USACO19JAN Gold problem solution

Memories of a nightmare. .

On Sunday in the engine room playing simulation game, the result is very tragic, it is the last question yy result of the positive solution of metaphysics took only 80

Examination Results: 0 + 0 + 80 = 80

When playing against T3 revised results or 2hours 90

Revised results: 90 + 100 + 100 = 290

I was too weak QAQ

T1 Luogu P5196 [USACO19JAN]Cow Poetry

Topic Link

Ideas: dp + magical mathematical derivation

Quick start power also wrote a pot, has been ridiculed ftq Gangster

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

Topic Link

Ideas: The Magic of derivation + Fenwick tree

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

Ideas: dij + shortest path tree

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;
}