考试前打模板

图论

dijkstra

#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<cmath>
#include<algorithm>
#include<queue>
#define ll long long
using namespace std;
const int maxn=200005;
inline ll read(){
    ll x=0,k=1;char ch=getchar();
    while(ch<'0'||ch>'9'){if(ch=='-') k=-1;ch=getchar();}
    while(ch>='0'&&ch<='9'){x=(x<<3)+(x<<1)+ch-'0';ch=getchar();}
    return k*x;
}
int fir[maxn],nex[maxn],to[maxn],w[maxn],ecnt;
int dis[maxn],vis[maxn];
void addedge(int u,int v,int wi){
    nex[++ecnt]=fir[u];fir[u]=ecnt;to[ecnt]=v;w[ecnt]=wi;
}
struct node{
    int d,id;
    bool operator < (const node&rhs) const{
        return d>rhs.d;
    }
};
void dij(int s){
    memset(dis,127,sizeof dis);
    memset(vis,0,sizeof vis);
    priority_queue<node> q;
    dis[s]=0;
    q.push((node){0,s});
    while(!q.empty()){
        node u=q.top();
        q.pop();
        if(vis[u.id]) continue;
        vis[u.id]=1;
        for(int i=fir[u.id];i;i=nex[i]){
            int v=to[i];
            if(u.d+w[i]<dis[v]){
                dis[v]=u.d+w[i];
                q.push((node){dis[v],v});
            }
        }
    }
}
int main(){
//    freopen(".in","r",stdin);
//    freopen(".out","w",stdout);
    int n,m,s;
    n=read();m=read();s=read();
    for(int i=1;i<=m;i++){
        int x,y,z;
        x=read();y=read();z=read();
        addedge(x,y,z);
    }
    dij(s);
    for(int i=1;i<=n;i++) cout<<dis[i]<<" ";
    return 0;
}

spfa判负环

#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<cmath>
#include<algorithm>
#include<queue>
#define ll long long
using namespace std;
const int maxn=6005;
inline ll read(){
    ll x=0,k=1;char ch=getchar();
    while(ch<'0'||ch>'9'){if(ch=='-') k=-1;ch=getchar();}
    while(ch>='0'&&ch<='9'){x=(x<<3)+(x<<1)+ch-'0';ch=getchar();}
    return k*x;
}
int fir[maxn],nex[maxn],to[maxn],w[maxn],ecnt;
int dis[maxn],vis[maxn],cnt[maxn];
void addedge(int u,int v,int wi){
    nex[++ecnt]=fir[u];fir[u]=ecnt;to[ecnt]=v;w[ecnt]=wi;
}
int n,m;
bool spfa(int s){
    memset(dis,127,sizeof dis);
    memset(vis,0,sizeof vis);
    memset(cnt,0,sizeof cnt);
    queue<int> q;
    q.push(s);
    dis[s]=0;vis[s]=1;
    while(!q.empty()){
        int u=q.front();
        q.pop();vis[u]=0;
        if(cnt[u]>=n) return true;
        for(int i=fir[u];i;i=nex[i]){
            if(dis[u]+w[i]<dis[to[i]]){
                dis[to[i]]=dis[u]+w[i];
                if(!vis[to[i]]){
                    q.push(to[i]);
                    vis[to[i]]=1;
                    cnt[to[i]]++;
                    if(cnt[to[i]]>=n) return true;
                }
            }
        }
    }
    return false;
}
int main(){
//    freopen(".in","r",stdin);
//    freopen(".out","w",stdout);
    int t;
    t=read();
    while(t--){
        ecnt=0;memset(fir,0,sizeof fir);
        n=read();m=read();
        for(int i=1;i<=m;i++){
            int a,b,w;
            a=read();b=read();w=read();
            addedge(a,b,w);
            if(w>=0) addedge(b,a,w);
        }
        if(spfa(1)) cout<<"YE5"<<endl;
        else cout<<"N0"<<endl;
    }
    return 0;
}

最短路计数

#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<cmath>
#include<algorithm>
#include<queue>
#define ll long long
using namespace std;
const int maxn=4000005;
const int mod=100003;
inline ll read(){
    ll x=0,k=1;char ch=getchar();
    while(ch<'0'||ch>'9'){if(ch=='-') k=-1;ch=getchar();}
    while(ch>='0'&&ch<='9'){x=(x<<3)+(x<<1)+ch-'0';ch=getchar();}
    return k*x;
}
int fir[maxn],nex[maxn],to[maxn],w[maxn],ecnt;
int dis[maxn],vis[maxn],cnt[maxn];
void addedge(int u,int v,int wi){
    nex[++ecnt]=fir[u];fir[u]=ecnt;to[ecnt]=v;w[ecnt]=wi;
}
int n,m;
void spfa(int s){
    memset(dis,127,sizeof dis);
    memset(vis,0,sizeof vis);
    queue<int> q;
    q.push(s);
    dis[s]=0;vis[s]=1;cnt[1]=1;
    while(!q.empty()){
        int u=q.front();
        q.pop();vis[u]=0;
        for(int i=fir[u];i;i=nex[i]){
            if(dis[u]+1<dis[to[i]]){
                dis[to[i]]=dis[u]+1;
                cnt[to[i]]=cnt[u];
                if(!vis[to[i]]){
                    q.push(to[i]);
                    vis[to[i]]=1;
                }
            }
            else if(dis[u]+1==dis[to[i]]){
                cnt[to[i]]=(cnt[to[i]]+cnt[u])%mod;
            }
        }
    }
}
int main(){
//    freopen(".in","r",stdin);
//    freopen(".out","w",stdout);
    n=read();m=read();
    for(int i=1;i<=m;i++){
        int a,b;
        a=read();b=read();
        addedge(a,b,1);
        addedge(b,a,1);
    }
    spfa(1);
    for(int i=1;i<=n;i++){
        cout<<cnt[i]<<endl;
    }
    return 0;
}

kruskal

#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<cmath>
#include<algorithm>
#include<queue>
#define ll long long
using namespace std;
const int maxn=200005;
const int mod=100003;
inline ll read(){
    ll x=0,k=1;char ch=getchar();
    while(ch<'0'||ch>'9'){if(ch=='-') k=-1;ch=getchar();}
    while(ch>='0'&&ch<='9'){x=(x<<3)+(x<<1)+ch-'0';ch=getchar();}
    return k*x;
}
struct node{
    int x,y,w;
}a[maxn];
bool cmp(node xx,node yy){
    return xx.w<yy.w;
}
int fa[maxn];
int find(int x){
    return x==fa[x]?x:fa[x]=find(fa[x]);
}
int n,m,ans;
void kruskal(){
    int cnt=0;
    sort(a+1,a+m+1,cmp);
    for(int i=1;i<=m;i++){
        if(find(a[i].x)!=find(a[i].y)){
            fa[find(a[i].x)]=find(a[i].y);
            ans+=a[i].w;
            cnt++;
        }
        if(cnt==n-1) break;
    }
}
int main(){
//    freopen(".in","r",stdin);
//    freopen(".out","w",stdout);
    n=read();m=read();
    for(int i=1;i<=m;i++){
        a[i].x=read();a[i].y=read();a[i].w=read();
    }
    for(int i=1;i<=n;i++) fa[i]=i;
    kruskal();
    cout<<ans;
    return 0;
}

数学

gcd

int gcd(int a,int b){
    return b?gcd(b,a%b):a;
}

exgcd

int exgcd(int a,int b,int &d,int &x,int &y){
    if(!b) {d=a;x=1;y=0;}
    else{exgcd(b,a%b,d,y,x);y-=x*(a/b)}
}