杂算法模板

一些不知怎么分类的算法。

huffman树：https://www.luogu.org/problemnew/show/P2168

#include<bits/stdc++.h>
#define ll long long
using namespace std;
const int N=1e5+99;
struct node{ll v;int h;};
int n,num,k;
ll ans;
priority_queue<node>q;
bool operator<(node a,node b){return (a.v!=b.v)?a.v>b.v:a.h>b.h;}
int main()
{
    scanf("%d%d",&n,&k);
    ll x;
    for(int i=1;i<=n;i++)
    {scanf("%lld",&x);q.push((node){x,0});}
    num=n;
    while((num-1)%(k-1))num++,q.push((node){0,0});
    while(num>1)
    {
        int maxh=0;ll sum=0;
        for(int i=1;i<=k;i++)
        {
            node p=q.top();q.pop();
            sum+=p.v;maxh=max(maxh,p.h);
        }
        num-=k-1;ans+=sum;
        q.push((node){sum,maxh+1});
    }
    node p=q.top();
    printf("%lld\n%d",ans,p.h);
}

矩阵树定理：https://www.luogu.org/problemnew/show/P4111

#include<cstdio>
#include<algorithm>
using namespace std;
typedef long long ll;
const int mod=1e9;
const int dx[4]={1,-1,0,0},dy[4]={0,0,1,-1}; 
int n,m,tot,id[107][107];
ll a[107][107];
char str[107];
ll Gauss()
{
    ll ret=1;
    for(int i=2;i<=tot;i++)
    {
        for(int j=i+1;j<=tot;j++)
        while(a[j][i])
        {
            ll t=a[i][i]/a[j][i];
            for(int k=i;k<=tot;k++)a[i][k]=(a[i][k]-a[j][k]*t)%mod;  
            for(int k=i;k<=tot;k++)swap(a[i][k],a[j][k]); 
            ret=-ret;
        }
        if(!a[i][i])return 0;
        ret=ret*a[i][i]%mod;
    }
    return (ret+mod)%mod;
}
int main()
{
    scanf("%d%d",&n,&m);
    for(int i=1;i<=n;i++)
    {
        scanf("%s",str+1);
        for(int j=1;j<=m;j++)if(str[j]=='.')id[i][j]=++tot;
    }
    for(int i=1;i<=n;i++)
    for(int j=1;j<=m;j++)
    for(int k=0;k<4;k++)
    {
        int x=i+dx[k],y=j+dy[k];
        if(id[x][y])a[id[x][y]][id[i][j]]--,a[id[i][j]][id[i][j]]++;
    }
    printf("%lld",Gauss());
}

分数规划：https://www.luogu.org/problemnew/show/P3199

#include<bits/stdc++.h>
using namespace std;
const int N=11100;
int n,m,ecnt,hd[N],v[N],nxt[N],vis[N],used[N],tim[N];
double w[N],d[N];
bool spfa(int S,double k)
{
    queue<int>q;q.push(S);
    for(int i=1;i<=n;i++)vis[i]=0,tim[i]=0,d[i]=1e18;
    d[S]=0,tim[S]=1;
    while(!q.empty())
    {
        int u=q.front();q.pop();vis[u]=0,used[u]=1;
        for(int i=hd[u];i;i=nxt[i])
        if(d[v[i]]>d[u]+w[i]-k)
        {
            d[v[i]]=d[u]+w[i]-k;
            if(!vis[v[i]])q.push(v[i]),vis[v[i]]=1,tim[v[i]]++;
            if(tim[v[i]]>50)return 1;
        }
    }
    return 0;
}
bool check(double val)
{
    memset(used,0,sizeof used);
    for(int i=1;i<=n;i++)if(!used[i]&&spfa(i,val))return 1;
    return 0;
}
int main()
{
    scanf("%d%d",&n,&m);
    for(int i=1,x,y;i<=m;i++)
    {
        double z;scanf("%d%d%lf",&x,&y,&z);
        v[++ecnt]=y,nxt[ecnt]=hd[x],w[ecnt]=z,hd[x]=ecnt;
    }
    double l=-1e7-100,r=1e7+100;
    while(r-l>1e-9)
    {
        double mid=(l+r)/2;
        if(check(mid))r=mid;else l=mid;
    }
    printf("%.8lf",l);
}

模拟退火：https://www.luogu.org/problemnew/show/P2503

注：可能要多交几发才能过

#include<bits/stdc++.h>
using namespace std;
int n,m,a[50],bel[50],sum[50];
double ans,ave;
void fire()
{
    double tot=0;
    memset(sum,0,sizeof sum);
    for(int i=1;i<=n;i++)bel[i]=rand()%m+1,sum[bel[i]]+=a[i];
    for(int i=1;i<=m;i++)tot+=(sum[i]-ave)*(sum[i]-ave);
    ans=min(ans,tot);
    double T=200;
    while(T>1e-16)
    {
        int x=rand()%n+1,mn=1;
        for(int i=2;i<=m;i++)if(sum[i]<sum[mn])mn=i;
        double now=tot-(sum[bel[x]]-ave)*(sum[bel[x]]-ave)-(sum[mn]-ave)*(sum[mn]-ave);
        sum[bel[x]]-=a[x],sum[mn]+=a[x];
        now+=(sum[bel[x]]-ave)*(sum[bel[x]]-ave)+(sum[mn]-ave)*(sum[mn]-ave);
        double delta=now-tot;
        if(delta<0)tot=now,bel[x]=mn;
        else if(exp(-delta/T)*RAND_MAX>=rand())tot=now,bel[x]=mn;
        else sum[bel[x]]+=a[x],sum[mn]-=a[x];
        ans=min(ans,tot);
        T*=0.996;
    }
}
int main()
{
    srand(time(NULL));
    scanf("%d%d",&n,&m);
    if(m==1){puts("0.00");return 0;}
    for(int i=1;i<=n;i++)scanf("%d",&a[i]),ave+=a[i];
    ave/=m;
    ans=1e18;
    for(int i=1;i<=100;i++)fire();
    ans=sqrt(ans/m);
    printf("%0.2f",ans);
}

不清楚还有没有