USACO(含training section)水题合集[5/未完待续]

(1) USACO2.1 Ordered Fractions

　　枚举 排序即可，注意1/1

#include<iostream>
#include<cstdio>
#include<algorithm>
#include<cstring>
using namespace std;
const int N=,L=1e5;
struct fr{
    int a,b;
    fr(int q=,int w=):a(q),b(w){}
}f[L];
int n,cnt=;
inline bool cmp(fr &x,fr &y){
    return (double)x.a/x.b<(double)y.a/y.b;
}
inline int gcd(int a,int b){
    return b==?a:gcd(b,a%b);
}
int main(){
    cin>>n;
    for(int i=;i<=n;i++)
        for(int j=i+;j<=n;j++)
            if(gcd(i,j)==)
                f[++cnt]=fr(i,j);
    sort(f+,f++cnt,cmp);
    for(int i=;i<=cnt;i++)
        printf("%d/%d\n",f[i].a,f[i].b);
    cout<<"1/1";
}

(2) USACO1.5Number Triangles

　　基础DP

#include<iostream>
#include<cstring>
#include<algorithm>
#include<cstdio>
using namespace std;
int r,d[][],a[][];
int dp(int i,int j){
    if(d[i][j]>=) return d[i][j];
    return d[i][j]=a[i][j]+(i==r?:max(dp(i+,j),dp(i+,j+)));
}
int main(){
    scanf("%d",&r);//cin>>r;
    memset(d,-,sizeof(d));
    for(int i=;i<=r;i++)
        for(int j=;j<=i;j++) scanf("%d",&a[i][j]);//cin>>a[i][j];
    int ans=-;
    cout<<dp (,);
}

(3) USACO1.2 Transformations

　　模拟

#include <iostream>
using namespace std;
const int N=;
int n;
char a[N][N],r[N][N],t[N][N];
bool ro90(char a[N][N]){
    for(int i=;i<=n;i++)
        for(int j=;j<=n;j++)
            if(a[i][j]!=r[j][n-i+]) return false;
    return true;
}
bool ro180(char a[N][N]){
    for(int i=;i<=n;i++)
        for(int j=;j<=n;j++)
            if(a[i][j]!=r[n-i+][n-j+]) return false;
    return true;
}
bool ro270(char a[N][N]){
    for(int i=;i<=n;i++)
        for(int j=;j<=n;j++)
            if(a[i][j]!=r[n-j+][i]) return false;
    return true;
}
void img(char a[N][N],char t[N][N]){
    for(int i=;i<=n;i++)
        for(int j=;j<=n;j++)
            t[i][n-j+]=a[i][j];
}
bool check(char r[N][N],char t[N][N]){
    for(int i=;i<=n;i++)
        for(int j=;j<=n;j++)
            if(r[i][j]!=t[i][j]) return false;
    return true;
}
 
int solve(){
    if(ro90(a)) return ;
    if(ro180(a)) return ;
    if(ro270(a)) return ;
    img(a,t);
    if(check(r,t)) return ;
    if(ro90(t)) return ;
    if(ro180(t)) return ;
    if(ro270(t)) return ;
    if(check(r,t)) return ;
    return ;
}
int main(int argc, const char * argv[]) {
    cin>>n;
    for(int i=;i<=n;i++)
        for(int j=;j<=n;j++)cin>>a[i][j];
 
    for(int i=;i<=n;i++)
        for(int j=;j<=n;j++)cin>>r[i][j];
 
    cout<<solve();
 
}

(4) USACO1.4Mother's Milk

　　dfs，六种倒水方法，fill简化

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
const int N=;
int vis[N][N][N];
int l[],ta,tb,tc;
int ans[N];
inline void fill(int &a,int &b,int num){
    int tmp=min(l[num]-a,b);
    a+=tmp;
    b-=tmp;
}
 
void dfs(int a,int b,int c){//printf("%d %d %d\n",a,b,c);
    if(vis[a][b][c]) return;
    if(a==) ans[c]=true;
    vis[a][b][c]=;
 
    ta=a;tb=b;tc=c;//
    fill(ta,tb,);dfs(ta,tb,tc);
 
    ta=a;tb=b;tc=c;//
    fill(ta,tc,);dfs(ta,tb,tc);
 
    ta=a;tb=b;tc=c;//
    fill(tb,ta,);dfs(ta,tb,tc);
 
    ta=a;tb=b;tc=c;//
    fill(tb,tc,);dfs(ta,tb,tc);
 
    ta=a;tb=b;tc=c;//
    fill(tc,ta,);dfs(ta,tb,tc);
 
    ta=a;tb=b;tc=c;//
    fill(tc,tb,);dfs(ta,tb,tc);
}
int main(){
    cin>>l[]>>l[]>>l[];
    dfs(,,l[]);
    for(int i=;i<=l[];i++) if(ans[i]) cout<<i<<" ";
 
}

（5）USACO迷宫

　　裸DFS

#include<iostream>
using namespace std;
int n,m,t,sx,sy,fx,fy,ans=;int x,y;
int e[][],vis[][],dx[]={-,,,},dy[]={,,,-};
void dfs(int x,int y){
    if(x<||y<||x>n||y>m) return;
    if(e[x][y]) return;
    if(x==fx&&y==fy) {ans++;return;}
    if(vis[x][y]) return;
    vis[x][y]=;
    for(int i=;i<;i++) dfs(x+dx[i],y+dy[i]);
    vis[x][y]=;
}
int main(){
    cin>>n>>m>>t>>sx>>sy>>fx>>fy;
    for(int i=;i<t;i++) {cin>>x>>y;e[x][y]=;}
    dfs(sx,sy);
    cout<<ans;
}