    For(i,n)
      if(!used[i]){
          A[k]=i;used[i]=true;
          DFS(k+1,s+A[k]*C[n][k]);
          if(flag) return;
          used[i]=false;
      }
}

int main(){
    freopen("bdsum.in","r",stdin);
    freopen("bdsum.out","w",stdout);
    C[1][1]=1;
    Rep(i,2,10)
      For(j,i)
        C[i][j]=C[i-1][j]+C[i-1][j-1];
    scanf("%d%d",&n,&sum);
    DFS(1,0);
    For(i,n-1) printf("%d ",A[i]);printf("%d
",A[n]);
    return 0;
}

T3:

二分枚举答案，只要枚举区间，用最大匹配检测即可

#include<set>
#include<map>
#include<cmath>
#include<queue>
#include<vector>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<iostream>
#include<algorithm>
using namespace std;
const int N = 1010;
const int B = 24;
#define For(i,n) for(int i=1;i<=n;i++)
#define Rep(i,l,r) for(int i=l;i<=r;i++)
#define Down(i,r,l) for(int i=r;i>=l;i--)

int n,b,rank[N][N],contain[N],con[N][N];
bool vis[N];
 
void init(){
    scanf("%d%d",&n,&b);
    For(i,n)
        For(j,b) {
            scanf("%d",&rank[i][j]);rank[i][rank[i][j]]=j;}
    For(i,b) scanf("%d",&contain[i]);
}

bool dfs(int Left,int S,int Right){
    For(i,b)
      if(Left<=rank[S][i]&&rank[S][i]<=Right)
          if(!vis[i]){vis[i]=true;
              For(j,contain[i])
                if(con[i][j]==-1){
                    con[i][j]=S;
                    return true;
                }
               For(j,contain[i])
                 if(dfs(Left,con[i][j],Right)){
                    con[i][j]=S;
                    return true;
                } 
          }
    return false;
}

bool Check(int Dis){
    int ans=0;
    For(Left,b-Dis+1){
        ans=0;memset(con,-1,sizeof(con));
        For(i,n){
            memset(vis,false,sizeof(vis));
            if(dfs(Left,i,Left+Dis-1)) ans++; 
        }
        if(ans==n) return true;
    }
    return false;
}

void Work(){
    int Left=1,Right=b;
    while(Right-Left>1){
        int Mid=(Left+Right)>>1;
        if(Check(Mid)) Right=Mid;
        else           Left =Mid;
    }
    if(!Check(Left))  Left=Right;
    printf("%d
",Left); 
}

int main(){
    freopen("stead.in","r",stdin);
    freopen("stead.out","w",stdout); 
    init();
    Work();
    return 0;
}