Namomo spring camp day1 div1 DP

Crystalfly

#include
using namespace std;
const int maxn=1e5+10;
typedef long long ll;
int h[maxn],e[maxn<<1],ne[maxn<<1],idx;
void add(int x,int y)
{
    e[idx]=y,ne[idx]=h[x],h[x]=idx++;
}
ll a[maxn],f[maxn],g[maxn];
int t[maxn];
void dfs(int u,int fa)
{
    g[u]=a[u];
    ll mx1=-1e16-9,mx2=-1e16-9;
    for(int i=h[u];~i;i=ne[i])
    {
        int v=e[i];
        if(v==fa)continue;
        dfs(v,u);
        g[u]+=f[v]-a[v];
        ll tmp=a[v]+g[v]-f[v];
        if(tmp>=mx1)mx2=mx1,mx1=tmp;
        else if(tmp>mx2)mx2=tmp;
    }
    f[u]=g[u];
    for(int i=h[u];~i;i=ne[i])
    {
        int v=e[i];
        if(v==fa)continue;
        f[u]=max(f[u],g[u]+a[v]);
        if(t[v]==3)
        {
            if(g[v]-f[v]+a[v]==mx1)f[u]=max(f[u],g[u]+mx2+a[v]);
            else f[u]=max(f[u],g[u]+mx1+a[v]);
        }
    }
}
signed main()
{
    ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);
    int T;cin>>T;
    while(T--)
    {
        int n;cin>>n;
        for(int i=1;i<=n;i++)h[i]=-1;
        idx=0;
        for(int i=1;i<=n;i++){cin>>a[i];f[i]=g[i]=0;}
        for(int i=1;i<=n;i++)cin>>t[i];
        for(int i=1;i>x>>y;add(x,y),add(y,x);}
        dfs(1,0);
        printf("%lldn",f[1]);
        // cout< 
Towers
 
 
#include
using namespace std;
const int maxn=2e5+10;
typedef long long ll;
typedef pair pll;
int w[maxn];
int e[maxn<<1],ne[maxn<<1],h[maxn],idx;
void add(int a,int b)
{
    e[idx]=b,ne[idx]=h[a],h[a]=idx++;
}
int n;
ll res;
int dfs(int u,int fa)
{
    int mx1=0,mx2=0;
    for(int i=h[u];~i;i=ne[i])
    {
        int v=e[i];
        if(v==fa)continue;
        int t=dfs(v,u);
        if(t>=mx1)mx2=mx1,mx1=t;
        else if(t>mx2)mx2=t;
    }
    if(fa){res+=max(0,w[u]-mx1);if(w[u]>mx1)mx1=w[u];}
    else res+=w[u]-mx1+w[u]-mx2;
    return mx1;
}
int main()
{
    scanf("%d",&n);
    for(int i=1;i<=n;i++)scanf("%d",&w[i]);
    memset(h,-1,sizeof(h));
    for(int i=1;iw[root])root=i;
    int t=dfs(root,0);
    printf("%lldn",res);
}
 
 
Werewolves
 
dp[u][sum]=dp[u][i]*dp[u][j]；
 
i+j和为sum
 
因为存在负值，所以需要加一个col_size，取答案的时候再减去就好了
 
Size每次dfs都算一遍是为了降低时间复杂度，不过对于树上背包的时间复杂度还是感觉挺困惑的
 
#include
using namespace std;
const int maxn=3e3+10;
typedef long long ll;
ll dp[maxn][maxn<<1];
const int mod=998244353;
int siz[maxn],col[maxn],n,col_siz[maxn];
int h[maxn],e[maxn<<1],ne[maxn<<1],idx,id,temp[maxn<<1];
void add(int a,int b){e[idx]=b,ne[idx]=h[a],h[a]=idx++;}
ll res;
void dfs(int u,int fa)
{ 
    siz[u]=1;
    if(col[u]==id)
    {
        dp[u][1+col_siz[id]]=1;
    }
    else dp[u][col_siz[id]-1]=1;
    for(int t=h[u];~t;t=ne[t])
    {
        int v=e[t];if(v==fa)continue;
        dfs(v,u);
        for(int i=0;i<=col_siz[id]*2;i++)temp[i]=0;
        int m1=min(siz[u],col_siz[id]),m2=min(siz[v],col_siz[id]);
        for(int i=-m1;i<=m1;i++)
        for(int j=-m2;j<=m2&&i+j<=col_siz[id];j++)
        if(i+j+col_siz[id]>=0)
        {
            temp[i+j+col_siz[id]]=(temp[i+j+col_siz[id]]+dp[u][i+col_siz[id]]*dp[v][j+col_siz[id]]%mod)%mod;
        }
        for(int i=0;i<=col_siz[id]*2;i++)
        dp[u][i]=(dp[u][i]+temp[i])%mod;
        siz[u]+=siz[v];
    }
}
int main()
{
    scanf("%d",&n);
    for(int i=1;i<=n;i++)scanf("%d",&col[i]),col_siz[col[i]]++;
    memset(h,-1,sizeof(h));
    for(int i=1;i 
[CERC2014]Outer space invaders
 
#include
using namespace std;
const int inf=0x3f3f3f3f;
const int BufferSize=1<<16;
char buffer[BufferSize],*head,*tail;
inline char Getchar() {
    if(head==tail) {
        int l=fread(buffer,1,BufferSize,stdin);
        tail=(head=buffer)+l;
    }
    return *head++;
}
inline int read() {
    int x=0,f=1;char c=Getchar();
    for(;!isdigit(c);c=Getchar()) if(c=='-') f=-1;
    for(;isdigit(c);c=Getchar()) x=x*10+c-'0';
    return x*f;
}
void print(int x)
{
    if(x>9) print(x/10);
    putchar(x%10|'0');
}
const int maxn=310,maxm=1e4+10;
struct Node
{
    int a,b,d;
}point[maxn];
int n,cnt,mp[maxm],dp[maxn<<1][maxn<<1];
void init()
{
    n=read(); cnt=0; memset(dp,0,sizeof(dp));memset(mp,0,sizeof(mp));
        for(int i=1;i<=n;i++)
        {
            point[i].a=read(),point[i].b=read(),point[i].d=read();
            mp[point[i].a]=1;mp[point[i].b]=1;
        }
        for(int i=1;i=l&&point[i].b<=r&&(id==-1||point[i].d>point[id].d))id=i;
         if(id==-1)continue;
         dp[l][r]=inf;
         for(int k=point[id].a;k<=point[id].b;k++)
         dp[l][r]=min(dp[l][r],dp[l][k-1]+point[id].d+dp[k+1][r]);
     }
     printf("%dn",dp[1][cnt]);
    }
}
 
 
Cities
 
经典区间DP了
 
#include 
using namespace std;
const int maxn=5e3+10;
int dp[maxn][maxn],lt[maxn],u[maxn],a[maxn];
const int BufferSize=1<<16;
char buffer[BufferSize],*head,*tail;
inline char Getchar() {
    if(head==tail) {
        int l=fread(buffer,1,BufferSize,stdin);
        tail=(head=buffer)+l;
    }
    return *head++;
}
inline int read() {
    int x=0,f=1;char c=Getchar();
    for(;!isdigit(c);c=Getchar()) if(c=='-') f=-1;
    for(;isdigit(c);c=Getchar()) x=x*10+c-'0';
    return x*f;
}
void print(int x)
{
    if(x>9) print(x/10);
    putchar(x%10|'0');
}
int main()
{
    int T;T=read();
    while(T--)
    {
        int n;n=read();
        for(int i=1;i<=n;i++)a[i]=read();
        memset(u,0,sizeof(u));
        for(int i=1;i<=n;i++)
        {
            lt[i]=u[a[i]];
            u[a[i]]=i;
            dp[i][i]=0;
        }
        for(int len=2;len<=n;len++)
            for(int l=1;l+len-1<=n;l++)
            {
                int r=l+len-1;
                dp[l][r]=dp[l][r-1]+1;
                for(int k=lt[r];k>=l;k=lt[k])
                {
                    dp[l][r]=min(dp[l][r],dp[l][k]+dp[k+1][r]);
                }
            }
        printf("%dn",dp[1][n]);
    }
}