USACO19JAN Gold题解

噩梦的回忆。。

上周日在机房打的模拟赛，结果十分惨烈，就最后一题yy出了正解结果玄学的只拿了80

考试结果：0+0+80=80

订正时对着T3打了2hours结果还是90

订正结果：100+100+90=290

我太弱了QAQ

T1 Luogu P5196 [USACO19JAN]Cow Poetry

题目链接

思路：dp+神奇的数学推导

快速幂一开始还写锅了，受到了ftq大佬的嘲笑

code

#include<bits/stdc++.h>
using namespace std;
const int MOD=1e9+7,MAXN=5000+10;
int f[5010][MAXN],s[MAXN],c[MAXN],g[MAXN],num[35],n,m,k;
long long ans,re=1;
long long pow(int b, int p) {
    if (p == 0) {
        return 1;
    }
    long long x = b;
    long long ans = 1;
    while (p > 0) {
        if (p % 2 == 1) {
            ans = ans * x % MOD;
        }
        x = x * x % MOD;
        p = p >> 1;
    }
    return ans % MOD;
}
void debug()
{
    for(int i=1;i<=5;++i){
        cout<<f[k][i]<<" ";
    }
    cout<<endl;
    for(int i=0;i<=5;++i){
        cout<<num[i]<<" ";
    }
    cout<<endl;
}
signed main()
{
//  freopen(".in","r",stdin);
//  freopen(".out","w",stdout);
    cin>>n>>m>>k;
    for(int i=1;i<=n;++i){
        cin>>s[i]>>c[i];
    }
    g[0]=1;
    for(int i=1;i<=k;i++){
        for(int j=1;j<=n;j++){
            if(i-s[j]>=0){
                (f[i][c[j]]+=g[i-s[j]])%=MOD;
                (g[i]+=g[i-s[j]])%=MOD;
            }
        }
    }
    for(int i=1;i<=m;++i){
        char ch;
        cin>>ch;
        num[ch-'A']++;
    }
//  debug();
    for(int i=0;i<26;++i){
        if(num[i]){
            ans=0;
            for(int j=1;j<=n;++j){
                if(f[k][j]){
                    (ans+=pow(f[k][j],num[i]))%=MOD;
//                  cout<<ans<<endl;
                    
                }
            }
            (re*=ans)%=MOD;
        }
    }
    cout<<re<<endl;
    return 0;
}

---

T2 Luogu P5200 [USACO19JAN]Sleepy Cow Sorting

题目链接

思路：神奇的推导+树状数组

code

#include<bits/stdc++.h>
using namespace std;
const int MAXN=1e5+10;
inline int lowbit(int x){return x&(-x);}
int ans[MAXN],num[MAXN],tree[MAXN],n,sum,k;
void add(int x)
{
    for(int i=x;i<=n;i+=lowbit(i)){
        tree[i]++;
    }
}
int query(int x)
{
    int re=0;
    for(int i=x;i;i-=lowbit(i)){
        re+=tree[i];
    }
    return re;
}
int main()
{
//  freopen(".in","r",stdin);
//  freopen(".out","w",stdout);
    cin>>n;
    for(int i=1;i<=n;++i){
        cin>>num[i];
    }
    sum=n,k=0;
    while(num[n-k]>num[n-k-1]){
        add(num[n-k]);
        sum--,k++;
    }
    add(num[n-k]);
    sum--;
    for(int i=1;i<=sum;++i){
        add(num[i]);
        ans[i]=sum-i+query(num[i]-1);
    }
    cout<<sum<<endl;
    for(int i=1;i<=sum;++i){
        cout<<ans[i]<<" ";
    }
    return 0;
}

---

T3 Luogu P5201 [USACO19JAN]Shortcut

思路：dij+最短路树

code

#include<bits/stdc++.h>
#define int long long 
#define ll long long 
using namespace std;
const int MAXN=1e5+10,INF=0x3f3f3f3f;
inline int read()
{
    int s=0,f=1;
    char ch=getchar();
    while(ch<'0'||ch>'9'){
        if(ch=='-')
            f=-1;
        ch=getchar();
    }
    while(ch>='0'&&ch<='9'){
        s=s*10+ch-'0';
        ch=getchar();
    }
    return s*f;
}

struct NODE {
    int first,second;
    bool operator<(NODE b) const { return (b.first==first)?b.second<second:b.first < first; }
};
int cnt,Cnt,m,n,T;
int head[MAXN],Head[MAXN],from[MAXN],siz[MAXN],v[MAXN];
ll dist[MAXN],ans=0;
priority_queue <NODE > q;
bool vis[MAXN],vi[MAXN];

void debug()
{
    puts("head  Head    from    siz dist");
    for(int i=1;i<=n;++i){
        cout<<head[i]<<"    "<<Head[i]<<"   "<<from[i]<<"   "<<siz[i]<<"    "<<dist[i]<<endl;
    }
}

struct node{
    int to,next,l;  
}edge[MAXN];
void addedge(int x,int y,int l)
{
    edge[++cnt].to=y;
    edge[cnt].l=l;
    edge[cnt].next=head[x];
    head[x]=cnt;
}

struct Node{
    int to,next;
}Edge[MAXN];
void Addedge(int x,int y)
{
    Edge[++Cnt].to=y;
    Edge[Cnt].next=Head[x];
    Head[x]=Cnt;
}

void dij()
{
    memset(dist,INF,sizeof(dist));
    dist[1]=0;
    NODE a;
    a.first=0,a.second=1;
    q.push(a);
    while(!q.empty()){
        NODE now=q.top();q.pop();
        int x=now.second;
//      if(vi[x])continue;
//      vi[x]=1;
//      cout<<x<<"while\n";
        for(int i=head[x];i;i=edge[i].next){
//          cout<<i<<"i\n";
            int y=edge[i].to;
//          cout<<y<<" y\n";
            if(dist[x]+edge[i].l<dist[y]){          
//              cout<<y<<"y\n";
                NODE aa;
                aa.second=y,aa.first=dist[y];
                dist[y]=dist[x]+edge[i].l;
                from[y]=x;
//              cout<<"to"<<y<<endl;
                q.push(aa);
            }
        }
    }
}

void build()
{
    for(int i=1;i<=n;++i){
        Addedge(i,from[i]);
        Addedge(from[i],i);
    }
}

int dfs(int x,int fa)
{
    vis[x]=1;
    siz[x]+=v[x];
    for(int i=Head[x];i;i=Edge[i].next){
        int y=Edge[i].to;
        if(!vis[y]&&y!=fa){
            siz[x]+=dfs(y,x);
        }
    }
    return siz[x];
}

signed main()
{
//  freopen("test08.in","r",stdin);
//  freopen("1.out","w",stdout);
    cin>>n>>m>>T;
    for(int i=1;i<=n;++i){
        v[i]=read();
    }
    for(int i=1;i<=m;++i){
        int x=read(),y=read(),t=read();
        addedge(x,y,t);
        addedge(y,x,t);
    }
    dij();
    build();
    dfs(1,0);
//  debug();
    for(int i=1;i<=n;++i){
        ans=max(ans,siz[i]*(dist[i]-T));
    }
    cout<<ans<<endl;
    return 0;
}