1.快读
inline int read(){int k=0,f=1;char c=getchar_unlocked();while(c<'0'||c>'9'){if(c=='-')f=-1;c=getchar_unlocked();}while(c>='0'&&c<='9')k=k*10+c-'0',c=getchar_unlocked();return k*f;
}
2.快速幂
long long qpow(long long a, long long b, long long p) {long long res = 1;while (b > 0) {if (b & 1) res = res * a % p;a = a * a % p;b >>= 1;}return res;
}
3.LCA
#include<bits/stdc++.h>
using namespace std;
const int N=5e5+5;
int n,m,R;
int dfn[N],dn,mi[20][N];
vector<int>g[N];
int get(int x,int y){return dfn[x]<dfn[y]?x:y;
}
void dfs(int id,int f){mi[0][dfn[id]=++dn]=f;for(int it=0;it<g[id].size();it++){if(g[id][it]!=f)dfs(g[id][it],id);}return;
}
int lca(int u,int v){if(u==v)return u;if((u=dfn[u])>(v=dfn[v]))swap(u,v);int d=__lg(v-u++);return get(mi[d][u],mi[d][v-(1<<d)+1]);
}
int main() {int u,v;ios::sync_with_stdio(0);cin.tie(0),cout.tie(0);cin>>n>>m>>R;for(int i=1;i<n;i++){cin>>u>>v;g[u].push_back(v);g[v].push_back(u);}dfs(R,0);for(int i=1;i<=__lg(n);i++){for(int j=1;j+(1<<i)-1<=n;j++){mi[i][j]=get(mi[i-1][j],mi[i-1][j+(1<<i-1)]);}}for(int i=1;i<=m;i++){cin>>u>>v;cout<<lca(u,v)<<'\n';}return 0;
}4.Dijkstra
#include<bits/stdc++.h>
using namespace std;
const int N=100005,M=500005;
struct edge{int to,dis,nxt;}e[M];
int head[N],dis[N],cnt;
bool vis[N];
int n,m,s;
void add(int u,int v,int d){e[++cnt].dis=d;e[cnt].to=v;e[cnt].nxt=head[u];head[u]=cnt;
}
struct node{int dis,pos;bool operator<(const node &x)const{return x.dis<dis;}
};
priority_queue<node>q;
void dijkstra(){dis[s]=0;q.push((node){0,s});while(!q.empty()){node tmp=q.top();q.pop();int x=tmp.pos,d=tmp.dis,i;if(vis[x])continue;vis[x]=1;for(i=head[x];i;i=e[i].nxt){int y=e[i].to;if(dis[y]>dis[x]+e[i].dis){dis[y]=dis[x]+e[i].dis;if(!vis[y])q.push((node){dis[y],y});}}}
}
int main() {int i,u,v,d;scanf("%d%d%d",&n,&m,&s);for(i=1;i<=n;i++)dis[i]=0x7fffffff;for(i=0;i<m;i++){scanf("%d%d%d",&u,&v,&d);add(u,v,d);}dijkstra();for(i=1;i<=n;i++)printf("%d ",dis[i]);return 0;
}5.SPFA(负环)
#include<bits/stdc++.h>
using namespace std;
struct Edge {int to,w;
};
int T,n,m;
vector<Edge>g[2005];
int dis[2005],cnt[2005];
bool f[2005];
bool spfa() {queue<int>q;dis[1]=0;q.push(1);f[1]=true;cnt[1]=1;while(!q.empty()) {int u=q.front();q.pop();f[u]=false;for(int i=0;i<g[u].size();i++) {Edge e=g[u][i];int v=e.to,w=e.w;if(dis[v]>dis[u]+w) {dis[v]=dis[u]+w;if(!f[v]) {cnt[v]++;if(cnt[v]>=n)return true;f[v]=true;q.push(v);}}}}return false;
}
int main() {ios::sync_with_stdio(0);cin.tie(0), cout.tie(0);cin>>T;while(T--) {cin>>n>>m;for(int i=1; i<=n; i++) {g[i].clear();dis[i]=1e9;cnt[i]=0;f[i]=false;}for(int i=0; i<m; i++) {int u,v,w;cin>>u>>v>>w;if(w>=0) {g[u].push_back({v,w});g[v].push_back({u,w});} else {g[u].push_back({v,w});}}if(spfa()) {cout<<"YES\n";} else {cout<<"NO\n";}}return 0;
}
6.a/b%mod
#include<bits/stdc++.h>
#define ll long long
using namespace std;
const int mod=19260817;
ll read() {string s;cin>>s;int res=0,len=s.length();for(int i=0;i<len;i++) {res=(res*10+(s[i]-'0'))%mod;}return res;
}
int exgcd(int a,int b,int&x,int&y) {if(b==0) {x=1;y=0;return a;}int d=exgcd(b,a%b,y,x);y-=a/b*x;return d;
}
int main() {ll A=read();ll B=read();if(B==0) {if(A==0)cout<<0;else cout<<"Angry!";return 0;}int x,y;exgcd(B,mod,x,y);x=(x%mod+mod)%mod;ll ans=(long long)A*x%mod;cout<<ans;return 0;
}
7.线段树
①最大值
#include<bits/stdc++.h>
using namespace std;
const int N=1e5+5;
int n,q,a[N];
struct Tree{int l,r,mx,o;
}t[4*N];
void build(int l,int r,int p){t[p].l=l,t[p].r=r;if(l==r){t[p].mx=a[l];return;}int m=(l+r)>>1;build(l,m,p*2),build(m+1,r,p*2+1);t[p].mx=max(t[p*2].mx,t[p*2+1].mx);return;
}
void lazy(int p){if(t[p].o){t[p*2].mx+=t[p].o*(t[p*2].r-t[p*2].l+1);t[p*2+1].mx+=t[p].o*(t[p*2+1].r-t[p*2+1].l+1);t[p*2].o+=t[p].o;t[p*2+1].o+=t[p].o;t[p].o=0;}return;
}
void change(int l,int r,int p,int x){if(t[p].l>=l&&t[p].r<=r){t[p].mx+=x*(t[p].r-t[p].l+1);t[p].o+=x;return;}lazy(p);int m=(t[p].l+t[p].r)>>1;if(l<=m)change(l,r,p*2,x);if(r>m)change(l,r,p*2+1,x);t[p].mx=max(t[p*2].mx,t[p*2+1].mx);return;
}
int query(int l,int r,int p){if(l<=t[p].l&&t[p].r<=r)return t[p].mx;lazy(p);int m=(t[p].l+t[p].r)>>1;int ans=-(1<<30);if(l<=m)ans=max(ans,query(l,r,p*2));if(m<r)ans=max(ans,query(l,r,p*2+1));return ans;
}
int main(){scanf("%d%d",&n,&q);for(int i=1;i<=n;i++){a[i]=0;}build(1,n,1);int op;int x,y;while(q--){scanf("%d",&op);if(op==1){scanf("%d%d",&x,&y);change(x,y,1,1);}if(op==2){scanf("%d%d",&x,&y);printf("%d\n",query(x,y,1));}}return 0;
}
②和
#include<bits/stdc++.h>
using namespace std;
const int N=1e5+5;
int n,q,a[N];
struct Tree{int l,r;long long v,o;
}t[4*N];
void build(int l,int r,int p){t[p].l=l,t[p].r=r;if(l==r){t[p].v=a[l];return;}int m=l+((r-l)>>1);build(l,m,p*2),build(m+1,r,p*2+1);t[p].v=t[p*2].v+t[p*2+1].v;return;
}
void lazy(int p){if(t[p].o){t[p*2].v+=t[p].o*(t[p*2].r-t[p*2].l+1);t[p*2+1].v+=t[p].o*(t[p*2+1].r-t[p*2+1].l+1);t[p*2].o+=t[p].o;t[p*2+1].o+=t[p].o;t[p].o=0;}return;
}
void change(int l,int r,int p,int x){if(t[p].l>=l&&t[p].r<=r){t[p].v+=x*(t[p].r-t[p].l+1);t[p].o+=x;return;}lazy(p);int m=(t[p].l+t[p].r)>>1;if(l<=m)change(l,r,p*2,x);if(r>m)change(l,r,p*2+1,x);t[p].v=t[p*2].v+t[p*2+1].v;return;
}
long long query(int l,int r,int p){if(l<=t[p].l&&r>=t[p].r)return t[p].v;lazy(p);int m=(t[p].l+t[p].r)>>1;long long ans=0;if(l<=m)ans+=query(l,r,p*2);if(r>m)ans+=query(l,r,p*2+1);return ans;
}
int main(){scanf("%d%d",&n,&q);for(int i=1;i<=n;i++){scanf("%d",&a[i]);}build(1,n,1);char op;int x,y,z;while(q--){scanf(" %c",&op);if(op=='C'){scanf("%d%d%d",&x,&y,&z);change(x,y,1,z);}if(op=='Q'){scanf("%d%d",&x,&y);printf("%lld\n",query(x,y,1));}}return 0;
}
