NOIP前的模板

1.筛(phi)

(logn)求少数(phi)

inline int phi(R int x){
	R int res=x,tmp=x;
	for(R int i=2;i*i<=x;i++){
		if(tmp%i==0)res=res*(i-1)/i;
		while(tmp%i==0)tmp/=i;
	}
	if(tmp>1)res=res*(tmp-1)/tmp;
	return res;
}

线性求(phi)

inline void getphi(R int n){
	vis[1]=0;
	for(R int i=2;i<=n;i++){
		if(!vis[i]){
			prime[++tot]=i;
			phi[i]=i-1;
		}
		for(R int j=1;j<=tot&&i*prime[j]<=n;j++){
			vis[prime[j]*i]=1;
			if(i%prime[j]==0){
				phi[prime[j]*i]=phi[i]*prime[j];break;
			}
			else phi[prime[j]*i]=phi[i]*(priem[j]-1);
		}
	}
}

线性筛约数个数和约数和

//num[i] 表示i的最小质因子出现次数
inline void get_d(){
	d[1]=1;num[1]=1;
	for(R int i=2;i<=n;i++){
		if(!vis[i]){
			prime[++tot]=i;
			d[i]=2;num[i]=1;
		}
		for(R int j=1;j<=tot&&i*prime[j]<=n;j++){
			vis[i*prime[j]]=1;
			if(i%prime[j]==0){
				num[i*prime[j]]=num[i]+1;
				d[i*prime[j]]=d[i]/num[i*prime[j]]*(num[i*prime[j]]+1);
				break;
			}
			d[prime[j]*i]=d[i]*(1+1);
			num[prime[j]*i]=1;
		}
	}
	
}
//sp[i] 表示i的(1+p[1]+p[1]^1+...+p[1]^a[1])
inline void get_sd(){
	sd[1]=1;sp[1]=1;
	for(R int i=2;i<=n;i++){
		if(!vis[i]){
			prime[++tot]=i;
			sd[i]=i+1;
			sp[i]=i+1;
		}
		for(R int j=1;j<=tot&&prime[j]*i<=n;j++){
			vis[i*prime[j]]=1;
			if(i%prime[j]==0){
				sp[i*prime[j]]=sp[i]*prime[j]+1;
				sd[i*prime[j]]=sd[i]/sp[i]*sp[i*prime[j]];
				break;
			}
			sd[i*prime[j]]=sd[i]*sd[prime[j]];
			sp[i*prime[j]]=prime[j]+1;
		}
	}
}

2.ST表

inline void pre(){
	mn[0]=-1;
	for(R int i=1;i<=n;i++){
		mn[i]=((i&(i-1))==0)? mn[i-1]+1:mn[i-1];
		stmax[i][0]=a[i];
	}
	for(R int j=1;j<=mn[n];j++)
		for(R int i=1;i+(1<<j)-1<=n;i++)
			stmax[i][j]=max(stmax[i][j-1],stmax[i+(1<<(j-1))][j-1]);
} 
inline int getmax(R int l,R int r){
	R int k=mn[r-l+1];
	return max(stmax[l][k],stmax[r-(1<<k)+1][k]);
}
int main(){
	read(n);read(m);
	for(R int i=1;i<=n;i++)read(a[i]);
	pre();
	for(R int i=1;i<=m;i++){
		read(l);read(r);
		printf("%d
",getmax(l,r));
	}
    return 0;
}

3.高斯消元

read(n);
for(R int i=1;i<=n;i++)
    for(R int j=1;j<=n+1;j++)
        scanf("%lf",&mp[i][j]);
for(R int i=1;i<=n;i++){
    R int mx=i;
    for(R int j=i+1;j<=n;j++)
        if(fabss(mp[mx][i])<fabss(mp[j][i]))mx=i;
    if(mx!=i)swap(mp[mx],mp[i]);
    if(fabss(mp[i][i])>eps){
        R double div=mp[i][i];
        for(R int j=i;j<=n+1;j++)
            mp[i][j]/=div;
        for(R int j=1;j<=n;j++){
            if(i==j)continue;
            div=mp[j][i];
            for(R int k=i;k<=n+1;k++)
                mp[j][k]-=div*mp[i][k];
        }
    }
}
for(R int i=1;i<=n;i++){
    R int cnt=1;
    while(fabss(mp[i][cnt])<eps&&cnt<=n+1)cnt++;
    if(cnt==n+1)pd_nojie=1;
    if(cnt>n+1)pd_wuqiong=1;
}
if(pd_nojie||pd_wuqiong){
    printf("No Solution
");
    return 0;
}
ans[n]=mp[n][n+1];
for(R int i=n-1;i>=1;i--){
    ans[i]=mp[i][n+1];
    for(R int j=i+1;j<=n;j++)
        ans[i]-=mp[i][j]*ans[j];
}
for(R int i=1;i<=n;i++)
    printf("%.2lf
",ans[i]);

4.悬线法

for(R int i=1;i<=n;i++){
    for(R int j=1;j<=m;j++){
        read(mp[i][j]);
        up[i][j]=1;
        l[i][j]=r[i][j]=j;
    }
}
for(R int i=1;i<=n;i++)
    for(R int j=2;j<=m;j++)
        if(mp[i][j]!=mp[i][j-1])
            l[i][j]=l[i][j-1];
for(R int i=1;i<=n;i++)
    for(R int j=m-1;j>=1;j--)
        if(mp[i][j]!=mp[i][j+1])
            r[i][j]=r[i][j+1];
for(R int i=1;i<=n;i++){
    for(R int j=1;j<=m;j++){
        if(i>1&&mp[i][j]!=mp[i-1][j]){
            l[i][j]=max(l[i][j],l[i-1][j]);
            r[i][j]=min(r[i][j],r[i-1][j]);
            up[i][j]=up[i-1][j]+1;
        }
        R int a=r[i][j]-l[i][j]+1;
        R int b=min(a,up[i][j]);
        ans1=max(ans1,b*b);
        ans2=max(ans2,a*up[i][j]);
    }
}

5.nim游戏

tmp=0;
read(n);
for(R int i=1;i<=n;i++)
    read(x),tmp^=x;
if(tmp)printf("Yes
");
else printf("No
");

6.线段树双lazy

#define ls(o) o<<1
#define rs(o) o<<1|1
#define up(o) t[o]=(t[ls(o)]+t[rs(o)])%mod
inline void build(R int o,R int l,R int r){
	mul[o]=1;add[o]=0;
	if(l==r){
		t[o]=a[l]%mod;
		return;
	}
	R int mid=(l+r)>>1;
	build(ls(o),l,mid);
	build(rs(o),mid+1,r);
	up(o);
}
inline void push_down(R int o,R int l,R int r){
	if(mul[o]!=1){
		t[ls(o)]=(mul[o]*t[ls(o)])%mod;
		t[rs(o)]=(mul[o]*t[rs(o)])%mod;
		add[ls(o)]=(add[ls(o)]*mul[o])%mod;
		add[rs(o)]=(add[rs(o)]*mul[o])%mod;
		mul[ls(o)]=(mul[o]*mul[ls(o)])%mod;
		mul[rs(o)]=(mul[o]*mul[rs(o)])%mod;
		mul[o]=1;
	}
	R int mid=(l+r)>>1;
	if(add[o]){
		t[ls(o)]=(t[ls(o)]+add[o]*(mid-l+1))%mod;
		t[rs(o)]=(t[rs(o)]+add[o]*(r-mid))%mod;
		add[ls(o)]=(add[ls(o)]+add[o])%mod;
		add[rs(o)]=(add[rs(o)]+add[o])%mod;
		add[o]=0;
	}
}
inline void update_add(R int o,R int nl,R int nr,R int l,R int r,R ll k){
	if(nl<=l&&nr>=r){
		t[o]=(t[o]+(r-l+1)*k)%mod;
		add[o]=(add[o]+k)%mod;
		return;
	}
	push_down(o,l,r);
	R int mid=(l+r)>>1;
	if(nl<=mid)update_add(ls(o),nl,nr,l,mid,k);
	if(nr>mid)update_add(rs(o),nl,nr,mid+1,r,k);
	up(o);
}
inline void update_mul(R int o,R int nl,R int nr,R int l,R int r,R ll k){
	if(nl<=l&&nr>=r){
		t[o]=t[o]*k%mod;
		add[o]=add[o]*k%mod;
		mul[o]=mul[o]*k%mod;
		return;
	}
	push_down(o,l,r);
	R int mid=(l+r)>>1;
	if(nl<=mid)update_mul(ls(o),nl,nr,l,mid,k);
	if(nr>mid)update_mul(rs(o),nl,nr,mid+1,r,k);
	up(o);
}

最大子段和

struct node{
    int lm,rm,sm,sum;
    void init(int x){
        lm=rm=sm=sum=x;
    }
    friend node operator + (node a,node b){
        node ans;
        ans.sum=a.sum+b.sum;
        ans.sm=max(max(a.sm,b.sm),a.rm+b.lm);
        ans.lm=max(a.lm,a.sum+b.lm);
        ans.rm=max(b.rm,b.sum+a.rm);
        return ans;
    }
}t[N];

7.有理数取余（附加快速幂）

char A[N],B[N];
ll a,b;
inline ll ksm(R ll x,R ll y){
	ll res=1;
	while(y){
		if(y&1)res=res*x%mod;
		x=x*x%mod;
		y>>=1;
	}
	return res;
}
int main(){
	scanf("%s%s",A+1,B+1);
	R int n=strlen(A+1);
	R int m=strlen(B+1);
	for(R int i=1;i<=n;i++)
		a=(a*10+A[i]-'0')%mod;
	for(R int i=1;i<=m;i++)
		b=(b*10+B[i]-'0')%mod;
	if(!b)printf("Angry!
");
	else printf("%lld
",a*ksm(b,mod-2)%mod);
    return 0;
}

8.割点（割顶）

inline void tarjan(R int x){
	R int rd=0;
	dfn[x]=low[x]=++num;
	for(R int i=h[x];i;i=edge[i].nex){
		R int xx=edge[i].to;
		if(!dfn[xx]){
			fa[xx]=fa[x];
			tarjan(xx);
			low[x]=min(low[x],low[xx]);
			if(low[xx]>=dfn[x]&&x!=fa[x])cut[x]=1;
			if(x==fa[x])rd++;
		}
		low[x]=min(low[x],dfn[xx]);
	}
	if(x==fa[x]&&rd>=2)cut[x]=1;
}
int main(){
	read(n);read(m);
	for(R int i=1,u,v;i<=m;i++)
		read(u),read(v),add(u,v),add(v,u);
	for(R int i=1;i<=n;i++)fa[i]=i;
	for(R int i=1;i<=n;i++)
		if(!dfn[i])tarjan(i);
	R int now=0;
	for(R int i=1;i<=n;i++)
		if(cut[i])ans[++now]=i;
	printf("%d
",now);
	for(R int i=1;i<=now;i++)printf("%d ",ans[i]);
	return 0;
} 

9.缩点

inline void tarjan(R int x){
	vis[x]=1;
	sta[++top]=x;
	dfn[x]=low[x]=++num;
	for(R int i=h[x];i;i=edge[i].nex){
		R int xx=edge[i].to;
		if(!dfn[xx]){
			tarjan(xx);
			low[x]=min(low[x],low[xx]);
		}
		else if(vis[xx])low[x]=min(low[x],dfn[xx]);
	}
	if(dfn[x]==low[x]){
		cnt++;
		R int now=-1;
		while(now!=x){
			now=sta[top];
			top--;
			col[now]=cnt;
			sum[cnt]+=val[now];
			vis[now]=0;
		}
	}
}

10.裴蜀定理

scanf("%d",&n);
scanf("%d",&ans);
ans=abs(ans);
for(R int i=2;i<=n;i++){
    scanf("%d",&x);
    ans=gcd(ans,abs(x));
}
printf("%d",ans);

11.负环

inline bool spfa(R int s){
	queue<int> q;
	for(R int i=1;i<=n;i++)dist[i]=INF,vis[i]=0;
	q.push(s);vis[s]=1;dist[s]=0;cnt[s]++;
	while(!q.empty()){
		R int x=q.front();q.pop();vis[x]=0;
		cnt[x]++;
		if(cnt[x]>=n)return 1;
		for(R int i=h[x];i;i=edge[i].nex){
			R int xx=edge[i].to;
			if(dist[xx]>dist[x]+edge[i].dis){
				dist[xx]=dist[x]+edge[i].dis;
				if(!vis[xx]){
					vis[xx]=1;
					q.push(xx);
				}
			}
		}
	}
	return 0;
}

11+.最短路计数

while(!q.empty()){
    int x=q.front();q.pop();vis[x]=0;
    for(int i=h[x];i;i=edge[i].nex){
        int xx=edge[i].to;
        if(dist[xx]==dist[x]+edge[i].dis){
            ans[xx]+=ans[x];ans[xx]%=mod;
            if(!vis[xx]){
                vis[xx]=1;
                q.push(xx);
            }
        }
        if(dist[xx]>dist[x]+edge[i].dis){
            dist[xx]=dist[x]+edge[i].dis;
            ans[xx]=ans[x]%mod;
            if(!vis[xx]){
                vis[xx]=1;
                q.push(xx);
            }
        }
    }

12.Dij堆优化

struct HeapNode{
	int u;ll d;
	friend bool operator < (const HeapNode &a,const HeapNode &b){
		return a.d>b.d;
	}
};
priority_queue<HeapNode> q;
inline void Dij(R int s){
	for(R int i=1;i<=n;i++)dist[i]=INF,vis[i]=0;
	q.push((HeapNode){s,0});dist[s]=0;
	while(!q.empty()){
		R int x=q.top().u;q.pop();
		if(vis[x])continue;vis[x]=1;
		for(R int i=h[x];i;i=edge[i].nex){
			R int xx=edge[i].to;
			if(dist[xx]>dist[x]+edge[i].dis){
				dist[xx]=dist[x]+edge[i].dis;
				q.push((HeapNode){xx,dist[xx]});
			}
		}
	}
}

13.manacher

scanf("%s",a);
n=strlen(a);
for(R int i=0;i<n;i++)s[i*2]='#',s[i*2+1]=a[i];
n=2*n+1;s[n-1]='#';
rl[0]=1;
for(R int i=0;i<n;i++){
    if(i<=maxright)rl[i]=min(rl[center*2-i],maxright-i);
    else rl[i]=1; 
    while(s[i+rl[i]]==s[i-rl[i]]&&i+rl[i]<n&&i-rl[i]>=0)rl[i]++;
    if(i+rl[i]-1>maxright)maxright=i+rl[i]-1,center=i;
}
for(R int i=0;i<n;i++)ans=max(ans,rl[i]-1);

14.KMP

scanf("%s%s",s1+1,s2+1);
l1=strlen(s1+1);
l2=strlen(s2+1);
R int j=0;
nex[1]=0;
for(R int i=2;i<=l2;i++){
    while(j&&s2[i]!=s2[j+1])j=nex[j];
    if(s2[i]==s2[j+1])j++;
    nex[i]=j;
}
j=0;
for(R int i=1;i<=l1;i++){
    while(j&&s1[i]!=s2[j+1])j=nex[j];
    if(s1[i]==s2[j+1])j++;
    if(j==l2){
        printf("%d
",i-l2+1);
        j=nex[j];
    }
}

15.线性求逆元

read(n);read(mod);
a[1]=1;
for(R int i=2;i<=n;i++)
    a[i]=(((-mod/i)*a[mod%i])%mod+mod)%mod;
for(R int i=1;i<=n;i++)printf("%lld
",a[i]);

阶乘及阶乘逆元

fac[0]=fac[1]=1;
for(R int i=2;i<=n;i++)fac[i]=(fac[i-1]*i)%mod;
inv[n]=ksm(fac[n],mod-2);
for(R int i=n-1;i>=0;i--)inv[i]=((i+1)*inv[i+1])%mod;

16.prim堆优化

struct node{
	int v,w;
	friend bool operator < (const node &a,const node &b){
		return a.w>b.w;
	}
};
vector<node> t[N];
bool vis[N];
ll ans;
inline void prim(){
	priority_queue<node> q;
	while(!q.empty())q.pop();
	ans=0;
	for(R int i=1;i<=n;i++)vis[i]=0;
	for(R int i=0;i<(int)t[1].size();i++)
		q.push(t[1][i]);
	vis[1]=1;
	R int bian=n-1;
	R node x;
	while(bian--){
		x=q.top();q.pop();
		if(vis[x.v])
			while(vis[x.v])
				x=q.top(),q.pop();
		ans=ans+x.w;
		vis[x.v]=1;
		for(R int i=0;i<t[x.v].size();i++)
			if(!vis[t[x.v][i].v])
				q.push(t[x.v][i]);
	} 
}
int main(){
	read(n);read(m);node x;
	for(R int i=1,u,v,w;i<=m;i++){
		read(u);read(v);read(w);
		x.v=v;x.w=w;
		t[u].push_back(x);
		x.v=u;
		t[v].push_back(x);
	}
	prim();
	printf("%lld
",ans);
	return 0;
}

17.树上差分

inline void dfs(R int x,R int f){
	dep[x]=dep[f]+1;fa[x][0]=f;
	for(R int i=1;(1<<i)<=dep[x];i++)
		fa[x][i]=fa[fa[x][i-1]][i-1];
	for(R int i=h[x];i;i=edge[i].nex){
		R int xx=edge[i].to;
		if(xx==f)continue;
		dfs(xx,x);
	}
}
inline int lca(R int x,R int y){
	if(dep[x]>dep[y])swap(x,y);
	for(R int i=20;i>=0;i--)
		if(dep[x]<=dep[y]-(1<<i))y=fa[y][i];
	if(x==y)return x;
	for(R int i=20;i>=0;i--)
		if(fa[x][i]!=fa[y][i])
			x=fa[x][i],y=fa[y][i];
	return fa[x][0];
}
inline void search(R int x){
	for(R int i=h[x];i;i=edge[i].nex){
		R int xx=edge[i].to;
		if(xx==fa[x][0])continue;
		search(xx);
		cnt[x]+=cnt[xx];
	}
}
//边差分
cnt[x]++;cnt[y]++;
cnt[LCA]-=2;
//点差分
cnt[x]++;cnt[y]++;
cnt[LCA]--;cnt[fa[LCA][0]]--;

18.并查集

inline int find(R int x){return fa[x]==x?fa[x]:fa[x]=find(fa[x]);}
inline void merge(R int x,R int y){fa[find(x)]=find(y);}

19.左偏堆

inline int merge(R int x,R int y){
	if(x==0||y==0)return x+y;
	if(val[x]>val[y]||(val[x]==val[y]&&x>y))swap(x,y);
	ch[x][1]=merge(ch[x][1],y);
	fa[ch[x][1]]=x;
	if(dep[ch[x][0]]<dep[ch[x][1]])swap(ch[x][0],ch[x][1]);
	dep[x]=dep[ch[x][1]]+1;
	return x;
}
inline int find(R int x){
	while(fa[x])x=fa[x];
	return x;
}
inline void pop(R int x){
	val[x]=-1;
	fa[ch[x][0]]=fa[ch[x][1]]=0;
	merge(ch[x][0],ch[x][1]);
}
int main(){
	read(n);read(m);
	dep[0]=-1;
	for(R int i=1;i<=n;i++)read(val[i]);
	while(m--){
		R int opt,x,y,xx,yy;
		read(opt);
		if(opt==1){
			read(x);read(y);
			if(val[x]==-1||val[y]==-1)continue;
			if(x==y)continue;
			xx=find(x),yy=find(y);
			merge(xx,yy);
		}
		else{
			read(x);
			if(val[x]==-1)puts("-1");
			else{
				y=find(x);
				printf("%d
",val[y]);
				pop(y);
			}
		}
	}
	return 0;
}

20.最小瓶颈路

struct MST{
	int u,v,w;
	friend bool operator < (const MST &a,const MST &b){
		return a.w<b.w;
	}
}t[N];
inline void ins(R int u,R int v,R int w){
	t[++num].u=u;
	t[num].v=v;
	t[num].w=w;
}
struct node{
	int nex,to,dis;
}edge[N<<1];
inline void add(R int u,R int v,R int w){
	edge[++tot].nex=h[u];
	edge[tot].to=v;
	edge[tot].dis=w;
	h[u]=tot;
}
inline int find(R int x){return fat[x]==x?fat[x]:fat[x]=find(fat[x]);}
inline void dfs(R int x,R int f,R int g){
	dep[x]=dep[f]+1;
	fa[x][0]=f;
	mx[x][0]=g;
	for(R int i=1;(1<<i)<=dep[x];i++)
		fa[x][i]=fa[fa[x][i-1]][i-1],
		mx[x][i]=max(mx[x][i-1],mx[fa[x][i-1]][i-1]);
	for(R int i=h[x];i;i=edge[i].nex){
		R int xx=edge[i].to;
		if(xx==f)continue;
		dfs(xx,x,edge[i].dis);
	}
}
inline int get_ans(R int x,R int y){
	R int res=0;
	if(dep[x]>dep[y])swap(x,y);
	for(R int i=20;i>=0;i--)
		if(dep[x]<=dep[y]-(1<<i))
			res=max(res,mx[y][i]),y=fa[y][i];
	if(x==y)return res;
	for(R int i=20;i>=0;i--)
		if(fa[x][i]!=fa[y][i])
			res=max(res,max(mx[x][i],mx[y][i])),
			x=fa[x][i],y=fa[y][i];
	res=max(res,max(mx[x][0],mx[y][0]));
	return res;
}
int main(){
	read(n);read(m);
	for(R int i=1;i<=n;i++)fat[i]=i;
	for(R int i=1,u,v,w;i<=m;i++)
		read(u),read(v),read(w),ins(u,v,w);
	sort(t+1,t+1+m);
	for(R int i=1;i<=m;i++){
		R int x=find(t[i].u);
		R int y=find(t[i].v);
		if(x!=y){
			fat[x]=y;
			add(x,y,t[i].w);
			add(y,x,t[i].w);
		}
	}
	dfs(1,0,0);
	read(q);
	while(q--){
		R int x,y;
		read(x);read(y);
		if(find(x)!=find(y))puts("impossible");
		else printf("%d
",get_ans(x,y));
	}
	return 0;
}

21.矩阵乘法(Fib)

struct Mar{
    ll a[10][10];
    Mar(){memset(a,0,sizeof(a));}
};
Mar cheng(Mar a,Mar b){
    Mar c;
    for(int i=1;i<=2;i++)
        for(int j=1;j<=2;j++)
            for(int k=1;k<=2;k++)
            c.a[i][j]=(c.a[i][j]+a.a[i][k]*b.a[k][j]%mod)%mod;
    return c;
}
Mar ksm(Mar x,ll y){
    Mar res=e;
    while(y){
        if(y&1)res=cheng(res,x);
        x=cheng(x,x);
        y>>=1;
    }
    return res;
}

22.中国剩余定理

void exgcd(ll a,ll b,ll &x,ll &y){
    if(!b){
        x=1;y=0;return;
    }
    exgcd(b,a%b,y,x);
    y-=a/b*x;
} 
ll msc(ll x,ll y,ll mod){
    ll ans=0;
    while(y){
        if(y&1)ans=(ans+x)%mod;
        x=x*2%mod;
        y>>=1;
    }
    return ans;
}
void China(){
    for(int i=1;i<=n;i++)N*=b[i];
    ll x,y;//所求的X是N/b[i]*y
    for(int i=1;i<=n;i++){
        ll m=N/b[i];
        exgcd(b[i],m,x,y);
        y=(y+b[i])%b[i];
        X=(X+msc(msc(a[i],m,N),y,N))%N;
    }
}
int main()
{
    n=read();
    for(int i=1;i<=n;i++) a[i]=read();
    for(int i=1;i<=n;i++) b[i]=read();
    China();
    printf("%lld",(X+N)%N);
    return 0;
}

23数列分块（余数求和）

int main(){
    read(n);read(k);
    ans=n*k;
    for(R ll l=1,r;l<=n;l=r+1){
        ll s=k/l;
        if(s!=0)r=min(k/s,n);
        else r=n;
        ans-=s*(r-l+1)*(l+r)/2;
    }
    printf("%lld",ans);
    return 0;
}

24.线性基

void insert(long long x){
    for(int i=63;i>=0;i--){
        if(x&(1LL<<i)){
            if(!p[i]){
                p[i]=x;break;
            }
            else x^=p[i];
        }
    }
}
int main(){
    scanf("%lld",&n);
    for(int i=1;i<=n;i++){
        scanf("%lld",&a[i]);
        insert(a[i]);
    }
    for(int i=63;i>=0;i--){
        if((ans^p[i])>ans)ans^=p[i];
    }
    printf("%lld
",ans);
    return 0;
} 

25.逆序对

inline void msort(R int l,R int r){
    if(l==r)return;
    R int mid=(l+r)>>1;
    msort(l,mid);msort(mid+1,r);
    R int i=l,j=mid+1,k=l;
    while(i<=mid&&j<=r)
        if(a[i]<=a[j])
            b[k]=a[i],k++,i++;
        else
            b[k]=a[j],k++,j++,ans+=(mid-i+1);
    while(i<=mid)
        b[k]=a[i],i++,k++;
    while(j<=r)
        b[k]=a[j],j++,k++;
    for(R int i=l;i<=r;i++)
        a[i]=b[i];
}

26.高精

struct big{
	int a[N];
}x,y,ed,one;
big operator + (big a,big b){
	big c;
	memset(c.a,0,sizeof(c.a));
	int len=max(a.a[0],b.a[0]);
	for(int i=1;i<=len;i++)c.a[i]=a.a[i]+b.a[i];
	for(int i=1;i<=len;i++)
		if(c.a[i]>=10){
			c.a[i+1]+=c.a[i]/10;
			c.a[i]%=10;
		}
	if(c.a[len+1])len++;
	c.a[0]=len;
	return c;
}
big operator - (big a,big b){
	big c;
	memset(c.a,0,sizeof(c.a));
	int len=max(a.a[0],b.a[0]);
	for(R int i=1;i<=len;i++)c.a[i]=a.a[i]-b.a[i];
	for(R int i=1;i<=len;i++){
		if(c.a[i]<0){
			c.a[i+1]--;
			c.a[i]+=10;
		}
	}
	while(!c.a[len])len--;
	c.a[0]=len;
	return c;
}
big operator / (big a,int x){
	big c;
	memset(c.a,0,sizeof(c.a));
	int len=0,tmp=0;
	for(R int i=a.a[0];i>=1;i--){
		tmp=tmp*10+a.a[i];
		if(tmp>=x){
			c.a[++len]=tmp/x;
			tmp%=x;
		}
		else c.a[++len]=0;
	}
	for(R int i=1;i<=len;i++)w[i]=c.a[len-i+1];
	for(R int i=1;i<=len;i++)c.a[i]=w[i];
	c.a[0]=len;
	return c;
}
inline void print(big x){
	if(x.a[0]==0)printf("0");
	for(int i=x.a[0];i>=1;i--)
		printf("%d",x.a[i]);
}

27.二分图

inline int find(R int x){
    for(R int i=1;i<=n;i++){
        if(!vis[i]&&mp[x][i]){
            vis[i]=1;
            if(!to[i]||find(to[i])){
                to[i]=x;
                return 1;
            }
        }
    }
    return 0;
}
for(R int i=1;i<=m;i++){
   memset(vis,0,sizeof(vis));
   if(find(i))ans++;
}

28.模拟退火

void SA(){
    double T = 2333.0;
    double xx = x,yy = y;
    while(T > 1e-16）{
        double vx = xx + T * (rand() * 2 - RAND_MAX),vy = yy + T * (rand() * 2 - RAND_MAX);
        double res = calc(vx,vy) - calc(xx,yy);
        if(res < 0){
        	x = xx = vx,y = yy = vy;
    	}
    	else if(exp(-res/ T) * RAND_MAX > rand())xx = x,yy = y;
    	T = T * 0.9982;
    }
}

29.Trie树

void insert(char *s,int rt){
    for(int i=0;s[i];i++){
        int v=s[i]-'a';
        if(!trie[rt][v]) trie[rt][v]=++tot;
        rt=trie[rt][v];
    }
}
int find(char *s,int rt){
    for(int i=0;s[i];i++){
        int v=s[i]-'a';
        if(!trie[rt][v])return 0;
        rt=trie[rt][v];
    }
    sum[rt]++;
    return sum[rt];
}

01 Trie树

inline void insert(R int x,R int rt){
    for(R int i=1<<30;i;i>>=1){
        bool c=x&i;
        if(!trie[rt][c])trie[rt][c]=++num;
        rt=trie[rt][c];
    }
}
inline int query(R int x,R int rt){
    R int ans=0;
    for(R int i=1<<30;i;i>>=1){
        bool c=x&i;
        if(trie[rt][c^1])ans+=i,rt=trie[rt][c^1];
        else rt=trie[rt][c];
    }
    return ans;
}

30.LCS && LIS

//LCS
for(R int i=1;i<=n;i++)
    for(R int j=1;j<=m;j++)
        dp[i][j]=max(dp[i-1][j],max(dp[i][j-1],dp[i-1][j-1]+(a[i]==b[j])));
printf("%d
",dp[n][m]);
//LIS
read(n);read(k);
for(R int i=1;i<=n;i++)read(b[i]);
for(R int i=1;i<=k-1;i++)
    if(b[i]<b[k])a[++tot]=b[i];
a[++tot]=b[k];
for(R int i=k+1;i<=n;i++)
    if(b[i]>b[k])a[++tot]=b[i];
low[1]=a[1];ans=1;
for(R int i=2;i<=tot;i++){
    if(a[i]>=low[ans])low[++ans]=a[i];
    else low[lower_bound(low+1,low+1+ans,a[i])-low]=a[i];
}
printf("%d
",ans);
//统计方案数
for(R int i=1;i<=n;i++){
    dp[i]=1;
    for(R int j=1;j<i;j++)
        if(a[j]>a[i])dp[i]=max(dp[i],dp[j]+1);
    ans=max(ans,dp[i]);
}
for(R int i=1;i<=n;i++){
    if(dp[i]==1)cnt[i]=1;
    for(R int j=1;j<i;j++){
        if(a[j]==a[i]&&dp[i]==dp[j])cnt[j]=0;
        if(a[j]>a[i]&&dp[i]==dp[j]+1)cnt[i]+=cnt[j];
    }
}
for(R int i=1;i<=n;i++)pos+=cnt[i]*(dp[i]==ans);
printf("%d %d
",ans,pos);

31.对顶堆

priority_queue<int> q1;
priority_queue<int,vector<int>,greater<int> > q2;
inline void ins(R int x){
    if(x>q1.top())q2.push(x);
    else q1.push(x);
}
inline void query(){
    int pos=q1.size()+q2.size();
    while(abss(q1.size()-q2.size())>1){
        if(q1.size()>q2.size())q2.push(q1.top()),q1.pop();
        else q1.push(q2.top()),q2.pop();
    }
    if(pos&1){
        if(q1.size()>q2.size())printf("%d
",q1.top());
        else printf("%d
",q2.top());
    }
    else {
        printf("%d
",min(q1.top(),q2.top()));
    }
}

32.康拓展开

inline ll contor(ll c[]){
    ll ans=0;
    for(R int i=1;i<=n;i++){
        ll sum=0;
        for(R int j=i+1;j<=n;j++)
            if(c[i]>c[j])sum++;
        ans+=sum*fac[n-i];
    }
    return ans+1;
}
inline ll revcontor(ll x){
    memset(vis,0,sizeof(vis));
    x--;ll j;
    for(R int i=1;i<=n;i++){
        ll t=x/fac[n-i];
        for(j=1;j<=n;j++){
            if(!vis[j]){
                if(!t)break;
                t--;
            }
        }
        printf("%lld ",j);
        vis[j]=1;
        x%=fac[n-i];
    }
    printf("
");
}

33.树链剖分

//---------------------线段树--------------------------- 
void build(int o,int l,int r){
	if(l==r){
		t[o]=a[tid[l]];  //guo
		tag[o]=0;
		return;
	}
	int mid=(l+r)>>1;
	build(ls(o),l,mid);
	build(rs(o),mid+1,r);
	up(o);
}

void chuan(int o,int l,int r,int k){
	tag[o]+=k;
	t[o]+=k*(r-l+1);
	t[o]%=mod;
}
void push_down(int o,int l,int r){
	int mid=(l+r)>>1;
	chuan(ls(o),l,mid,tag[o]);
	chuan(rs(o),mid+1,r,tag[o]);
	tag[o]=0;
	up(o);
}

void change(int o,int nl,int nr,int l,int r,int k){
	if(nl<=l&&nr>=r){
		t[o]+=k*(r-l+1);
		t[o]%=mod;
		tag[o]+=k;
		tag[o]%=mod;
		return;
	}
	push_down(o,l,r);
	int mid=(l+r)>>1;
	if(nl<=mid)change(ls(o),nl,nr,l,mid,k);
	if(nr>mid)change(rs(o),nl,nr,mid+1,r,k);
	up(o);
}

int query(int o,int nl,int nr,int l,int r){
	int ans=0;
	if(nl<=l&&nr>=r)return t[o]%mod;
	int mid=(l+r)>>1;
	push_down(o,l,r);
	if(nl<=mid)ans=(ans+query(ls(o),nl,nr,l,mid))%mod;
	if(nr>mid) ans=(ans+query(rs(o),nl,nr,mid+1,r))%mod;
	return ans%mod;
}
//---------------------线段树--------------------------- 
struct node{
	int nex,to;
}edge[N<<1];

void add(int u,int v){
	edge[++tot].nex=h[u];
	edge[tot].to=v;
	h[u]=tot;
}
//求 fa,dep,size,son(重儿子) 
void dfs1(int x,int f,int depth){
	fa[x]=f;dep[x]=depth;siz[x]=1;
	for(int i=h[x];i;i=edge[i].nex){
		int xx=edge[i].to;
		if(dep[xx])continue;
		dfs1(xx,x,depth+1);
		siz[x]+=siz[xx];
		if(son[x]==-1||siz[xx]>siz[son[x]])son[x]=xx;
	}
}
//求 dfn,tid,top; 
void dfs2(int x,int tp){
	dfn[x]=++num;tid[num]=x;top[x]=tp;
	if(son[x]==-1)return;
	dfs2(son[x],tp);
	for(int i=h[x];i;i=edge[i].nex){
		int xx=edge[i].to;
		if(dfn[xx])continue;
		dfs2(xx,xx);
	}
}

int ask_path(int x,int y){
	int ans=0;
	int fx=top[x],fy=top[y];
	while(fx!=fy){
		if(dep[fx]>dep[fy]){
			ans+=query(1,dfn[fx],dfn[x],1,n);
			ans%=mod;
			x=fa[fx];
		}
		else {
			ans+=query(1,dfn[fy],dfn[y],1,n);
			ans%=mod;
			y=fa[fy];
		}
		fx=top[x];fy=top[y];
	}
	if(dfn[x]>dfn[y])swap(x,y);
	ans+=query(1,dfn[x],dfn[y],1,n);
	ans%=mod;
	return ans%mod;
} 

void update(int x,int y,int z){
	int fx=top[x],fy=top[y];
	while(fx!=fy){
		if(dep[fx]>dep[fy]){
			change(1,dfn[fx],dfn[x],1,n,z);
			x=fa[fx];
		}
		else {
			change(1,dfn[fy],dfn[y],1,n,z);
			y=fa[fy];
		}
		fx=top[x];fy=top[y];
	}
	if(dfn[x]>dfn[y])swap(x,y);
	change(1,dfn[x],dfn[y],1,n,z);
}
//query(1,dfn[x],dfn[x]+siz[x]-1,1,n)子树操作

34.倍增Floyed

struct Mar{
    ll a[N][N];
    Mar(){memset(a,0x3f,sizeof(a));}
};
Mar e,ans;
Mar cheng(R Mar a,R Mar b){
    Mar c; 
    for(R int k=1;k<=tot;k++)
        for(R int i=1;i<=tot;i++)	
            for(R int j=1;j<=tot;j++)
                c.a[i][j]=min(c.a[i][j],a.a[i][k]+b.a[k][j]);
    return c;
}
Mar ksm(R Mar x,ll y){
    ans=x;
    while(y){
        if(y&1)ans=cheng(ans,x);
        x=cheng(x,x);
        y>>=1;
    }
}
int main(){
    read(n);read(m);read(s);read(t);
    for(R int i=1,w,u,v;i<=m;i++){
        read(w);read(u);read(v);
        if(!vis[u])vis[u]=++tot;
        if(!vis[v])vis[v]=++tot;
        e.a[vis[u]][vis[v]]=e.a[vis[v]][vis[u]]=w;
    }
    ksm(e,n-1);
    printf("%lld
",ans.a[vis[s]][vis[t]]);
    return 0;
}

35.A*（K短路）

int n,m,s,t,k,tot,ans;
int h1[M],h2[M];
struct bian{
	int nex,to,val;
}edge[M],E[M];
struct node{
	int f;//f=g+dist  估价函数 
	int g;//到当前点的路径长度 
	int from;
	bool operator < (node a)const {
		if(a.f==f)return g>a.g;
		return f>a.f;
	} 
};
void add(int u,int v,int w){
	edge[++tot].nex=h1[u];
	edge[tot].to=v;
	edge[tot].val=w;
	h1[u]=tot;
	E[tot].nex=h2[v]; 
	E[tot].to=u;
	E[tot].val=w;
	h2[v]=tot;
}
struct HeapNode{
	int u,d;
	bool operator < (const HeapNode & b) const {return d>b.d;}
}; 
int dist[M];
bool vis[M];
priority_queue<HeapNode> Q;
void dij(int s){
	for(int i=1;i<=n;i++)dist[i]=INF;
	dist[s]=0; Q.push((HeapNode){s,0});
	while(Q.size()){
		int x=Q.top().u;Q.pop();
		if(vis[x])continue; vis[x]=1;
		for(int i=h2[x];i;i=E[i].nex){
			int xx=E[i].to;
			if(dist[xx]>dist[x]+E[i].val){
				dist[xx]=dist[x]+E[i].val;
				Q.push( (HeapNode){xx,dist[xx]});
			}
		}
	}
}
int A_star(int s,int t,int k){
	if(s==t) return 0;         //起点即为终点 
	if(dist[s]==INF)return -1; //起点无联通 
	priority_queue<node> q;    //优先队列搜索 
	int cnt=0;                 //记录第X短路 
	node tmp={0,0,0},to={0,0,0};
	tmp.from=s;
	tmp.f=tmp.g+dist[tmp.from];//估价函数 
	q.push(tmp);
	while(!q.empty()){
		tmp=q.top();
		q.pop();
		if(tmp.from==t) cnt++; //到达终点 
		if(cnt==k)return tmp.g;//现在已经是第K短路 
		for(int i=h1[tmp.from];i;i=edge[i].nex){
			to.from=edge[i].to;
			to.g=tmp.g+edge[i].val;
			to.f=to.g+dist[to.from];
			q.push(to);
		}
	}
	return -1;
}

int main()
{
	n=read();m=read();
	for(int i=1;i<=m;i++){
		int u,v,w;
		u=read();v=read();w=read(); 
		add(u,v,w);
	}
	s=read();t=read();k=read();
	dij(t);					 //反向边跑最短路 
	ans=A_star(s,t,k);
	printf("%d",ans); 
	return 0;
}

end.对拍

@echo off
:loop
echo noip2018 rp++

data.exe>data.txt
a.exe<data.txt>a.txt
b.exe<data.txt>b.txt
fc a.txt b.txt
if not errorlevel 1 goto loop
pause
goto loop

ex

next_permutation(a+1,a+1+n);